%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO545^1 : TPTP v9.2.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:54:31 AM UTC 2026
% Result : Theorem 1.26s 1.47s
% Output : Refutation 1.26s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : SYO545^1 : TPTP v9.2.1. Released v5.2.0.
% 0.00/0.08 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.07/0.27 % Computer : n024.cluster.edu
% 0.07/0.27 % Model : x86_64 x86_64
% 0.07/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.27 % Memory : 8042.1875MB
% 0.07/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.27 % CPULimit : 300
% 0.07/0.27 % WCLimit : 300
% 0.07/0.27 % DateTime : Tue Feb 24 09:33:25 EST 2026
% 0.07/0.27 % CPUTime :
% 0.07/0.27 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.14/0.35 ---- Original DTF file ---
% 0.14/0.35 thf(spec,logic,$$dhol).
% 0.14/0.35 %------------------------------------------------------------------------------
% 0.14/0.35 % File : SYO545^1 : TPTP v9.2.1. Released v5.2.0.
% 0.14/0.35 % Domain : Syntactic
% 0.14/0.35 % Problem : Property of case from ($o>$o) to $i defined from choice on $i
% 0.14/0.35 % Version : Especial.
% 0.14/0.35 % English : A choice operator on $i is used to define an if-then-else operator
% 0.14/0.35 % at $i. Check that case always returns one of the four given
% 0.14/0.35 % results.
% 0.14/0.35
% 0.14/0.35 % Refs : [Bro11] Brown E. (2011), Email to Geoff Sutcliffe
% 0.14/0.35 % Source : [Bro11]
% 0.14/0.35 % Names : CHOICE22 [Bro11]
% 0.14/0.35
% 0.14/0.35 % Status : Theorem
% 0.14/0.35 % Rating : 0.22 v9.1.0, 0.38 v9.0.0, 0.40 v8.2.0, 0.62 v8.1.0, 0.64 v7.5.0, 0.43 v7.4.0, 0.67 v7.2.0, 0.62 v7.1.0, 0.75 v7.0.0, 0.71 v6.4.0, 0.67 v6.3.0, 0.80 v6.2.0, 0.86 v5.5.0, 0.83 v5.4.0, 0.80 v5.2.0
% 0.14/0.35 % Syntax : Number of formulae : 6 ( 1 unt; 3 typ; 1 def)
% 0.14/0.35 % Number of atoms : 20 ( 13 equ; 1 cnn)
% 0.14/0.35 % Maximal formula atoms : 4 ( 6 avg)
% 0.14/0.35 % Number of connectives : 36 ( 1 ~; 6 |; 4 &; 24 @)
% 0.14/0.35 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.14/0.35 % Maximal formula depth : 8 ( 5 avg)
% 0.14/0.35 % Number of types : 2 ( 0 usr)
% 0.14/0.35 % Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% 0.14/0.35 % Number of symbols : 7 ( 3 usr; 3 con; 0-5 aty)
% 0.14/0.35 % Number of variables : 15 ( 9 ^; 5 !; 1 ?; 15 :)
% 0.14/0.35 % SPC : TH0_THM_EQU_NAR
% 0.14/0.35
% 0.14/0.35 % Comments :
% 0.14/0.35 %------------------------------------------------------------------------------
% 0.14/0.35 thf(eps,type,
% 0.14/0.35 eps: ( $i > $o ) > $i ).
% 0.14/0.35
% 0.14/0.35 thf(choiceax,axiom,
% 0.14/0.35 ! [P: $i > $o] :
% 0.14/0.35 ( ? [X: $i] : ( P @ X )
% 0.14/0.35 => ( P @ ( eps @ P ) ) ) ).
% 0.14/0.35
% 0.14/0.35 thf(caseoo,type,
% 0.14/0.35 case: ( $o > $o ) > $i > $i > $i > $i > $i ).
% 0.14/0.35
% 0.14/0.35 thf(caseood,definition,
% 0.14/0.35 ( case
% 0.14/0.35 = ( ^ [B: $o > $o,X: $i,Y: $i,U: $i,V: $i] :
% 0.14/0.35 ( eps
% 0.14/0.35 @ ^ [Z: $i] :
% 0.14/0.35 ( ( ( B
% 0.14/0.35 = ( ^ [A: $o] : $false ) )
% 0.14/0.35 & ( Z = X ) )
% 0.14/0.35 | ( ( B = (~) )
% 0.14/0.35 & ( Z = Y ) )
% 0.14/0.35 | ( ( B
% 0.14/0.35 = ( ^ [A: $o] : A ) )
% 0.14/0.35 & ( Z = U ) )
% 0.14/0.35 | ( ( B
% 0.14/0.35 = ( ^ [A: $o] : $true ) )
% 0.14/0.35 & ( Z = V ) ) ) ) ) ) ).
% 0.14/0.35
% 0.14/0.35 thf(f,type,
% 0.14/0.35 f: $o > $o ).
% 0.14/0.35
% 0.14/0.35 thf(conj,conjecture,
% 0.14/0.35 ! [X: $i,Y: $i,U: $i,V: $i] :
% 0.14/0.35 ( ( ( case @ f @ X @ Y @ U @ V )
% 0.14/0.35 = X )
% 0.14/0.35 | ( ( case @ f @ X @ Y @ U @ V )
% 0.14/0.35 = Y )
% 0.14/0.35 | ( ( case @ f @ X @ Y @ U @ V )
% 0.14/0.35 = U )
% 0.14/0.35 | ( ( case @ f @ X @ Y @ U @ V )
% 0.14/0.35 = V ) ) ).
% 0.14/0.35
% 0.14/0.35 %------------------------------------------------------------------------------
% 0.14/0.35 ------------------------
% 1.02/1.01 ---- Embedded in THF ---
% 1.02/1.01 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.02/1.01 %%% Generated on Tue Feb 24 09:33:26 EST 2026
% 1.02/1.01 %%% using '$$dhol' embedding, version 1.3.0.
% 1.02/1.01 %%% Logic specification used:
% 1.02/1.01 %%% thf(spec, logic, $$dhol).
% 1.02/1.01
% 1.02/1.01 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.UHqTYDh04E/DTF2DTF2605.p
% 1.02/1.01 thf(eps, type, eps: (($i > $o) > $i)).
% 1.02/1.01 thf(choiceax, axiom, (! [P:($i > $o)]: (((? [X:$i]: ((P @ X))) => (P @ (eps @ P)))))).
% 1.02/1.01 thf(caseoo, type, case: (($o > $o) > ($i > ($i > ($i > ($i > $i)))))).
% 1.02/1.01 thf(caseood, definition, (case = (^ [B:($o > $o),X:$i,Y:$i,U:$i,V:$i]: ((eps @ (^ [Z:$i]: ((((B = (^ [A:$o]: ($false))) & (Z = X)) | (((B = (~)) & (Z = Y)) | (((B = (^ [A:$o]: (A))) & (Z = U)) | ((B = (^ [A:$o]: ($true))) & (Z = V)))))))))))).
% 1.02/1.01 thf(f, type, f: ($o > $o)).
% 1.02/1.01 thf(conj, conjecture, (! [X:$i,Y:$i,U:$i,V:$i]: ((((((((case @ f) @ X) @ Y) @ U) @ V) = X) | (((((((case @ f) @ X) @ Y) @ U) @ V) = Y) | (((((((case @ f) @ X) @ Y) @ U) @ V) = U) | ((((((case @ f) @ X) @ Y) @ U) @ V) = V))))))).
% 1.02/1.01 % SZS output end ListOfTHF for /export/starexec/sandbox2/tmp/tmp.UHqTYDh04E/DTF2DTF2605.p
% 1.02/1.01 ------------------------
% 1.02/1.02 ---- Cleaned THF ---
% 1.02/1.02 thf(eps,type,
% 1.02/1.02 eps: ( $i > $o ) > $i ).
% 1.02/1.02
% 1.02/1.02 thf(choiceax,axiom,
% 1.02/1.02 ! [P: $i > $o] :
% 1.02/1.02 ( ? [X: $i] : ( P @ X )
% 1.02/1.02 => ( P @ ( eps @ P ) ) ) ).
% 1.02/1.02
% 1.02/1.02 thf(caseoo,type,
% 1.02/1.02 case: ( $o > $o ) > $i > $i > $i > $i > $i ).
% 1.02/1.02
% 1.02/1.02 thf(caseood,definition,
% 1.02/1.02 ( case
% 1.02/1.02 = ( ^ [B: $o > $o,X: $i,Y: $i,U: $i,V: $i] :
% 1.02/1.02 ( eps
% 1.02/1.02 @ ^ [Z: $i] :
% 1.02/1.02 ( ( ( B
% 1.02/1.02 = ( ^ [A: $o] : $false ) )
% 1.02/1.02 & ( Z = X ) )
% 1.02/1.02 | ( ( B = (~) )
% 1.02/1.02 & ( Z = Y ) )
% 1.02/1.02 | ( ( B
% 1.02/1.02 = ( ^ [A: $o] : A ) )
% 1.02/1.02 & ( Z = U ) )
% 1.02/1.02 | ( ( B
% 1.02/1.02 = ( ^ [A: $o] : $true ) )
% 1.02/1.02 & ( Z = V ) ) ) ) ) ) ).
% 1.02/1.02
% 1.02/1.02 thf(f,type,
% 1.02/1.02 f: $o > $o ).
% 1.02/1.02
% 1.02/1.02 thf(conj,conjecture,
% 1.02/1.02 ! [X: $i,Y: $i,U: $i,V: $i] :
% 1.02/1.02 ( ( ( case @ f @ X @ Y @ U @ V )
% 1.02/1.02 = X )
% 1.02/1.02 | ( ( case @ f @ X @ Y @ U @ V )
% 1.02/1.02 = Y )
% 1.02/1.02 | ( ( case @ f @ X @ Y @ U @ V )
% 1.02/1.02 = U )
% 1.02/1.02 | ( ( case @ f @ X @ Y @ U @ V )
% 1.02/1.02 = V ) ) ).
% 1.02/1.02 ------------------------
% 1.26/1.03 % (2707)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_2605 for (2999ds/183Mi)
% 1.26/1.04 % (2709)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_2605 for (2999ds/27Mi)
% 1.26/1.04 % (2710)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_2605 for (2999ds/2Mi)
% 1.26/1.04 % (2711)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_2605 for (2999ds/2Mi)
% 1.26/1.04 % (2712)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_2605 for (2999ds/275Mi)
% 1.26/1.04 % (2713)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_2605 for (2999ds/18Mi)
% 1.26/1.04 % (2708)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_2605 for (2999ds/4Mi)
% 1.26/1.04 % (2710)Instruction limit reached!
% 1.26/1.04 % (2710)------------------------------
% 1.26/1.04 % (2710)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.04 % (2710)Termination reason: Unknown
% 1.26/1.04 % (2710)Termination phase: Property scanning
% 1.26/1.04 % (2711)Instruction limit reached!
% 1.26/1.04 % (2711)------------------------------
% 1.26/1.04 % (2711)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.04 % (2712)Refutation not found, incomplete strategy
% 1.26/1.04 % (2712)------------------------------
% 1.26/1.04 % (2712)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.04
% 1.26/1.04 % (2712)Termination reason: Refutation not found, incomplete strategy
% 1.26/1.04
% 1.26/1.04 % (2710)Memory used [KB]: 1023
% 1.26/1.04
% 1.26/1.04 % (2710)Time elapsed: 0.003 s
% 1.26/1.04 % (2710)Instructions burned: 3 (million)
% 1.26/1.04 % (2712)Memory used [KB]: 5500
% 1.26/1.04 % (2710)------------------------------
% 1.26/1.04 % (2710)------------------------------
% 1.26/1.04 % (2712)Time elapsed: 0.002 s
% 1.26/1.04 % (2712)Instructions burned: 1 (million)
% 1.26/1.04 % (2712)------------------------------
% 1.26/1.04 % (2712)------------------------------
% 1.26/1.04 % (2711)Termination reason: Unknown
% 1.26/1.04 % (2711)Termination phase: Property scanning
% 1.26/1.04
% 1.26/1.04 % (2711)Memory used [KB]: 1023
% 1.26/1.04 % (2711)Time elapsed: 0.003 s
% 1.26/1.04 % (2711)Instructions burned: 4 (million)
% 1.26/1.04 % (2711)------------------------------
% 1.26/1.04 % (2711)------------------------------
% 1.26/1.04 % (2708)Instruction limit reached!
% 1.26/1.04 % (2708)------------------------------
% 1.26/1.04 % (2708)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.04 % (2708)Termination reason: Unknown
% 1.26/1.04 % (2708)Termination phase: Saturation
% 1.26/1.04
% 1.26/1.04 % (2708)Memory used [KB]: 1023
% 1.26/1.04 % (2708)Time elapsed: 0.003 s
% 1.26/1.04 % (2708)Instructions burned: 4 (million)
% 1.26/1.04 % (2708)------------------------------
% 1.26/1.04 % (2708)------------------------------
% 1.26/1.05 % (2713)Instruction limit reached!
% 1.26/1.05 % (2713)------------------------------
% 1.26/1.05 % (2713)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.05 % (2713)Termination reason: Unknown
% 1.26/1.05 % (2713)Termination phase: Saturation
% 1.26/1.05
% 1.26/1.05 % (2713)Memory used [KB]: 5628
% 1.26/1.05 % (2713)Time elapsed: 0.011 s
% 1.26/1.05 % (2713)Instructions burned: 18 (million)
% 1.26/1.05 % (2713)------------------------------
% 1.26/1.05 % (2713)------------------------------
% 1.26/1.05 % (2709)Instruction limit reached!
% 1.26/1.05 % (2709)------------------------------
% 1.26/1.05 % (2709)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.05 % (2709)Termination reason: Unknown
% 1.26/1.05 % (2709)Termination phase: Saturation
% 1.26/1.05
% 1.26/1.05 % (2709)Memory used [KB]: 5500
% 1.26/1.05 % (2709)Time elapsed: 0.014 s
% 1.26/1.05 % (2709)Instructions burned: 28 (million)
% 1.26/1.05 % (2709)------------------------------
% 1.26/1.05 % (2709)------------------------------
% 1.26/1.06 % (2714)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_2605 for (2999ds/3Mi)
% 1.26/1.06 % (2716)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_2605 for (2999ds/15Mi)
% 1.26/1.06 % (2715)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_2605 for (2999ds/37Mi)
% 1.26/1.06 % (2717)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_2605 for (2999ds/3Mi)
% 1.26/1.06 % (2714)Instruction limit reached!
% 1.26/1.06 % (2714)------------------------------
% 1.26/1.06 % (2714)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.06 % (2714)Termination reason: Unknown
% 1.26/1.06 % (2714)Termination phase: Property scanning
% 1.26/1.06
% 1.26/1.06 % (2714)Memory used [KB]: 1023
% 1.26/1.06 % (2714)Time elapsed: 0.003 s
% 1.26/1.06 % (2714)Instructions burned: 4 (million)
% 1.26/1.06 % (2714)------------------------------
% 1.26/1.06 % (2714)------------------------------
% 1.26/1.06 % (2717)Instruction limit reached!
% 1.26/1.06 % (2717)------------------------------
% 1.26/1.06 % (2717)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.06 % (2717)Termination reason: Unknown
% 1.26/1.06 % (2717)Termination phase: Saturation
% 1.26/1.06
% 1.26/1.06 % (2717)Memory used [KB]: 5500
% 1.26/1.06 % (2717)Time elapsed: 0.003 s
% 1.26/1.06 % (2717)Instructions burned: 4 (million)
% 1.26/1.06 % (2717)------------------------------
% 1.26/1.06 % (2717)------------------------------
% 1.26/1.06 % (2716)Refutation not found, incomplete strategy
% 1.26/1.06 % (2716)------------------------------
% 1.26/1.06 % (2716)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.06 % (2716)Termination reason: Refutation not found, incomplete strategy
% 1.26/1.06
% 1.26/1.06
% 1.26/1.06 % (2716)Memory used [KB]: 5500
% 1.26/1.06 % (2716)Time elapsed: 0.004 s
% 1.26/1.06 % (2716)Instructions burned: 5 (million)
% 1.26/1.06 % (2716)------------------------------
% 1.26/1.06 % (2716)------------------------------
% 1.26/1.07 % (2718)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_2605 for (2999ds/1041Mi)
% 1.26/1.07 % (2719)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_2605 for (2999ds/7Mi)
% 1.26/1.07 % (2719)Instruction limit reached!
% 1.26/1.07 % (2719)------------------------------
% 1.26/1.07 % (2719)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.07 % (2719)Termination reason: Unknown
% 1.26/1.07 % (2719)Termination phase: Saturation
% 1.26/1.07
% 1.26/1.07 % (2719)Memory used [KB]: 1023
% 1.26/1.07 % (2719)Time elapsed: 0.005 s
% 1.26/1.07 % (2719)Instructions burned: 8 (million)
% 1.26/1.07 % (2719)------------------------------
% 1.26/1.07 % (2719)------------------------------
% 1.26/1.08 % (2720)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_2605 for (2999ds/16Mi)
% 1.26/1.08 % (2715)Instruction limit reached!
