%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO546^1 : 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 : n010.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 1.63s 1.40s
% Output : Refutation 1.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO546^1 : TPTP v9.2.1. Released v5.2.0.
% 0.13/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.33 % Computer : n010.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.33 % DateTime : Tue Feb 24 14:33:18 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.20/0.46 ---- Original DTF file ---
% 0.20/0.46 thf(spec,logic,$$dhol).
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 % File : SYO546^1 : TPTP v9.2.1. Released v5.2.0.
% 0.20/0.46 % Domain : Syntactic
% 0.20/0.46 % Problem : Property of case from ($o>$o) to $i defined from choice on $i
% 0.20/0.46 % Version : Especial.
% 0.20/0.46 % English : A choice operator on $i is used to define an if-then-else operator
% 0.20/0.46 % at $i. Check that case always returns one of the four given
% 0.20/0.46 % results.
% 0.20/0.46
% 0.20/0.46 % Refs : [Bro11] Brown E. (2011), Email to Geoff Sutcliffe
% 0.20/0.46 % Source : [Bro11]
% 0.20/0.46 % Names : CHOICE22c [Bro11]
% 0.20/0.46
% 0.20/0.46 % Status : Theorem
% 0.20/0.46 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.30 v8.2.0, 0.54 v8.1.0, 0.55 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
% 0.20/0.46 % Syntax : Number of formulae : 6 ( 2 unt; 3 typ; 1 def)
% 0.20/0.46 % Number of atoms : 14 ( 10 equ; 1 cnn)
% 0.20/0.46 % Maximal formula atoms : 1 ( 4 avg)
% 0.20/0.46 % Number of connectives : 18 ( 1 ~; 3 |; 4 &; 9 @)
% 0.20/0.46 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.20/0.46 % Maximal formula depth : 5 ( 3 avg)
% 0.20/0.46 % Number of types : 2 ( 0 usr