% 1.26/1.08 % (2715)------------------------------
% 1.26/1.08 % (2715)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.08 % (2715)Termination reason: Unknown
% 1.26/1.08 % (2715)Termination phase: Saturation
% 1.26/1.08
% 1.26/1.08 % (2715)Memory used [KB]: 5884
% 1.26/1.08 % (2715)Time elapsed: 0.019 s
% 1.26/1.08 % (2715)Instructions burned: 39 (million)
% 1.26/1.08 % (2715)------------------------------
% 1.26/1.08 % (2715)------------------------------
% 1.26/1.08 % (2721)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_2605 for (2999ds/3Mi)
% 1.26/1.08 % (2722)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_2605 for (2999ds/3Mi)
% 1.26/1.08 % (2721)Instruction limit reached!
% 1.26/1.08 % (2721)------------------------------
% 1.26/1.08 % (2721)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.08 % (2721)Termination reason: Unknown
% 1.26/1.08 % (2721)Termination phase: Property scanning
% 1.26/1.08
% 1.26/1.08 % (2721)Memory used [KB]: 1023
% 1.26/1.08 % (2721)Time elapsed: 0.003 s
% 1.26/1.08 % (2721)Instructions burned: 4 (million)
% 1.26/1.08 % (2721)------------------------------
% 1.26/1.08 % (2721)------------------------------
% 1.26/1.08 % (2722)Instruction limit reached!
% 1.26/1.08 % (2722)------------------------------
% 1.26/1.08 % (2722)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.08 % (2722)Termination reason: Unknown
% 1.26/1.08 % (2722)Termination phase: Property scanning
% 1.26/1.08
% 1.26/1.08 % (2722)Memory used [KB]: 1023
% 1.26/1.08 % (2722)Time elapsed: 0.003 s
% 1.26/1.08 % (2722)Instructions burned: 4 (million)
% 1.26/1.08 % (2722)------------------------------
% 1.26/1.08 % (2722)------------------------------
% 1.26/1.08 % (2720)Instruction limit reached!
% 1.26/1.08 % (2720)------------------------------
% 1.26/1.08 % (2720)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.08 % (2720)Termination reason: Unknown
% 1.26/1.08 % (2720)Termination phase: Saturation
% 1.26/1.08
% 1.26/1.08 % (2720)Memory used [KB]: 5756
% 1.26/1.08 % (2720)Time elapsed: 0.011 s
% 1.26/1.08 % (2720)Instructions burned: 17 (million)
% 1.26/1.08 % (2720)------------------------------
% 1.26/1.08 % (2720)------------------------------
% 1.26/1.09 % (2718)Refutation not found, incomplete strategy
% 1.26/1.09 % (2718)------------------------------
% 1.26/1.09 % (2718)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.09 % (2718)Termination reason: Refutation not found, incomplete strategy
% 1.26/1.09
% 1.26/1.09
% 1.26/1.09 % (2718)Memory used [KB]: 5628
% 1.26/1.09 % (2718)Time elapsed: 0.022 s
% 1.26/1.09 % (2718)Instructions burned: 42 (million)
% 1.26/1.09 % (2718)------------------------------
% 1.26/1.09 % (2718)------------------------------
% 1.26/1.09 % (2723)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_2605 for (2999ds/7Mi)
% 1.26/1.09 % (2707)Instruction limit reached!
% 1.26/1.09 % (2707)------------------------------
% 1.26/1.09 % (2707)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.09 % (2707)Termination reason: Unknown
% 1.26/1.09 % (2707)Termination phase: Saturation
% 1.26/1.09
% 1.26/1.09 % (2707)Memory used [KB]: 5884
% 1.26/1.09 % (2707)Time elapsed: 0.058 s
% 1.26/1.09 % (2707)Instructions burned: 185 (million)
% 1.26/1.09 % (2707)------------------------------
% 1.26/1.09 % (2707)------------------------------
% 1.26/1.09 % (2724)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_2605 for (2999ds/3Mi)
% 1.26/1.09 % (2723)Instruction limit reached!
% 1.26/1.09 % (2723)------------------------------
% 1.26/1.09 % (2723)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.09 % (2723)Termination reason: Unknown
% 1.26/1.09 % (2723)Termination phase: Saturation
% 1.26/1.09
% 1.26/1.09 % (2723)Memory used [KB]: 5500
% 1.26/1.09 % (2723)Time elapsed: 0.005 s
% 1.26/1.09 % (2723)Instructions burned: 7 (million)
% 1.26/1.09 % (2723)------------------------------
% 1.26/1.09 % (2723)------------------------------
% 1.26/1.09 % (2724)Instruction limit reached!
% 1.26/1.09 % (2724)------------------------------
% 1.26/1.09 % (2724)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.09 % (2724)Termination reason: Unknown
% 1.26/1.09 % (2724)Termination phase: Property scanning
% 1.26/1.09
% 1.26/1.09 % (2724)Memory used [KB]: 1023
% 1.26/1.09 % (2724)Time elapsed: 0.003 s
% 1.26/1.09 % (2724)Instructions burned: 3 (million)
% 1.26/1.09 % (2724)------------------------------
% 1.26/1.09 % (2724)------------------------------
% 1.26/1.09 % (2725)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_2605 for (2999ds/4Mi)
% 1.26/1.09 % (2726)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_2605 for (2999ds/18Mi)
% 1.26/1.09 % (2725)Instruction limit reached!
% 1.26/1.09 % (2725)------------------------------
% 1.26/1.09 % (2725)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.09 % (2725)Termination reason: Unknown
% 1.26/1.09 % (2725)Termination phase: Saturation
% 1.26/1.10
% 1.26/1.10 % (2725)Memory used [KB]: 5500
% 1.26/1.10 % (2725)Time elapsed: 0.003 s
% 1.26/1.10 % (2725)Instructions burned: 4 (million)
% 1.26/1.10 % (2725)------------------------------
% 1.26/1.10 % (2725)------------------------------
% 1.26/1.10 % (2729)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_2605 for (2999ds/902Mi)
% 1.26/1.10 % (2727)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_2605 for (2999ds/710Mi)
% 1.26/1.10 % (2729)Refutation not found, incomplete strategy
% 1.26/1.10 % (2729)------------------------------
% 1.26/1.10 % (2729)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.10 % (2729)Termination reason: Refutation not found, incomplete strategy
% 1.26/1.10
% 1.26/1.10
% 1.26/1.10 % (2729)Memory used [KB]: 5500
% 1.26/1.10 % (2729)Time elapsed: 0.002 s
% 1.26/1.10 % (2729)Instructions burned: 3 (million)
% 1.26/1.10 % (2729)------------------------------
% 1.26/1.10 % (2729)------------------------------
% 1.26/1.10 % (2728)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_2605 for (2999ds/6Mi)
% 1.26/1.10 % (2726)Instruction limit reached!
% 1.26/1.10 % (2726)------------------------------
% 1.26/1.10 % (2726)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.10 % (2726)Termination reason: Unknown
% 1.26/1.10 % (2726)Termination phase: Saturation
% 1.26/1.10
% 1.26/1.10 % (2726)Memory used [KB]: 5628
% 1.26/1.10 % (2726)Time elapsed: 0.010 s
% 1.26/1.10 % (2726)Instructions burned: 18 (million)
% 1.26/1.10 % (2726)------------------------------
% 1.26/1.10 % (2726)------------------------------
% 1.26/1.11 % (2728)Instruction limit reached!
% 1.26/1.11 % (2728)------------------------------
% 1.26/1.11 % (2728)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.11 % (2728)Termination reason: Unknown
% 1.26/1.11 % (2728)Termination phase: Saturation
% 1.26/1.11
% 1.26/1.11 % (2728)Memory used [KB]: 5500
% 1.26/1.11 % (2728)Time elapsed: 0.005 s
% 1.26/1.11 % (2728)Instructions burned: 8 (million)
% 1.26/1.11 % (2728)------------------------------
% 1.26/1.11 % (2728)------------------------------
% 1.26/1.11 % (2730)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_2605 for (2999ds/21Mi)
% 1.26/1.11 % (2731)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_2605 for (2999ds/5Mi)
% 1.26/1.11 % (2732)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_2605 for (2999ds/6Mi)
% 1.26/1.11 % (2733)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_2605 for (2999ds/377Mi)
% 1.26/1.11 % (2731)Instruction limit reached!
% 1.26/1.11 % (2731)------------------------------
% 1.26/1.11 % (2731)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.11 % (2731)Termination reason: Unknown
% 1.26/1.11 % (2731)Termination phase: Saturation
% 1.26/1.11
% 1.26/1.11 % (2731)Memory used [KB]: 5500
% 1.26/1.11 % (2731)Time elapsed: 0.004 s
% 1.26/1.11 % (2731)Instructions burned: 6 (million)
% 1.26/1.11 % (2731)------------------------------
% 1.26/1.11 % (2731)------------------------------
% 1.26/1.11 % (2732)Instruction limit reached!
% 1.26/1.11 % (2732)------------------------------
% 1.26/1.11 % (2732)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.11 % (2732)Termination reason: Unknown
% 1.26/1.11 % (2732)Termination phase: Saturation
% 1.26/1.11
% 1.26/1.11 % (2732)Memory used [KB]: 5500
% 1.26/1.11 % (2732)Time elapsed: 0.003 s
% 1.26/1.11 % (2732)Instructions burned: 7 (million)
% 1.26/1.11 % (2732)------------------------------
% 1.26/1.11 % (2732)------------------------------
% 1.26/1.12 % (2730)Instruction limit reached!
% 1.26/1.12 % (2730)------------------------------
% 1.26/1.12 % (2730)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.12 % (2730)Termination reason: Unknown
% 1.26/1.12 % (2730)Termination phase: Saturation
% 1.26/1.12
% 1.26/1.12 % (2730)Memory used [KB]: 5628
% 1.26/1.12 % (2730)Time elapsed: 0.013 s
% 1.26/1.12 % (2730)Instructions burned: 22 (million)
% 1.26/1.12 % (2730)------------------------------
% 1.26/1.12 % (2730)------------------------------
% 1.26/1.12 % (2734)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_2605 for (2999ds/779Mi)
% 1.26/1.12 % (2736)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_2605 for (2999ds/879Mi)
% 1.26/1.12 % (2735)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_2605 for (2999ds/19Mi)
% 1.26/1.12 % (2736)Refutation not found, incomplete strategy
% 1.26/1.12 % (2736)------------------------------
% 1.26/1.12 % (2736)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.12 % (2736)Termination reason: Refutation not found, incomplete strategy
% 1.26/1.12
% 1.26/1.12
% 1.26/1.12 % (2736)Memory used [KB]: 5500
% 1.26/1.12 % (2736)Time elapsed: 0.003 s
% 1.26/1.12 % (2736)Instructions burned: 7 (million)
% 1.26/1.12 % (2736)------------------------------
% 1.26/1.12 % (2736)------------------------------
% 1.26/1.13 % (2735)Refutation not found, incomplete strategy
% 1.26/1.13 % (2735)------------------------------
% 1.26/1.13 % (2735)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.13 % (2735)Termination reason: Refutation not found, incomplete strategy
% 1.26/1.13
% 1.26/1.13
% 1.26/1.13 % (2735)Memory used [KB]: 5500
% 1.26/1.13 % (2735)Time elapsed: 0.004 s
% 1.26/1.13 % (2735)Instructions burned: 3 (million)
% 1.26/1.13 % (2735)------------------------------
% 1.26/1.13 % (2735)------------------------------
% 1.26/1.13 % (2734)Refutation not found, incomplete strategy
% 1.26/1.13 % (2734)------------------------------
% 1.26/1.13 % (2734)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.13 % (2734)Termination reason: Refutation not found, incomplete strategy
% 1.26/1.13
% 1.26/1.13
% 1.26/1.13 % (2734)Memory used [KB]: 5500
% 1.26/1.13 % (2734)Time elapsed: 0.007 s
% 1.26/1.13 % (2734)Instructions burned: 13 (million)
% 1.26/1.13 % (2734)------------------------------
% 1.26/1.13 % (2734)------------------------------
% 1.26/1.13 % (2737)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_2605 for (2999ds/17Mi)
% 1.26/1.13 % (2739)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_2605 for (2999ds/30Mi)
% 1.26/1.14 % (2738)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_2605 for (2999ds/3Mi)
% 1.26/1.14 % (2738)Instruction limit reached!
% 1.26/1.14 % (2738)------------------------------
% 1.26/1.14 % (2738)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.14 % (2738)Termination reason: Unknown
% 1.26/1.14 % (2738)Termination phase: Saturation
% 1.26/1.14
% 1.26/1.14 % (2738)Memory used [KB]: 1023
% 1.26/1.14 % (2738)Time elapsed: 0.003 s
% 1.26/1.14 % (2737)Instruction limit reached!
% 1.26/1.14 % (2737)------------------------------
% 1.26/1.14 % (2737)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.14 % (2737)Termination reason: Unknown
% 1.26/1.14 % (2737)Termination phase: Saturation
% 1.26/1.14
% 1.26/1.14 % (2737)Memory used [KB]: 5628
% 1.26/1.14 % (2737)Time elapsed: 0.011 s
% 1.26/1.14 % (2737)Instructions burned: 18 (million)
% 1.26/1.14 % (2737)------------------------------
% 1.26/1.14 % (2737)------------------------------
% 1.26/1.14 % (2738)Instructions burned: 3 (million)
% 1.26/1.14 % (2738)------------------------------
% 1.26/1.14 % (2738)------------------------------
% 1.26/1.14 % (2739)Refutation not found, incomplete strategy
% 1.26/1.14 % (2739)------------------------------
% 1.26/1.14 % (2739)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.14 % (2739)Termination reason: Refutation not found, incomplete strategy
% 1.26/1.14
% 1.26/1.14
% 1.26/1.14 % (2739)Memory used [KB]: 5628
% 1.26/1.14 % (2739)Time elapsed: 0.006 s
% 1.26/1.14 % (2739)Instructions burned: 16 (million)
% 1.26/1.14 % (2739)------------------------------
% 1.26/1.14 % (2739)------------------------------
% 1.26/1.14 % (2741)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_2605 for (2999ds/100Mi)
% 1.26/1.14 % (2740)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_2605 for (2999ds/127Mi)
% 1.26/1.14 % (2741)Refutation not found, incomplete strategy
% 1.26/1.14 % (2741)------------------------------
% 1.26/1.14 % (2741)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.14 % (2741)Termination reason: Refutation not found, incomplete strategy
% 1.26/1.14
% 1.26/1.14
% 1.26/1.14 % (2741)Memory used [KB]: 5500
% 1.26/1.14 % (2741)Time elapsed: 0.004 s
% 1.26/1.14 % (2741)Instructions burned: 6 (million)
% 1.26/1.14 % (2741)------------------------------
% 1.26/1.14 % (2741)------------------------------
% 1.26/1.15 % (2744)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_2605 for (2998ds/86Mi)
% 1.26/1.15 % (2744)Refutation not found, incomplete strategy
% 1.26/1.15 % (2744)------------------------------
% 1.26/1.15 % (2744)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.15 % (2744)Termination reason: Refutation not found, incomplete strategy
% 1.26/1.15
% 1.26/1.15
% 1.26/1.15 % (2744)Memory used [KB]: 5500
% 1.26/1.15 % (2744)Time elapsed: 0.002 s
% 1.26/1.15 % (2744)Instructions burned: 4 (million)
% 1.26/1.15 % (2744)------------------------------
% 1.26/1.15 % (2744)------------------------------
% 1.26/1.15 % (2742)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_2605 for (2998ds/3Mi)
% 1.26/1.16 % (2743)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_2605 for (2998ds/20Mi)
% 1.26/1.16 % (2742)Instruction limit reached!
% 1.26/1.16 % (2742)------------------------------
% 1.26/1.16 % (2742)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.16 % (2742)Termination reason: Unknown
% 1.26/1.16 % (2742)Termination phase: Property scanning
% 1.26/1.16
% 1.26/1.16 % (2742)Memory used [KB]: 1023
% 1.26/1.16 % (2742)Time elapsed: 0.003 s
% 1.26/1.16 % (2742)Instructions burned: 4 (million)
% 1.26/1.16 % (2742)------------------------------
% 1.26/1.16 % (2742)------------------------------
% 1.26/1.16 % (2743)Refutation not found, incomplete strategy
% 1.26/1.16 % (2743)------------------------------
% 1.26/1.16 % (2743)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.16 % (2743)Termination reason: Refutation not found, incomplete strategy
% 1.26/1.16
% 1.26/1.16
% 1.26/1.16 % (2743)Memory used [KB]: 5500
% 1.26/1.16 % (2743)Time elapsed: 0.004 s
% 1.26/1.16 % (2743)Instructions burned: 3 (million)
% 1.26/1.16 % (2743)------------------------------
% 1.26/1.16 % (2743)------------------------------
% 1.26/1.16 % (2746)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_2605 for (2998ds/39Mi)
% 1.26/1.16 % (2745)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_2605 for (2998ds/107Mi)
% 1.26/1.16 % (2745)Refutation not found, incomplete strategy
% 1.26/1.16 % (2745)------------------------------
% 1.26/1.16 % (2745)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.16 % (2745)Termination reason: Refutation not found, incomplete strategy
% 1.26/1.16
% 1.26/1.16
% 1.26/1.16 % (2745)Memory used [KB]: 5500
% 1.26/1.16 % (2745)Time elapsed: 0.004 s
% 1.26/1.16 % (2745)Instructions burned: 4 (million)
% 1.26/1.16 % (2745)------------------------------
% 1.26/1.16 % (2745)------------------------------
% 1.26/1.17 % (2746)Instruction limit reached!
% 1.26/1.17 % (2746)------------------------------
% 1.26/1.17 % (2746)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.17 % (2746)Termination reason: Unknown
% 1.26/1.17 % (2746)Termination phase: Saturation
% 1.26/1.17
% 1.26/1.17 % (2746)Memory used [KB]: 5756
% 1.26/1.17 % (2746)Time elapsed: 0.012 s
% 1.26/1.17 % (2746)Instructions burned: 42 (million)
% 1.26/1.17 % (2746)------------------------------
% 1.26/1.17 % (2746)------------------------------
% 1.26/1.17 % (2747)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_2605 for (2998ds/448Mi)
% 1.26/1.17 % (2748)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_2605 for (2998ds/46Mi)
% 1.26/1.17 % (2747)Refutation not found, incomplete strategy
% 1.26/1.17 % (2747)------------------------------
% 1.26/1.17 % (2747)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.17 % (2747)Termination reason: Refutation not found, incomplete strategy
% 1.26/1.17
% 1.26/1.17
% 1.26/1.17 % (2747)Memory used [KB]: 5500
% 1.26/1.17 % (2747)Time elapsed: 0.003 s
% 1.26/1.17 % (2747)Instructions burned: 4 (million)
% 1.26/1.17 % (2747)------------------------------
% 1.26/1.17 % (2747)------------------------------
% 1.26/1.18 % (2750)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_2605 for (2998ds/507Mi)
% 1.26/1.18 % (2750)Refutation not found, incomplete strategy
% 1.26/1.18 % (2750)------------------------------
% 1.26/1.18 % (2750)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.18 % (2750)Termination reason: Refutation not found, incomplete strategy
% 1.26/1.18
% 1.26/1.18
% 1.26/1.18 % (2750)Memory used [KB]: 5500
% 1.26/1.18 % (2750)Time elapsed: 0.002 s
% 1.26/1.18 % (2750)Instructions burned: 4 (million)
% 1.26/1.18 % (2750)------------------------------
% 1.26/1.18 % (2750)------------------------------
% 1.26/1.18 % (2749)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_2605 for (2998ds/98Mi)
% 1.26/1.19 % (2751)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_2605 for (2998ds/149Mi)
% 1.26/1.19 % (2752)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_2605 for (2998ds/39Mi)
% 1.26/1.19 % (2749)Refutation not found, incomplete strategy
% 1.26/1.19 % (2749)------------------------------
% 1.26/1.19 % (2749)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.19 % (2749)Termination reason: Refutation not found, incomplete strategy
% 1.26/1.19
% 1.26/1.19
% 1.26/1.19 % (2749)Memory used [KB]: 1023
% 1.26/1.19 % (2749)Time elapsed: 0.010 s
% 1.26/1.19 % (2749)Instructions burned: 18 (million)
% 1.26/1.19 % (2749)------------------------------
% 1.26/1.19 % (2749)------------------------------
% 1.26/1.20 % (2748)Instruction limit reached!
% 1.26/1.20 % (2748)------------------------------
% 1.26/1.20 % (2748)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.20 % (2748)Termination reason: Unknown
% 1.26/1.20 % (2748)Termination phase: Saturation
% 1.26/1.20
% 1.26/1.20 % (2748)Memory used [KB]: 5628
% 1.26/1.20 % (2748)Time elapsed: 0.024 s
% 1.26/1.20 % (2748)Instructions burned: 47 (million)
% 1.26/1.20 % (2748)------------------------------
% 1.26/1.20 % (2748)------------------------------
% 1.26/1.21 % (2753)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_2605 for (2998ds/6Mi)
% 1.26/1.21 % (2740)Instruction limit reached!
% 1.26/1.21 % (2740)------------------------------
% 1.26/1.21 % (2740)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.21 % (2740)Termination reason: Unknown
% 1.26/1.21 % (2740)Termination phase: Saturation
% 1.26/1.21
% 1.26/1.21 % (2740)Memory used [KB]: 6140
% 1.26/1.21 % (2740)Time elapsed: 0.068 s
% 1.26/1.21 % (2740)Instructions burned: 127 (million)
% 1.26/1.21 % (2740)------------------------------
% 1.26/1.21 % (2740)------------------------------
% 1.26/1.21 % (2752)Instruction limit reached!
% 1.26/1.21 % (2752)------------------------------
% 1.26/1.21 % (2752)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.21 % (2752)Termination reason: Unknown
% 1.26/1.21 % (2752)Termination phase: Saturation
% 1.26/1.21
% 1.26/1.21 % (2752)Memory used [KB]: 5628
% 1.26/1.21 % (2752)Time elapsed: 0.018 s
% 1.26/1.21 % (2752)Instructions burned: 39 (million)
% 1.26/1.21 % (2752)------------------------------
% 1.26/1.21 % (2752)------------------------------
% 1.26/1.21 % (2753)Instruction limit reached!
% 1.26/1.21 % (2753)------------------------------
% 1.26/1.21 % (2753)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.21 % (2753)Termination reason: Unknown
% 1.26/1.21 % (2753)Termination phase: Saturation
% 1.26/1.21
% 1.26/1.21 % (2753)Memory used [KB]: 9978
% 1.26/1.21 % (2753)Time elapsed: 0.005 s
% 1.26/1.21 % (2753)Instructions burned: 7 (million)
% 1.26/1.21 % (2753)------------------------------
% 1.26/1.21 % (2753)------------------------------
% 1.26/1.21 % (2754)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_2605 for (2998ds/1087Mi)
% 1.26/1.22 % (2754)Refutation not found, incomplete strategy
% 1.26/1.22 % (2754)------------------------------
% 1.26/1.22 % (2754)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.22 % (2754)Termination reason: Refutation not found, incomplete strategy
% 1.26/1.22
% 1.26/1.22
% 1.26/1.22 % (2754)Memory used [KB]: 5500
% 1.26/1.22 % (2754)Time elapsed: 0.027 s
% 1.26/1.22 % (2754)Instructions burned: 7 (million)
% 1.26/1.22 % (2754)------------------------------
% 1.26/1.22 % (2754)------------------------------
% 1.26/1.22 % (2755)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_2605 for (2998ds/47Mi)
% 1.26/1.23 % (2756)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_2605 for (2998ds/44Mi)
% 1.26/1.23 % (2757)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_2605 for (2998ds/432Mi)
% 1.26/1.23 % (2756)Refutation not found, incomplete strategy
% 1.26/1.23 % (2756)------------------------------
% 1.26/1.23 % (2756)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.23 % (2756)Termination reason: Refutation not found, incomplete strategy
% 1.26/1.23
% 1.26/1.23
% 1.26/1.23 % (2756)Memory used [KB]: 1023
% 1.26/1.23 % (2756)Time elapsed: 0.003 s
% 1.26/1.23 % (2756)Instructions burned: 4 (million)
% 1.26/1.23 % (2756)------------------------------
% 1.26/1.23 % (2756)------------------------------
% 1.26/1.23 % (2758)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_2605 for (2998ds/62Mi)
% 1.26/1.24 % (2759)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_2605 for (2998ds/31Mi)
% 1.26/1.25 % (2755)Instruction limit reached!
% 1.26/1.25 % (2755)------------------------------
% 1.26/1.25 % (2755)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.25 % (2755)Termination reason: Unknown
% 1.26/1.25 % (2755)Termination phase: Saturation
% 1.26/1.25
% 1.26/1.25 % (2755)Memory used [KB]: 5756
% 1.26/1.25 % (2755)Time elapsed: 0.046 s
% 1.26/1.25 % (2755)Instructions burned: 47 (million)
% 1.26/1.25 % (2755)------------------------------
% 1.26/1.25 % (2755)------------------------------
% 1.26/1.25 % (2733)Instruction limit reached!
% 1.26/1.25 % (2733)------------------------------
% 1.26/1.25 % (2733)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.25 % (2733)Termination reason: Unknown
% 1.26/1.25 % (2733)Termination phase: Saturation
% 1.26/1.25
% 1.26/1.25 % (2733)Memory used [KB]: 6396
% 1.26/1.25 % (2733)Time elapsed: 0.144 s
% 1.26/1.25 % (2733)Instructions burned: 380 (million)
% 1.26/1.25 % (2733)------------------------------
% 1.26/1.25 % (2733)------------------------------
% 1.26/1.26 % (2759)Instruction limit reached!
% 1.26/1.26 % (2759)------------------------------
% 1.26/1.26 % (2759)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.26 % (2759)Termination reason: Unknown
% 1.26/1.26 % (2759)Termination phase: Saturation
% 1.26/1.26
% 1.26/1.26 % (2759)Memory used [KB]: 5500
% 1.26/1.26 % (2759)Time elapsed: 0.037 s
% 1.26/1.26 % (2759)Instructions burned: 31 (million)
% 1.26/1.26 % (2759)------------------------------
% 1.26/1.26 % (2759)------------------------------
% 1.26/1.26 % (2758)Instruction limit reached!
% 1.26/1.26 % (2758)------------------------------
% 1.26/1.26 % (2758)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.26 % (2758)Termination reason: Unknown
% 1.26/1.26 % (2758)Termination phase: Saturation
% 1.26/1.26
% 1.26/1.26 % (2758)Memory used [KB]: 5628
% 1.26/1.26 % (2758)Time elapsed: 0.052 s
% 1.26/1.26 % (2758)Instructions burned: 64 (million)
% 1.26/1.26 % (2758)------------------------------
% 1.26/1.26 % (2758)------------------------------
% 1.26/1.26 % (2751)Instruction limit reached!
% 1.26/1.26 % (2751)------------------------------
% 1.26/1.26 % (2751)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.26 % (2751)Termination reason: Unknown
% 1.26/1.26 % (2751)Termination phase: Saturation
% 1.26/1.26
% 1.26/1.26 % (2751)Memory used [KB]: 6268
% 1.26/1.26 % (2751)Time elapsed: 0.074 s
% 1.26/1.26 % (2751)Instructions burned: 149 (million)
% 1.26/1.26 % (2751)------------------------------
% 1.26/1.26 % (2751)------------------------------
% 1.26/1.26 % (2761)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_2605 for (2997ds/453Mi)
% 1.26/1.26 % (2760)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_2605 for (2997ds/96Mi)
% 1.26/1.27 % (2761)Refutation not found, incomplete strategy
% 1.26/1.27 % (2761)------------------------------
% 1.26/1.27 % (2761)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.27 % (2761)Termination reason: Refutation not found, incomplete strategy
% 1.26/1.27
% 1.26/1.27
% 1.26/1.27 % (2761)Memory used [KB]: 5500
% 1.26/1.27 % (2761)Time elapsed: 0.009 s
% 1.26/1.27 % (2761)Instructions burned: 17 (million)
% 1.26/1.27 % (2761)------------------------------
% 1.26/1.27 % (2761)------------------------------
% 1.26/1.27 % (2762)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_2605 for (2997ds/71Mi)
% 1.26/1.28 % (2763)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_2605 for (2997ds/83Mi)
% 1.26/1.28 % (2764)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_2605 for (2997ds/11Mi)
% 1.26/1.28 % (2763)Refutation not found, incomplete strategy
% 1.26/1.28 % (2763)------------------------------
% 1.26/1.28 % (2763)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.28 % (2763)Termination reason: Refutation not found, incomplete strategy
% 1.26/1.28
% 1.26/1.28
% 1.26/1.28 % (2763)Memory used [KB]: 5500
% 1.26/1.28 % (2763)Time elapsed: 0.002 s
% 1.26/1.28 % (2763)Instructions burned: 2 (million)
% 1.26/1.28 % (2763)------------------------------
% 1.26/1.28 % (2763)------------------------------
% 1.26/1.28 % (2764)Instruction limit reached!
% 1.26/1.28 % (2764)------------------------------
% 1.26/1.28 % (2764)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.28 % (2764)Termination reason: Unknown
% 1.26/1.28 % (2764)Termination phase: Saturation
% 1.26/1.28
% 1.26/1.28 % (2764)Memory used [KB]: 5500
% 1.26/1.28 % (2764)Time elapsed: 0.007 s
% 1.26/1.28 % (2764)Instructions burned: 11 (million)
% 1.26/1.28 % (2764)------------------------------
% 1.26/1.28 % (2764)------------------------------
% 1.26/1.29 % (2765)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_2605 for (2997ds/41Mi)
% 1.26/1.30 % (2766)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_2605 for (2997ds/6Mi)
% 1.26/1.30 % (2765)Refutation not found, incomplete strategy
% 1.26/1.30 % (2765)------------------------------
% 1.26/1.30 % (2765)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.30 % (2765)Termination reason: Refutation not found, incomplete strategy
% 1.26/1.30
% 1.26/1.30
% 1.26/1.30 % (2765)Memory used [KB]: 5500
% 1.26/1.30 % (2765)Time elapsed: 0.008 s
% 1.26/1.30 % (2765)Instructions burned: 15 (million)
% 1.26/1.30 % (2765)------------------------------
% 1.26/1.30 % (2765)------------------------------
% 1.26/1.30 % (2766)Instruction limit reached!
% 1.26/1.30 % (2766)------------------------------
% 1.26/1.30 % (2766)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.30 % (2766)Termination reason: Unknown
% 1.26/1.30 % (2766)Termination phase: Saturation
% 1.26/1.30
% 1.26/1.30 % (2766)Memory used [KB]: 5500
% 1.26/1.30 % (2766)Time elapsed: 0.004 s
% 1.26/1.30 % (2766)Instructions burned: 6 (million)
% 1.26/1.30 % (2766)------------------------------
% 1.26/1.30 % (2766)------------------------------
% 1.26/1.30 % (2767)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_2605 for (2997ds/150Mi)
% 1.26/1.31 % (2762)Instruction limit reached!
% 1.26/1.31 % (2762)------------------------------
% 1.26/1.31 % (2762)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.31 % (2762)Termination reason: Unknown
% 1.26/1.31 % (2762)Termination phase: Saturation
% 1.26/1.31
% 1.26/1.31 % (2762)Memory used [KB]: 5756
% 1.26/1.31 % (2762)Time elapsed: 0.036 s
% 1.26/1.31 % (2762)Instructions burned: 71 (million)
% 1.26/1.31 % (2762)------------------------------
% 1.26/1.31 % (2762)------------------------------
% 1.26/1.31 % (2767)Refutation not found, incomplete strategy
% 1.26/1.31 % (2767)------------------------------
% 1.26/1.31 % (2767)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.31 % (2767)Termination reason: Refutation not found, incomplete strategy
% 1.26/1.31
% 1.26/1.31
% 1.26/1.31 % (2767)Memory used [KB]: 5628
% 1.26/1.31 % (2767)Time elapsed: 0.011 s
% 1.26/1.31 % (2767)Instructions burned: 20 (million)
% 1.26/1.31 % (2767)------------------------------
% 1.26/1.31 % (2767)------------------------------
% 1.26/1.31 % (2760)Instruction limit reached!
% 1.26/1.31 % (2760)------------------------------
% 1.26/1.31 % (2760)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.31 % (2760)Termination reason: Unknown
% 1.26/1.31 % (2760)Termination phase: Saturation
% 1.26/1.31
% 1.26/1.31 % (2760)Memory used [KB]: 5628
% 1.26/1.31 % (2760)Time elapsed: 0.048 s
% 1.26/1.31 % (2760)Instructions burned: 96 (million)
% 1.26/1.31 % (2760)------------------------------
% 1.26/1.31 % (2760)------------------------------
% 1.26/1.31 % (2768)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_2605 for (2997ds/343Mi)
% 1.26/1.31 % (2769)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_2605 for (2997ds/109Mi)
% 1.26/1.32 % (2768)Refutation not found, incomplete strategy
% 1.26/1.32 % (2768)------------------------------
% 1.26/1.32 % (2768)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.32 % (2768)Termination reason: Refutation not found, incomplete strategy
% 1.26/1.32
% 1.26/1.32
% 1.26/1.32 % (2768)Memory used [KB]: 5500
% 1.26/1.32 % (2768)Time elapsed: 0.004 s
% 1.26/1.32 % (2768)Instructions burned: 5 (million)
% 1.26/1.32 % (2768)------------------------------
% 1.26/1.32 % (2768)------------------------------
% 1.26/1.32 % (2770)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_2605 for (2997ds/253Mi)
% 1.26/1.33 % (2770)Refutation not found, incomplete strategy
% 1.26/1.33 % (2770)------------------------------
% 1.26/1.33 % (2770)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.33 % (2770)Termination reason: Refutation not found, incomplete strategy
% 1.26/1.33
% 1.26/1.33
% 1.26/1.33 % (2770)Memory used [KB]: 5500
% 1.26/1.33 % (2770)Time elapsed: 0.002 s
% 1.26/1.33 % (2770)Instructions burned: 1 (million)
% 1.26/1.33 % (2770)------------------------------
% 1.26/1.33 % (2770)------------------------------
% 1.26/1.33 % (2771)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_2605 for (2997ds/140Mi)
% 1.26/1.33 % (2772)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_2605 for (2997ds/614Mi)
% 1.26/1.33 % (2771)Refutation not found, incomplete strategy
% 1.26/1.33 % (2771)------------------------------
% 1.26/1.33 % (2771)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.33 % (2771)Termination reason: Refutation not found, incomplete strategy
% 1.26/1.33
% 1.26/1.33
% 1.26/1.33 % (2771)Memory used [KB]: 5500
% 1.26/1.33 % (2771)Time elapsed: 0.004 s
% 1.26/1.33 % (2771)Instructions burned: 6 (million)
% 1.26/1.33 % (2771)------------------------------
% 1.26/1.33 % (2771)------------------------------
% 1.26/1.33 % (2773)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_2605 for (2997ds/202Mi)
% 1.26/1.33 % (2773)Refutation not found, incomplete strategy
% 1.26/1.33 % (2773)------------------------------
% 1.26/1.33 % (2773)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.33 % (2773)Termination reason: Refutation not found, incomplete strategy
% 1.26/1.33
% 1.26/1.33
% 1.26/1.33 % (2773)Memory used [KB]: 5500
% 1.26/1.33 % (2773)Time elapsed: 0.003 s
% 1.26/1.33 % (2773)Instructions burned: 3 (million)
% 1.26/1.33 % (2773)------------------------------
% 1.26/1.33 % (2773)------------------------------
% 1.26/1.33 % (2772)Refutation not found, incomplete strategy
% 1.26/1.33 % (2772)------------------------------
% 1.26/1.33 % (2772)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.33 % (2772)Termination reason: Refutation not found, incomplete strategy
% 1.26/1.33
% 1.26/1.33
% 1.26/1.33 % (2772)Memory used [KB]: 5628
% 1.26/1.33 % (2772)Time elapsed: 0.006 s
% 1.26/1.33 % (2772)Instructions burned: 9 (million)
% 1.26/1.33 % (2772)------------------------------
% 1.26/1.33 % (2772)------------------------------
% 1.26/1.34 % (2774)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on DTF2THF_2605 for (2997ds/339Mi)
% 1.26/1.35 % (2775)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=283:si=on:rtra=on_0 on DTF2THF_2605 for (2996ds/283Mi)
% 1.26/1.35 % (2774)Refutation not found, incomplete strategy
% 1.26/1.35 % (2774)------------------------------
% 1.26/1.35 % (2774)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.35 % (2774)Termination reason: Refutation not found, incomplete strategy
% 1.26/1.35
% 1.26/1.35
% 1.26/1.35 % (2774)Memory used [KB]: 5500
% 1.26/1.35 % (2774)Time elapsed: 0.008 s
% 1.26/1.35 % (2774)Instructions burned: 13 (million)
% 1.26/1.35 % (2774)------------------------------
% 1.26/1.35 % (2774)------------------------------
% 1.26/1.35 % (2776)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_2605 for (2996ds/134Mi)
% 1.26/1.35 % (2777)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_2605 for (2996ds/298Mi)
% 1.26/1.36 % (2757)Instruction limit reached!
% 1.26/1.36 % (2757)------------------------------
% 1.26/1.36 % (2757)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.36 % (2757)Termination reason: Unknown
% 1.26/1.36 % (2757)Termination phase: Saturation
% 1.26/1.36
% 1.26/1.36 % (2757)Memory used [KB]: 3198
% 1.26/1.36 % (2757)Time elapsed: 0.156 s
% 1.26/1.36 % (2757)Instructions burned: 432 (million)
% 1.26/1.36 % (2757)------------------------------
% 1.26/1.36 % (2757)------------------------------
% 1.26/1.36 % (2769)Instruction limit reached!
% 1.26/1.36 % (2769)------------------------------
% 1.26/1.36 % (2769)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.36 % (2769)Termination reason: Unknown
% 1.26/1.36 % (2769)Termination phase: Saturation
% 1.26/1.36
% 1.26/1.36 % (2769)Memory used [KB]: 5500
% 1.26/1.36 % (2769)Time elapsed: 0.048 s
% 1.26/1.36 % (2769)Instructions burned: 109 (million)
% 1.26/1.36 % (2769)------------------------------
% 1.26/1.36 % (2769)------------------------------
% 1.26/1.37 % (2778)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_2605 for (2996ds/192Mi)
% 1.26/1.37 % (2778)Refutation not found, incomplete strategy
% 1.26/1.37 % (2778)------------------------------
% 1.26/1.37 % (2778)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.37 % (2778)Termination reason: Refutation not found, incomplete strategy
% 1.26/1.37
% 1.26/1.37
% 1.26/1.37 % (2778)Memory used [KB]: 5500
% 1.26/1.37 % (2778)Time elapsed: 0.004 s
% 1.26/1.37 % (2778)Instructions burned: 5 (million)
% 1.26/1.37 % (2778)------------------------------
% 1.26/1.37 % (2778)------------------------------
% 1.26/1.37 % (2779)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on DTF2THF_2605 for (2996ds/258Mi)
% 1.26/1.37 % (2779)Refutation not found, incomplete strategy
% 1.26/1.37 % (2779)------------------------------
% 1.26/1.37 % (2779)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.37 % (2779)Termination reason: Refutation not found, incomplete strategy
% 1.26/1.37
% 1.26/1.37
% 1.26/1.37 % (2779)Memory used [KB]: 5500
% 1.26/1.37 % (2779)Time elapsed: 0.002 s
% 1.26/1.37 % (2779)Instructions burned: 4 (million)
% 1.26/1.37 % (2779)------------------------------
% 1.26/1.37 % (2779)------------------------------
% 1.26/1.38 % (2780)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_2605 for (2996ds/90Mi)
% 1.26/1.38 % (2782)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on DTF2THF_2605 for (2996ds/458Mi)
% 1.26/1.38 % (2782)Refutation not found, incomplete strategy
% 1.26/1.38 % (2782)------------------------------
% 1.26/1.38 % (2782)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.38 % (2782)Termination reason: Refutation not found, incomplete strategy
% 1.26/1.38
% 1.26/1.38
% 1.26/1.38 % (2782)Memory used [KB]: 5500
% 1.26/1.38 % (2782)Time elapsed: 0.003 s
% 1.26/1.38 % (2782)Instructions burned: 6 (million)
% 1.26/1.38 % (2782)------------------------------
% 1.26/1.38 % (2782)------------------------------
% 1.26/1.39 % (2781)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on DTF2THF_2605 for (2996ds/231Mi)
% 1.26/1.39 % (2783)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_2605 for (2996ds/31Mi)
% 1.26/1.40 % (2783)Instruction limit reached!
% 1.26/1.40 % (2783)------------------------------
% 1.26/1.40 % (2783)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.40 % (2783)Termination reason: Unknown
% 1.26/1.40 % (2783)Termination phase: Saturation
% 1.26/1.40
% 1.26/1.40 % (2783)Memory used [KB]: 5500
% 1.26/1.40 % (2783)Time elapsed: 0.010 s
% 1.26/1.40 % (2783)Instructions burned: 34 (million)
% 1.26/1.40 % (2783)------------------------------
% 1.26/1.40 % (2783)------------------------------
% 1.26/1.41 % (2784)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on DTF2THF_2605 for (2996ds/297Mi)
% 1.26/1.42 % (2776)Instruction limit reached!
% 1.26/1.42 % (2776)------------------------------
% 1.26/1.42 % (2776)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.42 % (2776)Termination reason: Unknown
% 1.26/1.42 % (2776)Termination phase: Saturation
% 1.26/1.42
% 1.26/1.42 % (2776)Memory used [KB]: 6140
% 1.26/1.42 % (2776)Time elapsed: 0.068 s
% 1.26/1.42 % (2776)Instructions burned: 135 (million)
% 1.26/1.42 % (2776)------------------------------
% 1.26/1.42 % (2776)------------------------------
% 1.26/1.42 % (2784)Refutation not found, incomplete strategy
% 1.26/1.42 % (2784)------------------------------
% 1.26/1.42 % (2784)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.42 % (2784)Termination reason: Refutation not found, incomplete strategy
% 1.26/1.42
% 1.26/1.42
% 1.26/1.42 % (2784)Memory used [KB]: 5500
% 1.26/1.42 % (2784)Time elapsed: 0.008 s
% 1.26/1.42 % (2784)Instructions burned: 23 (million)
% 1.26/1.42 % (2784)------------------------------
% 1.26/1.42 % (2784)------------------------------
% 1.26/1.42 % (2780)Instruction limit reached!
% 1.26/1.42 % (2780)------------------------------
% 1.26/1.42 % (2780)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.42 % (2780)Termination reason: Unknown
% 1.26/1.42 % (2780)Termination phase: Saturation
% 1.26/1.42
% 1.26/1.42 % (2780)Memory used [KB]: 5756
% 1.26/1.42 % (2780)Time elapsed: 0.048 s
% 1.26/1.42 % (2780)Instructions burned: 91 (million)
% 1.26/1.42 % (2780)------------------------------
% 1.26/1.42 % (2780)------------------------------
% 1.26/1.43 % (2786)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on DTF2THF_2605 for (2996ds/182Mi)
% 1.26/1.43 % (2785)dis+2_1:4_amm=off:au=on:cbe=off:cnfonf=lazy_gen:hfaw=0:hfsq=on:hfsql=off:plsq=on:plsqc=1:plsqr=35,4:sac=on:i=987:si=on:rtra=on_0 on DTF2THF_2605 for (2996ds/987Mi)
% 1.26/1.44 % (2787)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on DTF2THF_2605 for (2996ds/182Mi)
% 1.26/1.45 % (2785)Refutation not found, incomplete strategy
% 1.26/1.45 % (2785)------------------------------
% 1.26/1.45 % (2785)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.45 % (2785)Termination reason: Refutation not found, incomplete strategy
% 1.26/1.45
% 1.26/1.45
% 1.26/1.45 % (2785)Memory used [KB]: 5628
% 1.26/1.45 % (2785)Time elapsed: 0.019 s
% 1.26/1.45 % (2785)Instructions burned: 38 (million)
% 1.26/1.45 % (2785)------------------------------
% 1.26/1.45 % (2785)------------------------------
% 1.26/1.46 % (2786)First to succeed.
% 1.26/1.46 % (2727)Instruction limit reached!
% 1.26/1.46 % (2727)------------------------------
% 1.26/1.46 % (2727)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.46 % (2727)Termination reason: Unknown
% 1.26/1.46 % (2727)Termination phase: Saturation
% 1.26/1.46
% 1.26/1.46 % (2727)Memory used [KB]: 7036
% 1.26/1.46 % (2727)Time elapsed: 0.362 s
% 1.26/1.46 % (2727)Instructions burned: 711 (million)
% 1.26/1.46 % (2727)------------------------------
% 1.26/1.46 % (2727)------------------------------
% 1.26/1.47 % (2788)dis+10_1:8_cha=on:cnfonf=lazy_pi_sigma_gen:fe=axiom:hud=5:plsq=on:plsqr=32,1:prag=on:sos=all:i=154:si=on:rtra=on_0 on DTF2THF_2605 for (2995ds/154Mi)
% 1.26/1.47 % (2775)Instruction limit reached!
% 1.26/1.47 % (2775)------------------------------
% 1.26/1.47 % (2775)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.47 % (2775)Termination reason: Unknown
% 1.26/1.47 % (2775)Termination phase: Saturation
% 1.26/1.47
% 1.26/1.47 % (2775)Memory used [KB]: 6524
% 1.26/1.47 % (2775)Time elapsed: 0.124 s
% 1.26/1.47 % (2775)Instructions burned: 283 (million)
% 1.26/1.47 % (2775)------------------------------
% 1.26/1.47 % (2775)------------------------------
% 1.26/1.47 % (2786)Refutation found. Thanks to Tanya!
% 1.26/1.47 % SZS status Theorem for DTF2THF_2605
% 1.26/1.47 % SZS output start Proof for DTF2THF_2605
% 1.26/1.47 thf(func_def_0, type, eps: ($i > $o) > $i).
% 1.26/1.47 thf(func_def_2, type, case: ($o > $o) > $i > $i > $i > $i > $i).
% 1.26/1.47 thf(func_def_4, type, f: $o > $o).
% 1.26/1.47 thf(func_def_5, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.26/1.47 thf(func_def_23, type, ph5: !>[X0: $tType]:(X0)).
% 1.26/1.47 thf(f678,plain,(
% 1.26/1.47 $false),
% 1.26/1.47 inference(avatar_sat_refutation,[status(thm)],[f353,f372,f391,f410,f460,f469,f471,f474,f489,f498,f534,f543,f545,f587,f590,f593,f597,f615,f617,f640,f660,f675,f677])).
% 1.26/1.47 thf(f677,plain,(
% 1.26/1.47 ~spl4_8),
% 1.26/1.47 inference(avatar_contradiction_clause,[status(thm)],[f676])).
% 1.26/1.47 thf(f676,plain,(
% 1.26/1.47 $false | ~spl4_8),
% 1.26/1.47 inference(equality_resolution,[status(thm)],[f396])).
% 1.26/1.47 thf(f396,plain,(
% 1.26/1.47 ( ! [X1 : $i] : ((sK0 != X1)) ) | ~spl4_8),
% 1.26/1.47 inference(avatar_component_clause,[status(thm)],[f395])).
% 1.26/1.47 thf(f395,definition,(
% 1.26/1.47 spl4_8 <=> ! [X1 : $i] : (sK0 != X1)),
% 1.26/1.47 introduced(definition,[new_symbols(naming,[spl4_8])],[avatar_definition])).
% 1.26/1.47 thf(f675,plain,(
% 1.26/1.47 spl4_5 | ~spl4_13 | ~spl4_15 | spl4_19 | ~spl4_20),
% 1.26/1.47 inference(avatar_contradiction_clause,[status(thm)],[f674])).
% 1.26/1.47 thf(f674,plain,(
% 1.26/1.47 $false | (spl4_5 | ~spl4_13 | ~spl4_15 | spl4_19 | ~spl4_20)),
% 1.26/1.47 inference(subsumption_resolution,[status(thm)],[f673,f672])).
% 1.26/1.47 thf(f672,plain,(
% 1.26/1.47 ((f @ $false) = $false) | (~spl4_13 | ~spl4_15)),
% 1.26/1.47 inference(forward_demodulation,[status(thm)],[f493,f484])).
% 1.26/1.47 thf(f484,plain,(
% 1.26/1.47 (sK7 = $false) | ~spl4_13),
% 1.26/1.47 inference(avatar_component_clause,[status(thm)],[f482])).
% 1.26/1.47 thf(f482,definition,(
% 1.26/1.47 spl4_13 <=> (sK7 = $false)),
% 1.26/1.47 introduced(definition,[new_symbols(naming,[spl4_13])],[avatar_definition])).
% 1.26/1.47 thf(f493,plain,(
% 1.26/1.47 ($false = (f @ sK7)) | ~spl4_15),
% 1.26/1.47 inference(avatar_component_clause,[status(thm)],[f491])).
% 1.26/1.47 thf(f491,definition,(
% 1.26/1.47 spl4_15 <=> ($false = (f @ sK7))),
% 1.26/1.47 introduced(definition,[new_symbols(naming,[spl4_15])],[avatar_definition])).
% 1.26/1.47 thf(f673,plain,(
% 1.26/1.47 ((f @ $false) != $false) | (spl4_5 | spl4_19 | ~spl4_20)),
% 1.26/1.47 inference(superposition,[status(thm)],[f506,f654])).
% 1.26/1.47 thf(f654,plain,(
% 1.26/1.47 (sK9 = $false) | (spl4_5 | spl4_19 | ~spl4_20)),
% 1.26/1.47 inference(subsumption_resolution,[status(thm)],[f630,f537])).
% 1.26/1.47 thf(f537,plain,(
% 1.26/1.47 ($false != sK10) | spl4_19),
% 1.26/1.47 inference(avatar_component_clause,[status(thm)],[f536])).
% 1.26/1.47 thf(f536,definition,(
% 1.26/1.47 spl4_19 <=> ($false = sK10)),
% 1.26/1.47 introduced(definition,[new_symbols(naming,[spl4_19])],[avatar_definition])).
% 1.26/1.47 thf(f630,plain,(
% 1.26/1.47 (sK9 = $false) | ($false = sK10) | (spl4_5 | ~spl4_20)),
% 1.26/1.47 inference(binary_proxy_clausification,[status(thm)],[f628])).
% 1.26/1.47 thf(f628,plain,(
% 1.26/1.47 (sK9 != sK10) | (spl4_5 | ~spl4_20)),
% 1.26/1.47 inference(trivial_inequality_removal,[status(thm)],[f627])).
% 1.26/1.47 thf(f627,plain,(
% 1.26/1.47 ($false != $false) | (sK9 != sK10) | (spl4_5 | ~spl4_20)),
% 1.26/1.47 inference(constrained_superposition,[status(thm)],[f506,f542])).
% 1.26/1.47 thf(f542,plain,(
% 1.26/1.47 ((f @ sK10) = $false) | ~spl4_20),
% 1.26/1.47 inference(avatar_component_clause,[status(thm)],[f540])).
% 1.26/1.47 thf(f540,definition,(
% 1.26/1.47 spl4_20 <=> ((f @ sK10) = $false)),
% 1.26/1.47 introduced(definition,[new_symbols(naming,[spl4_20])],[avatar_definition])).
% 1.26/1.47 thf(f506,plain,(
% 1.26/1.47 ($false != (f @ sK9)) | spl4_5),
% 1.26/1.47 inference(beta_eta_normalization,[status(thm)],[f505])).
% 1.26/1.47 thf(f505,plain,(
% 1.26/1.47 (((^[Y0 : $o]: ($false)) @ sK9) != (f @ sK9)) | spl4_5),
% 1.26/1.47 inference(negative_extensionality,[status(thm)],[f332])).
% 1.26/1.47 thf(f332,plain,(
% 1.26/1.47 (f != (^[Y0 : $o]: ($false))) | spl4_5),
% 1.26/1.47 inference(avatar_component_clause,[status(thm)],[f331])).
% 1.26/1.47 thf(f331,definition,(
% 1.26/1.47 spl4_5 <=> (f = (^[Y0 : $o]: ($false)))),
% 1.26/1.47 introduced(definition,[new_symbols(naming,[spl4_5])],[avatar_definition])).
% 1.26/1.47 thf(f660,plain,(
% 1.26/1.47 spl4_15 | ~spl4_16 | ~spl4_18 | ~spl4_20),
% 1.26/1.47 inference(avatar_contradiction_clause,[status(thm)],[f659])).
% 1.26/1.47 thf(f659,plain,(
% 1.26/1.47 $false | (spl4_15 | ~spl4_16 | ~spl4_18 | ~spl4_20)),
% 1.26/1.47 inference(subsumption_resolution,[status(thm)],[f657,f603])).
% 1.26/1.47 thf(f603,plain,(
% 1.26/1.47 ((f @ $true) != $false) | (spl4_15 | ~spl4_16)),
% 1.26/1.47 inference(forward_demodulation,[status(thm)],[f492,f497])).
% 1.26/1.47 thf(f497,plain,(
% 1.26/1.47 (sK7 = $true) | ~spl4_16),
% 1.26/1.47 inference(avatar_component_clause,[status(thm)],[f495])).
% 1.26/1.47 thf(f495,definition,(
% 1.26/1.47 spl4_16 <=> (sK7 = $true)),
% 1.26/1.47 introduced(definition,[new_symbols(naming,[spl4_16])],[avatar_definition])).
% 1.26/1.47 thf(f492,plain,(
% 1.26/1.47 ($false != (f @ sK7)) | spl4_15),
% 1.26/1.47 inference(avatar_component_clause,[status(thm)],[f491])).
% 1.26/1.47 thf(f657,plain,(
% 1.26/1.47 ((f @ $true) = $false) | (~spl4_18 | ~spl4_20)),
% 1.26/1.47 inference(superposition,[status(thm)],[f542,f533])).
% 1.26/1.47 thf(f533,plain,(
% 1.26/1.47 ($true = sK10) | ~spl4_18),
% 1.26/1.47 inference(avatar_component_clause,[status(thm)],[f531])).
% 1.26/1.47 thf(f531,definition,(
% 1.26/1.47 spl4_18 <=> ($true = sK10)),
% 1.26/1.47 introduced(definition,[new_symbols(naming,[spl4_18])],[avatar_definition])).
% 1.26/1.47 thf(f640,plain,(
% 1.26/1.47 ~spl4_17 | ~spl4_20),
% 1.26/1.47 inference(avatar_contradiction_clause,[status(thm)],[f639])).
% 1.26/1.47 thf(f639,plain,(
% 1.26/1.47 $false | (~spl4_17 | ~spl4_20)),
% 1.26/1.47 inference(trivial_inequality_removal,[status(thm)],[f622])).
% 1.26/1.47 thf(f622,plain,(
% 1.26/1.47 ($false = $true) | (~spl4_17 | ~spl4_20)),
% 1.26/1.47 inference(superposition,[status(thm)],[f542,f529])).
% 1.26/1.47 thf(f529,plain,(
% 1.26/1.47 ((f @ sK10) = $true) | ~spl4_17),
% 1.26/1.47 inference(avatar_component_clause,[status(thm)],[f527])).
% 1.26/1.47 thf(f527,definition,(
% 1.26/1.47 spl4_17 <=> ((f @ sK10) = $true)),
% 1.26/1.47 introduced(definition,[new_symbols(naming,[spl4_17])],[avatar_definition])).
% 1.26/1.47 thf(f617,plain,(
% 1.26/1.47 ~spl4_7),
% 1.26/1.47 inference(avatar_contradiction_clause,[status(thm)],[f616])).
% 1.26/1.47 thf(f616,plain,(
% 1.26/1.47 $false | ~spl4_7),
% 1.26/1.47 inference(equality_resolution,[status(thm)],[f378])).
% 1.26/1.47 thf(f378,plain,(
% 1.26/1.47 ( ! [X1 : $i] : ((sK2 != X1)) ) | ~spl4_7),
% 1.26/1.47 inference(avatar_component_clause,[status(thm)],[f377])).
% 1.26/1.47 thf(f377,definition,(
% 1.26/1.47 spl4_7 <=> ! [X1 : $i] : (sK2 != X1)),
% 1.26/1.47 introduced(definition,[new_symbols(naming,[spl4_7])],[avatar_definition])).
% 1.26/1.47 thf(f615,plain,(
% 1.26/1.47 spl4_3 | ~spl4_9 | spl4_10 | ~spl4_17 | ~spl4_19),
% 1.26/1.47 inference(avatar_contradiction_clause,[status(thm)],[f614])).
% 1.26/1.47 thf(f614,plain,(
% 1.26/1.47 $false | (spl4_3 | ~spl4_9 | spl4_10 | ~spl4_17 | ~spl4_19)),
% 1.26/1.47 inference(subsumption_resolution,[status(thm)],[f613,f602])).
% 1.26/1.47 thf(f602,plain,(
% 1.26/1.47 ((f @ $false) = $true) | (~spl4_17 | ~spl4_19)),
% 1.26/1.47 inference(forward_demodulation,[status(thm)],[f529,f538])).
% 1.26/1.47 thf(f538,plain,(
% 1.26/1.47 ($false = sK10) | ~spl4_19),
% 1.26/1.47 inference(avatar_component_clause,[status(thm)],[f536])).
% 1.26/1.47 thf(f613,plain,(
% 1.26/1.47 ((f @ $false) != $true) | (spl4_3 | ~spl4_9 | spl4_10)),
% 1.26/1.47 inference(superposition,[status(thm)],[f502,f612])).
% 1.26/1.47 thf(f612,plain,(
% 1.26/1.47 (sK8 = $false) | (spl4_3 | ~spl4_9 | spl4_10)),
% 1.26/1.47 inference(subsumption_resolution,[status(thm)],[f611,f458])).
% 1.26/1.47 thf(f458,plain,(
% 1.26/1.47 (sK6 != $false) | spl4_10),
% 1.26/1.47 inference(avatar_component_clause,[status(thm)],[f457])).
% 1.26/1.47 thf(f457,definition,(
% 1.26/1.47 spl4_10 <=> (sK6 = $false)),
% 1.26/1.47 introduced(definition,[new_symbols(naming,[spl4_10])],[avatar_definition])).
% 1.26/1.47 thf(f611,plain,(
% 1.26/1.47 (sK6 = $false) | (sK8 = $false) | (spl4_3 | ~spl4_9)),
% 1.26/1.47 inference(binary_proxy_clausification,[status(thm)],[f609])).
% 1.26/1.47 thf(f609,plain,(
% 1.26/1.47 (sK6 != sK8) | (spl4_3 | ~spl4_9)),
% 1.26/1.47 inference(trivial_inequality_removal,[status(thm)],[f608])).
% 1.26/1.47 thf(f608,plain,(
% 1.26/1.47 ($true != $true) | (sK6 != sK8) | (spl4_3 | ~spl4_9)),
% 1.26/1.47 inference(constrained_superposition,[status(thm)],[f502,f455])).
% 1.26/1.47 thf(f455,plain,(
% 1.26/1.47 ((f @ sK6) = $true) | ~spl4_9),
% 1.26/1.47 inference(avatar_component_clause,[status(thm)],[f453])).
% 1.26/1.47 thf(f453,definition,(
% 1.26/1.47 spl4_9 <=> ((f @ sK6) = $true)),
% 1.26/1.47 introduced(definition,[new_symbols(naming,[spl4_9])],[avatar_definition])).
% 1.26/1.47 thf(f502,plain,(
% 1.26/1.47 ((f @ sK8) != $true) | spl4_3),
% 1.26/1.47 inference(beta_eta_normalization,[status(thm)],[f501])).
% 1.26/1.47 thf(f501,plain,(
% 1.26/1.47 ((f @ sK8) != ((^[Y0 : $o]: ($true)) @ sK8)) | spl4_3),
% 1.26/1.47 inference(negative_extensionality,[status(thm)],[f318])).
% 1.26/1.47 thf(f318,plain,(
% 1.26/1.47 (f != (^[Y0 : $o]: ($true))) | spl4_3),
% 1.26/1.47 inference(avatar_component_clause,[status(thm)],[f317])).
% 1.26/1.47 thf(f317,definition,(
% 1.26/1.47 spl4_3 <=> (f = (^[Y0 : $o]: ($true)))),
% 1.26/1.47 introduced(definition,[new_symbols(naming,[spl4_3])],[avatar_definition])).
% 1.26/1.47 thf(f597,plain,(
% 1.26/1.47 ~spl4_18 | ~spl4_19),
% 1.26/1.47 inference(avatar_contradiction_clause,[status(thm)],[f596])).
% 1.26/1.47 thf(f596,plain,(
% 1.26/1.47 $false | (~spl4_18 | ~spl4_19)),
% 1.26/1.47 inference(trivial_inequality_removal,[status(thm)],[f595])).
% 1.26/1.47 thf(f595,plain,(
% 1.26/1.47 ($false = $true) | (~spl4_18 | ~spl4_19)),
% 1.26/1.47 inference(forward_demodulation,[status(thm)],[f533,f538])).
% 1.26/1.47 thf(f593,plain,(
% 1.26/1.47 ~spl4_14 | ~spl4_15),
% 1.26/1.47 inference(avatar_contradiction_clause,[status(thm)],[f592])).
% 1.26/1.47 thf(f592,plain,(
% 1.26/1.47 $false | (~spl4_14 | ~spl4_15)),
% 1.26/1.47 inference(trivial_inequality_removal,[status(thm)],[f591])).
% 1.26/1.47 thf(f591,plain,(
% 1.26/1.47 ($false = $true) | (~spl4_14 | ~spl4_15)),
% 1.26/1.47 inference(forward_demodulation,[status(thm)],[f488,f493])).
% 1.26/1.47 thf(f488,plain,(
% 1.26/1.47 ($true = (f @ sK7)) | ~spl4_14),
% 1.26/1.47 inference(avatar_component_clause,[status(thm)],[f486])).
% 1.26/1.47 thf(f486,definition,(
% 1.26/1.47 spl4_14 <=> ($true = (f @ sK7))),
% 1.26/1.47 introduced(definition,[new_symbols(naming,[spl4_14])],[avatar_definition])).
% 1.26/1.47 thf(f590,plain,(
% 1.26/1.47 spl4_9 | ~spl4_10 | ~spl4_17 | ~spl4_19),
% 1.26/1.47 inference(avatar_contradiction_clause,[status(thm)],[f589])).
% 1.26/1.47 thf(f589,plain,(
% 1.26/1.47 $false | (spl4_9 | ~spl4_10 | ~spl4_17 | ~spl4_19)),
% 1.26/1.47 inference(subsumption_resolution,[status(thm)],[f546,f584])).
% 1.26/1.47 thf(f584,plain,(
% 1.26/1.47 ((f @ $false) != $true) | (spl4_9 | ~spl4_10)),
% 1.26/1.47 inference(forward_demodulation,[status(thm)],[f454,f459])).
% 1.26/1.47 thf(f459,plain,(
% 1.26/1.47 (sK6 = $false) | ~spl4_10),
% 1.26/1.47 inference(avatar_component_clause,[status(thm)],[f457])).
% 1.26/1.47 thf(f454,plain,(
% 1.26/1.47 ((f @ sK6) != $true) | spl4_9),
% 1.26/1.47 inference(avatar_component_clause,[status(thm)],[f453])).
% 1.26/1.47 thf(f546,plain,(
% 1.26/1.47 ((f @ $false) = $true) | (~spl4_17 | ~spl4_19)),
% 1.26/1.47 inference(superposition,[status(thm)],[f529,f538])).
% 1.26/1.47 thf(f587,plain,(
% 1.26/1.47 ~spl4_10 | ~spl4_12),
% 1.26/1.47 inference(avatar_contradiction_clause,[status(thm)],[f586])).
% 1.26/1.47 thf(f586,plain,(
% 1.26/1.47 $false | (~spl4_10 | ~spl4_12)),
% 1.26/1.47 inference(trivial_inequality_removal,[status(thm)],[f585])).
% 1.26/1.47 thf(f585,plain,(
% 1.26/1.47 ($false = $true) | (~spl4_10 | ~spl4_12)),
% 1.26/1.47 inference(forward_demodulation,[status(thm)],[f468,f459])).
% 1.26/1.47 thf(f468,plain,(
% 1.26/1.47 (sK6 = $true) | ~spl4_12),
% 1.26/1.47 inference(avatar_component_clause,[status(thm)],[f466])).
% 1.26/1.47 thf(f466,definition,(
% 1.26/1.47 spl4_12 <=> (sK6 = $true)),
% 1.26/1.47 introduced(definition,[new_symbols(naming,[spl4_12])],[avatar_definition])).
% 1.26/1.47 thf(f545,plain,(
% 1.26/1.47 ~spl4_2),
% 1.26/1.47 inference(avatar_contradiction_clause,[status(thm)],[f544])).
% 1.26/1.47 thf(f544,plain,(
% 1.26/1.47 $false | ~spl4_2),
% 1.26/1.47 inference(equality_resolution,[status(thm)],[f315])).
% 1.26/1.47 thf(f315,plain,(
% 1.26/1.47 ( ! [X1 : $i] : ((sK3 != X1)) ) | ~spl4_2),
% 1.26/1.47 inference(avatar_component_clause,[status(thm)],[f314])).
% 1.26/1.47 thf(f314,definition,(
% 1.26/1.47 spl4_2 <=> ! [X1 : $i] : (sK3 != X1)),
% 1.26/1.47 introduced(definition,[new_symbols(naming,[spl4_2])],[avatar_definition])).
% 1.26/1.47 thf(f543,plain,(
% 1.26/1.47 spl4_19 | spl4_20 | spl4_4),
% 1.26/1.47 inference(avatar_split_clause,[status(thm)],[f525,f321,f540,f536])).
% 1.26/1.47 thf(f321,definition,(
% 1.26/1.47 spl4_4 <=> (f = (^[Y0 : $o]: (Y0)))),
% 1.26/1.47 introduced(definition,[new_symbols(naming,[spl4_4])],[avatar_definition])).
% 1.26/1.47 thf(f525,plain,(
% 1.26/1.47 ((f @ sK10) = $false) | ($false = sK10) | spl4_4),
% 1.26/1.47 inference(binary_proxy_clausification,[status(thm)],[f523])).
% 1.26/1.47 thf(f523,plain,(
% 1.26/1.47 ((f @ sK10) != sK10) | spl4_4),
% 1.26/1.47 inference(beta_eta_normalization,[status(thm)],[f522])).
% 1.26/1.47 thf(f522,plain,(
% 1.26/1.47 ((f @ sK10) != ((^[Y0 : $o]: (Y0)) @ sK10)) | spl4_4),
% 1.26/1.47 inference(negative_extensionality,[status(thm)],[f323])).
% 1.26/1.47 thf(f323,plain,(
% 1.26/1.47 (f != (^[Y0 : $o]: (Y0))) | spl4_4),
% 1.26/1.47 inference(avatar_component_clause,[status(thm)],[f321])).
% 1.26/1.47 thf(f534,plain,(
% 1.26/1.47 spl4_17 | spl4_18 | spl4_4),
% 1.26/1.47 inference(avatar_split_clause,[status(thm)],[f524,f321,f531,f527])).
% 1.26/1.47 thf(f524,plain,(
% 1.26/1.47 ((f @ sK10) = $true) | ($true = sK10) | spl4_4),
% 1.26/1.47 inference(binary_proxy_clausification,[status(thm)],[f523])).
% 1.26/1.47 thf(f498,plain,(
% 1.26/1.47 spl4_15 | spl4_16 | spl4_1),
% 1.26/1.47 inference(avatar_split_clause,[status(thm)],[f479,f310,f495,f491])).
% 1.26/1.47 thf(f310,definition,(
% 1.26/1.47 spl4_1 <=> (~ = f)),
% 1.26/1.47 introduced(definition,[new_symbols(naming,[spl4_1])],[avatar_definition])).
% 1.26/1.47 thf(f479,plain,(
% 1.26/1.47 (sK7 = $true) | ($false = (f @ sK7)) | spl4_1),
% 1.26/1.47 inference(not_proxy_clausification,[status(thm)],[f478])).
% 1.26/1.47 thf(f478,plain,(
% 1.26/1.47 ((~ sK7) = $false) | ($false = (f @ sK7)) | spl4_1),
% 1.26/1.47 inference(binary_proxy_clausification,[status(thm)],[f476])).
% 1.26/1.47 thf(f476,plain,(
% 1.26/1.47 ((~ sK7) != (f @ sK7)) | spl4_1),
% 1.26/1.47 inference(negative_extensionality,[status(thm)],[f311])).
% 1.26/1.47 thf(f311,plain,(
% 1.26/1.47 (~ != f) | spl4_1),
% 1.26/1.47 inference(avatar_component_clause,[status(thm)],[f310])).
% 1.26/1.47 thf(f489,plain,(
% 1.26/1.47 spl4_13 | spl4_14 | spl4_1),
% 1.26/1.47 inference(avatar_split_clause,[status(thm)],[f480,f310,f486,f482])).
% 1.26/1.47 thf(f480,plain,(
% 1.26/1.47 (sK7 = $false) | ($true = (f @ sK7)) | spl4_1),
% 1.26/1.47 inference(not_proxy_clausification,[status(thm)],[f477])).
% 1.26/1.47 thf(f477,plain,(
% 1.26/1.47 ($true = (f @ sK7)) | ((~ sK7) = $true) | spl4_1),
% 1.26/1.47 inference(binary_proxy_clausification,[status(thm)],[f476])).
% 1.26/1.47 thf(f474,plain,(
% 1.26/1.47 ~spl4_9 | ~spl4_11),
% 1.26/1.47 inference(avatar_contradiction_clause,[status(thm)],[f473])).
% 1.26/1.47 thf(f473,plain,(
% 1.26/1.47 $false | (~spl4_9 | ~spl4_11)),
% 1.26/1.47 inference(trivial_inequality_removal,[status(thm)],[f472])).
% 1.26/1.47 thf(f472,plain,(
% 1.26/1.47 ($false = $true) | (~spl4_9 | ~spl4_11)),
% 1.26/1.47 inference(forward_demodulation,[status(thm)],[f455,f464])).
% 1.26/1.47 thf(f464,plain,(
% 1.26/1.47 ($false = (f @ sK6)) | ~spl4_11),
% 1.26/1.47 inference(avatar_component_clause,[status(thm)],[f462])).
% 1.26/1.47 thf(f462,definition,(
% 1.26/1.47 spl4_11 <=> ($false = (f @ sK6))),
% 1.26/1.47 introduced(definition,[new_symbols(naming,[spl4_11])],[avatar_definition])).
% 1.26/1.47 thf(f471,plain,(
% 1.26/1.47 ~spl4_6),
% 1.26/1.47 inference(avatar_contradiction_clause,[status(thm)],[f470])).
% 1.26/1.47 thf(f470,plain,(
% 1.26/1.47 $false | ~spl4_6),
% 1.26/1.47 inference(equality_resolution,[status(thm)],[f359])).
% 1.26/1.47 thf(f359,plain,(
% 1.26/1.47 ( ! [X1 : $i] : ((sK1 != X1)) ) | ~spl4_6),
% 1.26/1.47 inference(avatar_component_clause,[status(thm)],[f358])).
% 1.26/1.47 thf(f358,definition,(
% 1.26/1.47 spl4_6 <=> ! [X1 : $i] : (sK1 != X1)),
% 1.26/1.47 introduced(definition,[new_symbols(naming,[spl4_6])],[avatar_definition])).
% 1.26/1.47 thf(f469,plain,(
% 1.26/1.47 spl4_11 | spl4_12 | spl4_1),
% 1.26/1.47 inference(avatar_split_clause,[status(thm)],[f450,f310,f466,f462])).
% 1.26/1.47 thf(f450,plain,(
% 1.26/1.47 ($false = (f @ sK6)) | (sK6 = $true) | spl4_1),
% 1.26/1.47 inference(not_proxy_clausification,[status(thm)],[f449])).
% 1.26/1.47 thf(f449,plain,(
% 1.26/1.47 ($false = (f @ sK6)) | ((~ sK6) = $false) | spl4_1),
% 1.26/1.47 inference(binary_proxy_clausification,[status(thm)],[f447])).
% 1.26/1.47 thf(f447,plain,(
% 1.26/1.47 ((~ sK6) != (f @ sK6)) | spl4_1),
% 1.26/1.47 inference(negative_extensionality,[status(thm)],[f311])).
% 1.26/1.47 thf(f460,plain,(
% 1.26/1.47 spl4_9 | spl4_10 | spl4_1),
% 1.26/1.47 inference(avatar_split_clause,[status(thm)],[f451,f310,f457,f453])).
% 1.26/1.47 thf(f451,plain,(
% 1.26/1.47 (sK6 = $false) | ((f @ sK6) = $true) | spl4_1),
% 1.26/1.47 inference(not_proxy_clausification,[status(thm)],[f448])).
% 1.26/1.47 thf(f448,plain,(
% 1.26/1.47 ((f @ sK6) = $true) | ((~ sK6) = $true) | spl4_1),
% 1.26/1.47 inference(binary_proxy_clausification,[status(thm)],[f447])).
% 1.26/1.47 thf(f410,plain,(
% 1.26/1.47 spl4_8 | ~spl4_5),
% 1.26/1.47 inference(avatar_split_clause,[status(thm)],[f409,f331,f395])).
% 1.26/1.47 thf(f409,plain,(
% 1.26/1.47 ( ! [X1 : $i] : ((sK0 != X1) | (f != (^[Y0 : $o]: ($false)))) )),
% 1.26/1.47 inference(subsumption_resolution,[status(thm)],[f408,f27])).
% 1.26/1.47 thf(f27,plain,(
% 1.26/1.47 (sK1 != (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0))))))),
% 1.26/1.47 inference(beta_eta_normalization,[status(thm)],[f21])).
% 1.26/1.47 thf(f21,plain,(
% 1.26/1.47 (sK1 != ((^[Y0 : $o > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (eps @ (^[Y5 : $i]: ((((((^[Y6 : $o]: ($false)) = Y0) & (Y1 = Y5)) | ((Y4 = Y5) & (Y0 = (^[Y6 : $o]: ($true))))) | ((Y2 = Y5) & (~ = Y0))) | (((^[Y6 : $o]: (Y6)) = Y0) & (Y3 = Y5)))))))))))))) @ f @ sK0 @ sK1 @ sK3 @ sK2))),
% 1.26/1.47 inference(definition_unfolding,[status(thm)],[f18,f19])).
% 1.26/1.47 thf(f19,plain,(
% 1.26/1.47 (case = (^[Y0 : $o > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (eps @ (^[Y5 : $i]: ((((((^[Y6 : $o]: ($false)) = Y0) & (Y1 = Y5)) | ((Y4 = Y5) & (Y0 = (^[Y6 : $o]: ($true))))) | ((Y2 = Y5) & (~ = Y0))) | (((^[Y6 : $o]: (Y6)) = Y0) & (Y3 = Y5)))))))))))))))),
% 1.26/1.47 inference(cnf_transformation,[status(thm)],[f7])).
% 1.26/1.47 thf(f7,plain,(
% 1.26/1.47 (case = (^[Y0 : $o > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (eps @ (^[Y5 : $i]: ((((((^[Y6 : $o]: ($false)) = Y0) & (Y1 = Y5)) | ((Y4 = Y5) & (Y0 = (^[Y6 : $o]: ($true))))) | ((Y2 = Y5) & (~ = Y0))) | (((^[Y6 : $o]: (Y6)) = Y0) & (Y3 = Y5)))))))))))))))),
% 1.26/1.47 inference(fool_elimination,[status(thm)],[f6])).
% 1.26/1.47 thf(f6,plain,(
% 1.26/1.47 ((^[X0 : $o > $o, X1 : $i, X2 : $i, X3 : $i, X4 : $i] : (eps @ (^[X5 : $i] : (((X3 = X5) & ((^[X6 : $o] : (X6)) = X0)) | ((~ = X0) & (X2 = X5)) | ((X0 = (^[X7 : $o] : ($true))) & (X4 = X5)) | ((X1 = X5) & ((^[X8 : $o] : ($false)) = X0)))))) = case)),
% 1.26/1.47 inference(rectify,[status(thm)],[f2])).
% 1.26/1.47 thf(f2,axiom,(
% 1.26/1.47 ((^[X2 : $o > $o, X1 : $i, X3 : $i, X4 : $i, X5 : $i] : (eps @ (^[X6 : $i] : (((X4 = X6) & ((^[X7 : $o] : (X7)) = X2)) | ((~ = X2) & (X3 = X6)) | ((X2 = (^[X7 : $o] : ($true))) & (X5 = X6)) | ((X1 = X6) & ((^[X7 : $o] : ($false)) = X2)))))) = case)),
% 1.26/1.47 file('/export/starexec/sandbox2/tmp/tmp.UHqTYDh04E/DTF2THF_2605.p',caseood)).
% 1.26/1.47 thf(f18,plain,(
% 1.26/1.47 ((case @ f @ sK0 @ sK1 @ sK3 @ sK2) != sK1)),
% 1.26/1.47 inference(cnf_transformation,[status(thm)],[f14])).
% 1.26/1.47 thf(f14,plain,(
% 1.26/1.47 ((case @ f @ sK0 @ sK1 @ sK3 @ sK2) != sK1) & (sK2 != (case @ f @ sK0 @ sK1 @ sK3 @ sK2)) & ((case @ f @ sK0 @ sK1 @ sK3 @ sK2) != sK3) & ((case @ f @ sK0 @ sK1 @ sK3 @ sK2) != sK0)),
% 1.26/1.47 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f11,f13])).
% 1.26/1.47 thf(f13,plain,(
% 1.26/1.47 ? [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : (((case @ f @ X0 @ X1 @ X3 @ X2) != X1) & ((case @ f @ X0 @ X1 @ X3 @ X2) != X2) & ((case @ f @ X0 @ X1 @ X3 @ X2) != X3) & ((case @ f @ X0 @ X1 @ X3 @ X2) != X0)) => (((case @ f @ sK0 @ sK1 @ sK3 @ sK2) != sK1) & (sK2 != (case @ f @ sK0 @ sK1 @ sK3 @ sK2)) & ((case @ f @ sK0 @ sK1 @ sK3 @ sK2) != sK3) & ((case @ f @ sK0 @ sK1 @ sK3 @ sK2) != sK0))),
% 1.26/1.47 introduced(definition,[],[choice_axiom])).
% 1.26/1.47 thf(f11,plain,(
% 1.26/1.47 ? [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : (((case @ f @ X0 @ X1 @ X3 @ X2) != X1) & ((case @ f @ X0 @ X1 @ X3 @ X2) != X2) & ((case @ f @ X0 @ X1 @ X3 @ X2) != X3) & ((case @ f @ X0 @ X1 @ X3 @ X2) != X0))),
% 1.26/1.47 inference(ennf_transformation,[status(thm)],[f10])).
% 1.26/1.47 thf(f10,plain,(
% 1.26/1.47 ~! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : (((case @ f @ X0 @ X1 @ X3 @ X2) = X1) | ((case @ f @ X0 @ X1 @ X3 @ X2) = X0) | ((case @ f @ X0 @ X1 @ X3 @ X2) = X3) | ((case @ f @ X0 @ X1 @ X3 @ X2) = X2))),
% 1.26/1.47 inference(rectify,[status(thm)],[f4])).
% 1.26/1.47 thf(f4,negated_conjecture,(
% 1.26/1.47 ~! [X1 : $i,X3 : $i,X5 : $i,X4 : $i] : (((case @ f @ X1 @ X3 @ X4 @ X5) = X3) | ((case @ f @ X1 @ X3 @ X4 @ X5) = X1) | ((case @ f @ X1 @ X3 @ X4 @ X5) = X5) | ((case @ f @ X1 @ X3 @ X4 @ X5) = X4))),
% 1.26/1.47 inference(negated_conjecture,[status(cth)],[f3])).
% 1.26/1.47 thf(f3,conjecture,(
% 1.26/1.47 ! [X1 : $i,X3 : $i,X5 : $i,X4 : $i] : (((case @ f @ X1 @ X3 @ X4 @ X5) = X3) | ((case @ f @ X1 @ X3 @ X4 @ X5) = X1) | ((case @ f @ X1 @ X3 @ X4 @ X5) = X5) | ((case @ f @ X1 @ X3 @ X4 @ X5) = X4))),
% 1.26/1.47 file('/export/starexec/sandbox2/tmp/tmp.UHqTYDh04E/DTF2THF_2605.p',conj)).
% 1.26/1.47 thf(f408,plain,(
% 1.26/1.47 ( ! [X1 : $i] : ((f != (^[Y0 : $o]: ($false))) | (sK1 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) | (sK0 != X1)) )),
% 1.26/1.47 inference(subsumption_resolution,[status(thm)],[f407,f26])).
% 1.26/1.47 thf(f26,plain,(
% 1.26/1.47 ((eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0))))) != sK0)),
% 1.26/1.47 inference(beta_eta_normalization,[status(thm)],[f24])).
% 1.26/1.47 thf(f24,plain,(
% 1.26/1.47 (((^[Y0 : $o > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (eps @ (^[Y5 : $i]: ((((((^[Y6 : $o]: ($false)) = Y0) & (Y1 = Y5)) | ((Y4 = Y5) & (Y0 = (^[Y6 : $o]: ($true))))) | ((Y2 = Y5) & (~ = Y0))) | (((^[Y6 : $o]: (Y6)) = Y0) & (Y3 = Y5)))))))))))))) @ f @ sK0 @ sK1 @ sK3 @ sK2) != sK0)),
% 1.26/1.47 inference(definition_unfolding,[status(thm)],[f15,f19])).
% 1.26/1.47 thf(f15,plain,(
% 1.26/1.47 ((case @ f @ sK0 @ sK1 @ sK3 @ sK2) != sK0)),
% 1.26/1.47 inference(cnf_transformation,[status(thm)],[f14])).
% 1.26/1.47 thf(f407,plain,(
% 1.26/1.47 ( ! [X1 : $i] : (((eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0))))) = sK0) | (f != (^[Y0 : $o]: ($false))) | (sK1 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) | (sK0 != X1)) )),
% 1.26/1.47 inference(subsumption_resolution,[status(thm)],[f406,f25])).
% 1.26/1.47 thf(f25,plain,(
% 1.26/1.47 (sK2 != (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0))))))),
% 1.26/1.47 inference(beta_eta_normalization,[status(thm)],[f22])).
% 1.26/1.47 thf(f22,plain,(
% 1.26/1.47 (sK2 != ((^[Y0 : $o > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (eps @ (^[Y5 : $i]: ((((((^[Y6 : $o]: ($false)) = Y0) & (Y1 = Y5)) | ((Y4 = Y5) & (Y0 = (^[Y6 : $o]: ($true))))) | ((Y2 = Y5) & (~ = Y0))) | (((^[Y6 : $o]: (Y6)) = Y0) & (Y3 = Y5)))))))))))))) @ f @ sK0 @ sK1 @ sK3 @ sK2))),
% 1.26/1.47 inference(definition_unfolding,[status(thm)],[f17,f19])).
% 1.26/1.47 thf(f17,plain,(
% 1.26/1.47 (sK2 != (case @ f @ sK0 @ sK1 @ sK3 @ sK2))),
% 1.26/1.47 inference(cnf_transformation,[status(thm)],[f14])).
% 1.26/1.47 thf(f406,plain,(
% 1.26/1.47 ( ! [X1 : $i] : ((sK2 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) | ((eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0))))) = sK0) | (f != (^[Y0 : $o]: ($false))) | (sK1 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) | (sK0 != X1)) )),
% 1.26/1.47 inference(subsumption_resolution,[status(thm)],[f169,f28])).
% 1.26/1.47 thf(f28,plain,(
% 1.26/1.47 (sK3 != (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0))))))),
% 1.26/1.47 inference(beta_eta_normalization,[status(thm)],[f23])).
% 1.26/1.47 thf(f23,plain,(
% 1.26/1.47 (sK3 != ((^[Y0 : $o > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (eps @ (^[Y5 : $i]: ((((((^[Y6 : $o]: ($false)) = Y0) & (Y1 = Y5)) | ((Y4 = Y5) & (Y0 = (^[Y6 : $o]: ($true))))) | ((Y2 = Y5) & (~ = Y0))) | (((^[Y6 : $o]: (Y6)) = Y0) & (Y3 = Y5)))))))))))))) @ f @ sK0 @ sK1 @ sK3 @ sK2))),
% 1.26/1.47 inference(definition_unfolding,[status(thm)],[f16,f19])).
% 1.26/1.47 thf(f16,plain,(
% 1.26/1.47 ((case @ f @ sK0 @ sK1 @ sK3 @ sK2) != sK3)),
% 1.26/1.47 inference(cnf_transformation,[status(thm)],[f14])).
% 1.26/1.47 thf(f169,plain,(
% 1.26/1.47 ( ! [X1 : $i] : ((sK3 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) | (f != (^[Y0 : $o]: ($false))) | ((eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0))))) = sK0) | (sK2 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) | (sK0 != X1) | (sK1 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0))))))) )),
% 1.26/1.47 inference(equality_proxy_clausification,[status(thm)],[f168])).
% 1.26/1.47 thf(f168,plain,(
% 1.26/1.47 ( ! [X1 : $i] : ((f != (^[Y0 : $o]: ($false))) | (sK1 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) | (sK3 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) | ((eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0))))) = sK0) | (sK0 != X1) | ((sK2 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) = $true)) )),
% 1.26/1.47 inference(binary_proxy_clausification,[status(thm)],[f166])).
% 1.26/1.47 thf(f166,plain,(
% 1.26/1.47 ( ! [X1 : $i] : ((sK1 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) | (((sK2 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) & (f = (^[Y0 : $o]: ($true)))) = $true) | (sK0 != X1) | (sK3 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) | (f != (^[Y0 : $o]: ($false))) | ((eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0))))) = sK0)) )),
% 1.26/1.47 inference(equality_proxy_clausification,[status(thm)],[f163])).
% 1.26/1.47 thf(f163,plain,(
% 1.26/1.47 ( ! [X1 : $i] : ((f != (^[Y0 : $o]: ($false))) | (sK0 != X1) | (sK1 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) | (sK3 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) | ($true = (sK0 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0))))))) | (((sK2 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) & (f = (^[Y0 : $o]: ($true)))) = $true)) )),
% 1.26/1.47 inference(binary_proxy_clausification,[status(thm)],[f162])).
% 1.26/1.47 thf(f162,plain,(
% 1.26/1.47 ( ! [X1 : $i] : ((sK3 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) | (sK1 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) | (f != (^[Y0 : $o]: ($false))) | ($true = (((^[Y0 : $o]: ($false)) = f) & (sK0 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))))) | (((sK2 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) & (f = (^[Y0 : $o]: ($true)))) = $true) | (sK0 != X1)) )),
% 1.26/1.47 inference(equality_proxy_clausification,[status(thm)],[f161])).
% 1.26/1.47 thf(f161,plain,(
% 1.26/1.47 ( ! [X1 : $i] : ((sK3 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) | ($false = (sK0 = X1)) | (f != (^[Y0 : $o]: ($false))) | ($true = (((^[Y0 : $o]: ($false)) = f) & (sK0 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))))) | (sK1 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) | (((sK2 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) & (f = (^[Y0 : $o]: ($true)))) = $true)) )),
% 1.26/1.47 inference(equality_proxy_clausification,[status(thm)],[f160])).
% 1.26/1.47 thf(f160,plain,(
% 1.26/1.47 ( ! [X1 : $i] : (($true = (sK1 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0))))))) | ($true = (((^[Y0 : $o]: ($false)) = f) & (sK0 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))))) | (((sK2 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) & (f = (^[Y0 : $o]: ($true)))) = $true) | ($false = (sK0 = X1)) | (f != (^[Y0 : $o]: ($false))) | (sK3 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0))))))) )),
% 1.26/1.47 inference(binary_proxy_clausification,[status(thm)],[f158])).
% 1.26/1.47 thf(f158,plain,(
% 1.26/1.47 ( ! [X1 : $i] : ((((sK1 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) & (~ = f)) = $true) | (f != (^[Y0 : $o]: ($false))) | ($false = (sK0 = X1)) | (sK3 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) | (((sK2 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) & (f = (^[Y0 : $o]: ($true)))) = $true) | ($true = (((^[Y0 : $o]: ($false)) = f) & (sK0 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0))))))))) )),
% 1.26/1.47 inference(equality_proxy_clausification,[status(thm)],[f157])).
% 1.26/1.47 thf(f157,plain,(
% 1.26/1.47 ( ! [X1 : $i] : ((((^[Y0 : $o]: ($false)) = f) = $false) | (sK3 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) | ($true = (((^[Y0 : $o]: ($false)) = f) & (sK0 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))))) | (((sK2 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) & (f = (^[Y0 : $o]: ($true)))) = $true) | ($false = (sK0 = X1)) | (((sK1 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) & (~ = f)) = $true)) )),
% 1.26/1.47 inference(binary_proxy_clausification,[status(thm)],[f156])).
% 1.26/1.47 thf(f156,plain,(
% 1.26/1.47 ( ! [X1 : $i] : (((((^[Y0 : $o]: ($false)) = f) & (sK0 = X1)) = $false) | (((sK1 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) & (~ = f)) = $true) | (((sK2 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) & (f = (^[Y0 : $o]: ($true)))) = $true) | ($true = (((^[Y0 : $o]: ($false)) = f) & (sK0 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))))) | (sK3 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0))))))) )),
% 1.26/1.47 inference(binary_proxy_clausification,[status(thm)],[f155])).
% 1.26/1.47 thf(f155,plain,(
% 1.26/1.47 ( ! [X1 : $i] : ((((((^[Y0 : $o]: ($false)) = f) & (sK0 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0))))))) | ((sK2 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) & (f = (^[Y0 : $o]: ($true))))) = $true) | (((sK1 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) & (~ = f)) = $true) | ((((^[Y0 : $o]: ($false)) = f) & (sK0 = X1)) = $false) | (sK3 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0))))))) )),
% 1.26/1.47 inference(binary_proxy_clausification,[status(thm)],[f153])).
% 1.26/1.47 thf(f153,plain,(
% 1.26/1.47 ( ! [X1 : $i] : ((sK3 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) | ($false = ((((^[Y0 : $o]: ($false)) = f) & (sK0 = X1)) | ((sK2 = X1) & (f = (^[Y0 : $o]: ($true)))))) | (((((^[Y0 : $o]: ($false)) = f) & (sK0 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0))))))) | ((sK2 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) & (f = (^[Y0 : $o]: ($true))))) = $true) | (((sK1 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) & (~ = f)) = $true)) )),
% 1.26/1.47 inference(binary_proxy_clausification,[status(thm)],[f152])).
% 1.26/1.47 thf(f152,plain,(
% 1.26/1.47 ( ! [X1 : $i] : ((sK3 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) | ((((((^[Y0 : $o]: ($false)) = f) & (sK0 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0))))))) | ((sK2 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) & (f = (^[Y0 : $o]: ($true))))) | ((sK1 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) & (~ = f))) = $true) | ($false = ((((^[Y0 : $o]: ($false)) = f) & (sK0 = X1)) | ((sK2 = X1) & (f = (^[Y0 : $o]: ($true))))))) )),
% 1.26/1.47 inference(equality_proxy_clausification,[status(thm)],[f151])).
% 1.26/1.47 thf(f151,plain,(
% 1.26/1.47 ( ! [X1 : $i] : (((sK3 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) = $true) | ((((((^[Y0 : $o]: ($false)) = f) & (sK0 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0))))))) | ((sK2 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) & (f = (^[Y0 : $o]: ($true))))) | ((sK1 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) & (~ = f))) = $true) | ($false = ((((^[Y0 : $o]: ($false)) = f) & (sK0 = X1)) | ((sK2 = X1) & (f = (^[Y0 : $o]: ($true))))))) )),
% 1.26/1.47 inference(binary_proxy_clausification,[status(thm)],[f149])).
% 1.26/1.47 thf(f149,plain,(
% 1.26/1.47 ( ! [X1 : $i] : (((((((^[Y0 : $o]: ($false)) = f) & (sK0 = X1)) | ((sK2 = X1) & (f = (^[Y0 : $o]: ($true))))) | ((sK1 = X1) & (~ = f))) = $false) | ((sK3 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) = $true) | ((((((^[Y0 : $o]: ($false)) = f) & (sK0 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0))))))) | ((sK2 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) & (f = (^[Y0 : $o]: ($true))))) | ((sK1 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) & (~ = f))) = $true)) )),
% 1.26/1.47 inference(binary_proxy_clausification,[status(thm)],[f32])).
% 1.26/1.47 thf(f32,plain,(
% 1.26/1.47 ( ! [X1 : $i] : (($false = ((((((^[Y0 : $o]: ($false)) = f) & (sK0 = X1)) | ((sK2 = X1) & (f = (^[Y0 : $o]: ($true))))) | ((sK1 = X1) & (~ = f))) | (((^[Y0 : $o]: (Y0)) = f) & (sK3 = X1)))) | ((((((^[Y0 : $o]: ($false)) = f) & (sK0 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0))))))) | ((sK2 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) & (f = (^[Y0 : $o]: ($true))))) | ((sK1 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) & (~ = f))) = $true) | ((sK3 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) = $true)) )),
% 1.26/1.47 inference(binary_proxy_clausification,[status(thm)],[f31])).
% 1.26/1.47 thf(f31,plain,(
% 1.26/1.47 ( ! [X1 : $i] : (((((^[Y0 : $o]: (Y0)) = f) & (sK3 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0))))))) = $true) | ($false = ((((((^[Y0 : $o]: ($false)) = f) & (sK0 = X1)) | ((sK2 = X1) & (f = (^[Y0 : $o]: ($true))))) | ((sK1 = X1) & (~ = f))) | (((^[Y0 : $o]: (Y0)) = f) & (sK3 = X1)))) | ((((((^[Y0 : $o]: ($false)) = f) & (sK0 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0))))))) | ((sK2 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) & (f = (^[Y0 : $o]: ($true))))) | ((sK1 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) & (~ = f))) = $true)) )),
% 1.26/1.47 inference(binary_proxy_clausification,[status(thm)],[f30])).
% 1.26/1.47 thf(f30,plain,(
% 1.26/1.47 ( ! [X1 : $i] : ((((((((^[Y0 : $o]: ($false)) = f) & (sK0 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0))))))) | ((sK2 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) & (f = (^[Y0 : $o]: ($true))))) | ((sK1 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) & (~ = f))) | (((^[Y0 : $o]: (Y0)) = f) & (sK3 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))))) = $true) | ($false = ((((((^[Y0 : $o]: ($false)) = f) & (sK0 = X1)) | ((sK2 = X1) & (f = (^[Y0 : $o]: ($true))))) | ((sK1 = X1) & (~ = f))) | (((^[Y0 : $o]: (Y0)) = f) & (sK3 = X1))))) )),
% 1.26/1.47 inference(beta_eta_normalization,[status(thm)],[f29])).
% 1.26/1.47 thf(f29,plain,(
% 1.26/1.47 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))) @ (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0))))))) | (((^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))) @ X1) = $false)) )),
% 1.26/1.47 introduced(definition,[],[choice_axiom])).
% 1.26/1.47 thf(f391,plain,(
% 1.26/1.47 spl4_7 | ~spl4_3 | spl4_5),
% 1.26/1.47 inference(avatar_split_clause,[status(thm)],[f390,f331,f317,f377])).
% 1.26/1.47 thf(f390,plain,(
% 1.26/1.47 ( ! [X1 : $i] : ((sK2 != X1) | (f != (^[Y0 : $o]: ($true))) | (f = (^[Y0 : $o]: ($false)))) )),
% 1.26/1.47 inference(subsumption_resolution,[status(thm)],[f389,f28])).
% 1.26/1.47 thf(f389,plain,(
% 1.26/1.47 ( ! [X1 : $i] : ((sK3 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) | (sK2 != X1) | (f = (^[Y0 : $o]: ($false))) | (f != (^[Y0 : $o]: ($true)))) )),
% 1.26/1.47 inference(subsumption_resolution,[status(thm)],[f388,f27])).
% 1.26/1.47 thf(f388,plain,(
% 1.26/1.47 ( ! [X1 : $i] : ((sK2 != X1) | (f != (^[Y0 : $o]: ($true))) | (sK1 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) | (sK3 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) | (f = (^[Y0 : $o]: ($false)))) )),
% 1.26/1.47 inference(subsumption_resolution,[status(thm)],[f198,f25])).
% 1.26/1.47 thf(f198,plain,(
% 1.26/1.47 ( ! [X1 : $i] : ((f != (^[Y0 : $o]: ($true))) | (f = (^[Y0 : $o]: ($false))) | (sK2 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) | (sK3 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) | (sK1 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) | (sK2 != X1)) )),
% 1.26/1.47 inference(equality_proxy_clausification,[status(thm)],[f197])).
% 1.26/1.47 thf(f197,plain,(
% 1.26/1.47 ( ! [X1 : $i] : ((sK3 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) | (f = (^[Y0 : $o]: ($false))) | ((sK2 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) = $true) | (sK1 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) | (sK2 != X1) | (f != (^[Y0 : $o]: ($true)))) )),
% 1.26/1.47 inference(binary_proxy_clausification,[status(thm)],[f195])).
% 1.26/1.47 thf(f195,plain,(
% 1.26/1.47 ( ! [X1 : $i] : ((sK2 != X1) | (sK1 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) | (f != (^[Y0 : $o]: ($true))) | (f = (^[Y0 : $o]: ($false))) | (((sK2 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) & (f = (^[Y0 : $o]: ($true)))) = $true) | (sK3 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0))))))) )),
% 1.26/1.47 inference(equality_proxy_clausification,[status(thm)],[f194])).
% 1.26/1.47 thf(f194,plain,(
% 1.26/1.47 ( ! [X1 : $i] : ((((^[Y0 : $o]: ($false)) = f) = $true) | (sK2 != X1) | (((sK2 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) & (f = (^[Y0 : $o]: ($true)))) = $true) | (f != (^[Y0 : $o]: ($true))) | (sK1 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) | (sK3 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0))))))) )),
% 1.26/1.47 inference(binary_proxy_clausification,[status(thm)],[f192])).
% 1.26/1.47 thf(f192,plain,(
% 1.26/1.47 ( ! [X1 : $i] : (($true = (((^[Y0 : $o]: ($false)) = f) & (sK0 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))))) | (f != (^[Y0 : $o]: ($true))) | (sK1 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) | (((sK2 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) & (f = (^[Y0 : $o]: ($true)))) = $true) | (sK2 != X1) | (sK3 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0))))))) )),
% 1.26/1.47 inference(binary_proxy_clausification,[status(thm)],[f191])).
% 1.26/1.47 thf(f191,plain,(
% 1.26/1.47 ( ! [X1 : $i] : ((sK1 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) | (f != (^[Y0 : $o]: ($true))) | (((((^[Y0 : $o]: ($false)) = f) & (sK0 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0))))))) | ((sK2 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) & (f = (^[Y0 : $o]: ($true))))) = $true) | (sK2 != X1) | (sK3 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0))))))) )),
% 1.26/1.47 inference(equality_proxy_clausification,[status(thm)],[f190])).
% 1.26/1.47 thf(f190,plain,(
% 1.26/1.47 ( ! [X1 : $i] : (($false = (f = (^[Y0 : $o]: ($true)))) | (sK2 != X1) | (sK1 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) | (((((^[Y0 : $o]: ($false)) = f) & (sK0 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0))))))) | ((sK2 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) & (f = (^[Y0 : $o]: ($true))))) = $true) | (sK3 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0))))))) )),
% 1.26/1.47 inference(equality_proxy_clausification,[status(thm)],[f189])).
% 1.26/1.47 thf(f189,plain,(
% 1.26/1.47 ( ! [X1 : $i] : (($true = (sK1 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0))))))) | (sK3 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) | ($false = (f = (^[Y0 : $o]: ($true)))) | (((((^[Y0 : $o]: ($false)) = f) & (sK0 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0))))))) | ((sK2 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) & (f = (^[Y0 : $o]: ($true))))) = $true) | (sK2 != X1)) )),
% 1.26/1.47 inference(equality_proxy_clausification,[status(thm)],[f188])).
% 1.26/1.47 thf(f188,plain,(
% 1.26/1.47 ( ! [X1 : $i] : ((sK3 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) | ($false = (sK2 = X1)) | (((((^[Y0 : $o]: ($false)) = f) & (sK0 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0))))))) | ((sK2 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) & (f = (^[Y0 : $o]: ($true))))) = $true) | ($false = (f = (^[Y0 : $o]: ($true)))) | ($true = (sK1 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))))) )),
% 1.26/1.47 inference(binary_proxy_clausification,[status(thm)],[f187])).
% 1.26/1.47 thf(f187,plain,(
% 1.26/1.47 ( ! [X1 : $i] : ((((sK2 = X1) & (f = (^[Y0 : $o]: ($true)))) = $false) | (sK3 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) | ($true = (sK1 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0))))))) | (((((^[Y0 : $o]: ($false)) = f) & (sK0 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0))))))) | ((sK2 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) & (f = (^[Y0 : $o]: ($true))))) = $true)) )),
% 1.26/1.47 inference(binary_proxy_clausification,[status(thm)],[f154])).
% 1.26/1.47 thf(f154,plain,(
% 1.26/1.47 ( ! [X1 : $i] : ((((sK1 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) & (~ = f)) = $true) | (((sK2 = X1) & (f = (^[Y0 : $o]: ($true)))) = $false) | (((((^[Y0 : $o]: ($false)) = f) & (sK0 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0))))))) | ((sK2 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) & (f = (^[Y0 : $o]: ($true))))) = $true) | (sK3 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0))))))) )),
% 1.26/1.47 inference(binary_proxy_clausification,[status(thm)],[f153])).
% 1.26/1.47 thf(f372,plain,(
% 1.26/1.47 ~spl4_1 | spl4_5 | spl4_6),
% 1.26/1.47 inference(avatar_split_clause,[status(thm)],[f371,f358,f331,f310])).
% 1.26/1.47 thf(f371,plain,(
% 1.26/1.47 ( ! [X1 : $i] : ((sK1 != X1) | (~ != f) | (f = (^[Y0 : $o]: ($false)))) )),
% 1.26/1.47 inference(subsumption_resolution,[status(thm)],[f370,f25])).
% 1.26/1.47 thf(f370,plain,(
% 1.26/1.47 ( ! [X1 : $i] : ((sK1 != X1) | (~ != f) | (f = (^[Y0 : $o]: ($false))) | (sK2 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0))))))) )),
% 1.26/1.47 inference(subsumption_resolution,[status(thm)],[f369,f28])).
% 1.26/1.47 thf(f369,plain,(
% 1.26/1.47 ( ! [X1 : $i] : ((sK3 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) | (sK1 != X1) | (sK2 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) | (f = (^[Y0 : $o]: ($false))) | (~ != f)) )),
% 1.26/1.47 inference(subsumption_resolution,[status(thm)],[f243,f27])).
% 1.26/1.47 thf(f243,plain,(
% 1.26/1.47 ( ! [X1 : $i] : ((~ != f) | (f = (^[Y0 : $o]: ($false))) | (sK1 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) | (sK1 != X1) | (sK3 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) | (sK2 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0))))))) )),
% 1.26/1.47 inference(equality_proxy_clausification,[status(thm)],[f242])).
% 1.26/1.47 thf(f242,plain,(
% 1.26/1.47 ( ! [X1 : $i] : ((f = (^[Y0 : $o]: ($false))) | (sK1 != X1) | ((sK2 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) = $true) | (sK1 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) | (~ != f) | (sK3 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0))))))) )),
% 1.26/1.47 inference(equality_proxy_clausification,[status(thm)],[f241])).
% 1.26/1.47 thf(f241,plain,(
% 1.26/1.47 ( ! [X1 : $i] : ((sK1 != X1) | (sK3 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) | (sK1 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) | (((^[Y0 : $o]: ($false)) = f) = $true) | ((sK2 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) = $true) | (~ != f)) )),
% 1.26/1.47 inference(binary_proxy_clausification,[status(thm)],[f239])).
% 1.26/1.47 thf(f239,plain,(
% 1.26/1.47 ( ! [X1 : $i] : ((sK1 != X1) | ($true = (((^[Y0 : $o]: ($false)) = f) & (sK0 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))))) | ((sK2 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) = $true) | (sK1 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) | (sK3 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) | (~ != f)) )),
% 1.26/1.47 inference(equality_proxy_clausification,[status(thm)],[f238])).
% 1.26/1.47 thf(f238,plain,(
% 1.26/1.47 ( ! [X1 : $i] : ((~ != f) | ($true = (sK1 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0))))))) | ((sK2 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) = $true) | (sK1 != X1) | ($true = (((^[Y0 : $o]: ($false)) = f) & (sK0 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))))) | (sK3 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0))))))) )),
% 1.26/1.47 inference(binary_proxy_clausification,[status(thm)],[f236])).
% 1.26/1.47 thf(f236,plain,(
% 1.26/1.47 ( ! [X1 : $i] : ((~ != f) | (sK3 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) | (((sK2 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) & (f = (^[Y0 : $o]: ($true)))) = $true) | (sK1 != X1) | ($true = (sK1 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0))))))) | ($true = (((^[Y0 : $o]: ($false)) = f) & (sK0 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0))))))))) )),
% 1.26/1.47 inference(binary_proxy_clausification,[status(thm)],[f235])).
% 1.26/1.47 thf(f235,plain,(
% 1.26/1.47 ( ! [X1 : $i] : ((sK3 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) | (((((^[Y0 : $o]: ($false)) = f) & (sK0 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0))))))) | ((sK2 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) & (f = (^[Y0 : $o]: ($true))))) = $true) | ($true = (sK1 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0))))))) | (sK1 != X1) | (~ != f)) )),
% 1.26/1.47 inference(equality_proxy_clausification,[status(thm)],[f234])).
% 1.26/1.47 thf(f234,plain,(
% 1.26/1.47 ( ! [X1 : $i] : (($false = (sK1 = X1)) | (((((^[Y0 : $o]: ($false)) = f) & (sK0 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0))))))) | ((sK2 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) & (f = (^[Y0 : $o]: ($true))))) = $true) | (~ != f) | (sK3 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) | ($true = (sK1 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))))) )),
% 1.26/1.47 inference(equality_proxy_clausification,[status(thm)],[f233])).
% 1.26/1.47 thf(f233,plain,(
% 1.26/1.47 ( ! [X1 : $i] : (((~ = f) = $false) | ($false = (sK1 = X1)) | (sK3 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) | (((((^[Y0 : $o]: ($false)) = f) & (sK0 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0))))))) | ((sK2 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) & (f = (^[Y0 : $o]: ($true))))) = $true) | ($true = (sK1 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))))) )),
% 1.26/1.47 inference(binary_proxy_clausification,[status(thm)],[f232])).
% 1.26/1.47 thf(f232,plain,(
% 1.26/1.47 ( ! [X1 : $i] : (($false = ((sK1 = X1) & (~ = f))) | ($true = (sK1 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0))))))) | (sK3 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) | (((((^[Y0 : $o]: ($false)) = f) & (sK0 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0))))))) | ((sK2 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) & (f = (^[Y0 : $o]: ($true))))) = $true)) )),
% 1.26/1.47 inference(binary_proxy_clausification,[status(thm)],[f230])).
% 1.26/1.47 thf(f230,plain,(
% 1.26/1.47 ( ! [X1 : $i] : ((((sK1 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) & (~ = f)) = $true) | (sK3 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) | ($false = ((sK1 = X1) & (~ = f))) | (((((^[Y0 : $o]: ($false)) = f) & (sK0 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0))))))) | ((sK2 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) & (f = (^[Y0 : $o]: ($true))))) = $true)) )),
% 1.26/1.47 inference(binary_proxy_clausification,[status(thm)],[f229])).
% 1.26/1.47 thf(f229,plain,(
% 1.26/1.47 ( ! [X1 : $i] : ((sK3 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) | ((((((^[Y0 : $o]: ($false)) = f) & (sK0 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0))))))) | ((sK2 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) & (f = (^[Y0 : $o]: ($true))))) | ((sK1 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) & (~ = f))) = $true) | ($false = ((sK1 = X1) & (~ = f)))) )),
% 1.26/1.47 inference(equality_proxy_clausification,[status(thm)],[f150])).
% 1.26/1.47 thf(f150,plain,(
% 1.26/1.47 ( ! [X1 : $i] : (((sK3 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) = $true) | ($false = ((sK1 = X1) & (~ = f))) | ((((((^[Y0 : $o]: ($false)) = f) & (sK0 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0))))))) | ((sK2 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) & (f = (^[Y0 : $o]: ($true))))) | ((sK1 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) & (~ = f))) = $true)) )),
% 1.26/1.47 inference(binary_proxy_clausification,[status(thm)],[f149])).
% 1.26/1.47 thf(f353,plain,(
% 1.26/1.47 ~spl4_4 | spl4_2 | spl4_5),
% 1.26/1.47 inference(avatar_split_clause,[status(thm)],[f352,f331,f314,f321])).
% 1.26/1.47 thf(f352,plain,(
% 1.26/1.47 ( ! [X1 : $i] : ((sK3 != X1) | (f != (^[Y0 : $o]: (Y0))) | (f = (^[Y0 : $o]: ($false)))) )),
% 1.26/1.47 inference(subsumption_resolution,[status(thm)],[f351,f27])).
% 1.26/1.47 thf(f351,plain,(
% 1.26/1.47 ( ! [X1 : $i] : ((f = (^[Y0 : $o]: ($false))) | (sK1 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) | (sK3 != X1) | (f != (^[Y0 : $o]: (Y0)))) )),
% 1.26/1.47 inference(subsumption_resolution,[status(thm)],[f350,f28])).
% 1.26/1.47 thf(f350,plain,(
% 1.26/1.47 ( ! [X1 : $i] : ((f = (^[Y0 : $o]: ($false))) | (sK3 != X1) | (f != (^[Y0 : $o]: (Y0))) | (sK3 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) | (sK1 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0))))))) )),
% 1.26/1.47 inference(subsumption_resolution,[status(thm)],[f285,f25])).
% 1.26/1.47 thf(f285,plain,(
% 1.26/1.47 ( ! [X1 : $i] : ((sK2 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) | (f != (^[Y0 : $o]: (Y0))) | (sK3 != X1) | (sK1 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) | (sK3 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) | (f = (^[Y0 : $o]: ($false)))) )),
% 1.26/1.47 inference(equality_proxy_clausification,[status(thm)],[f284])).
% 1.26/1.47 thf(f284,plain,(
% 1.26/1.47 ( ! [X1 : $i] : ((sK1 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) | (sK3 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) | (sK2 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) | (f != (^[Y0 : $o]: (Y0))) | (((^[Y0 : $o]: ($false)) = f) = $true) | (sK3 != X1)) )),
% 1.26/1.47 inference(binary_proxy_clausification,[status(thm)],[f282])).
% 1.26/1.47 thf(f282,plain,(
% 1.26/1.47 ( ! [X1 : $i] : (($true = (((^[Y0 : $o]: ($false)) = f) & (sK0 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))))) | (sK2 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) | (sK1 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) | (sK3 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) | (f != (^[Y0 : $o]: (Y0))) | (sK3 != X1)) )),
% 1.26/1.47 inference(equality_proxy_clausification,[status(thm)],[f281])).
% 1.26/1.47 thf(f281,plain,(
% 1.26/1.47 ( ! [X1 : $i] : ((sK3 != X1) | (sK3 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) | ((sK2 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) = $true) | ($true = (((^[Y0 : $o]: ($false)) = f) & (sK0 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))))) | (sK1 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) | (f != (^[Y0 : $o]: (Y0)))) )),
% 1.26/1.47 inference(binary_proxy_clausification,[status(thm)],[f279])).
% 1.26/1.47 thf(f279,plain,(
% 1.26/1.47 ( ! [X1 : $i] : ((sK1 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) | (sK3 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) | (((sK2 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) & (f = (^[Y0 : $o]: ($true)))) = $true) | ($true = (((^[Y0 : $o]: ($false)) = f) & (sK0 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))))) | (sK3 != X1) | (f != (^[Y0 : $o]: (Y0)))) )),
% 1.26/1.47 inference(binary_proxy_clausification,[status(thm)],[f278])).
% 1.26/1.47 thf(f278,plain,(
% 1.26/1.47 ( ! [X1 : $i] : ((f != (^[Y0 : $o]: (Y0))) | (((((^[Y0 : $o]: ($false)) = f) & (sK0 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0))))))) | ((sK2 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) & (f = (^[Y0 : $o]: ($true))))) = $true) | (sK1 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) | (sK3 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) | (sK3 != X1)) )),
% 1.26/1.47 inference(equality_proxy_clausification,[status(thm)],[f277])).
% 1.26/1.47 thf(f277,plain,(
% 1.26/1.47 ( ! [X1 : $i] : ((sK3 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) | (sK3 != X1) | ($true = (sK1 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0))))))) | (((((^[Y0 : $o]: ($false)) = f) & (sK0 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0))))))) | ((sK2 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) & (f = (^[Y0 : $o]: ($true))))) = $true) | (f != (^[Y0 : $o]: (Y0)))) )),
% 1.26/1.47 inference(binary_proxy_clausification,[status(thm)],[f275])).
% 1.26/1.47 thf(f275,plain,(
% 1.26/1.47 ( ! [X1 : $i] : ((((sK1 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) & (~ = f)) = $true) | (sK3 != X1) | (((((^[Y0 : $o]: ($false)) = f) & (sK0 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0))))))) | ((sK2 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) & (f = (^[Y0 : $o]: ($true))))) = $true) | (f != (^[Y0 : $o]: (Y0))) | (sK3 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0))))))) )),
% 1.26/1.47 inference(equality_proxy_clausification,[status(thm)],[f274])).
% 1.26/1.47 thf(f274,plain,(
% 1.26/1.47 ( ! [X1 : $i] : (($false = (sK3 = X1)) | (sK3 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) | (((((^[Y0 : $o]: ($false)) = f) & (sK0 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0))))))) | ((sK2 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) & (f = (^[Y0 : $o]: ($true))))) = $true) | (((sK1 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) & (~ = f)) = $true) | (f != (^[Y0 : $o]: (Y0)))) )),
% 1.26/1.47 inference(binary_proxy_clausification,[status(thm)],[f273])).
% 1.26/1.47 thf(f273,plain,(
% 1.26/1.47 ( ! [X1 : $i] : ((sK3 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) | ((((((^[Y0 : $o]: ($false)) = f) & (sK0 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0))))))) | ((sK2 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) & (f = (^[Y0 : $o]: ($true))))) | ((sK1 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) & (~ = f))) = $true) | ($false = (sK3 = X1)) | (f != (^[Y0 : $o]: (Y0)))) )),
% 1.26/1.47 inference(equality_proxy_clausification,[status(thm)],[f272])).
% 1.26/1.47 thf(f272,plain,(
% 1.26/1.47 ( ! [X1 : $i] : ((((^[Y0 : $o]: (Y0)) = f) = $false) | (sK3 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) | ($false = (sK3 = X1)) | ((((((^[Y0 : $o]: ($false)) = f) & (sK0 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0))))))) | ((sK2 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) & (f = (^[Y0 : $o]: ($true))))) | ((sK1 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) & (~ = f))) = $true)) )),
% 1.26/1.47 inference(binary_proxy_clausification,[status(thm)],[f271])).
% 1.26/1.47 thf(f271,plain,(
% 1.26/1.47 ( ! [X1 : $i] : ((sK3 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) | ((((^[Y0 : $o]: (Y0)) = f) & (sK3 = X1)) = $false) | ((((((^[Y0 : $o]: ($false)) = f) & (sK0 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0))))))) | ((sK2 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) & (f = (^[Y0 : $o]: ($true))))) | ((sK1 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) & (~ = f))) = $true)) )),
% 1.26/1.47 inference(equality_proxy_clausification,[status(thm)],[f148])).
% 1.26/1.47 thf(f148,plain,(
% 1.26/1.47 ( ! [X1 : $i] : (((sK3 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) = $true) | ((((^[Y0 : $o]: (Y0)) = f) & (sK3 = X1)) = $false) | ((((((^[Y0 : $o]: ($false)) = f) & (sK0 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0))))))) | ((sK2 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) & (f = (^[Y0 : $o]: ($true))))) | ((sK1 = (eps @ (^[Y0 : $i]: ((((((^[Y1 : $o]: ($false)) = f) & (sK0 = Y0)) | ((sK2 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((sK1 = Y0) & (~ = f))) | (((^[Y1 : $o]: (Y1)) = f) & (sK3 = Y0)))))) & (~ = f))) = $true)) )),
% 1.26/1.47 inference(binary_proxy_clausification,[status(thm)],[f32])).
% 1.26/1.47 % SZS output end Proof for DTF2THF_2605
% 1.26/1.47 % (2786)------------------------------
% 1.26/1.47 % (2786)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.26/1.47 % (2786)Termination reason: Refutation
% 1.26/1.47
% 1.26/1.47 % (2786)Memory used [KB]: 5884
% 1.26/1.47 % (2786)Time elapsed: 0.041 s
% 1.26/1.47 % (2786)Instructions burned: 114 (million)
% 1.26/1.47 % (2786)------------------------------
% 1.26/1.47 % (2786)------------------------------
% 1.26/1.47 % (2705)Success in time 0.434 s
%------------------------------------------------------------------------------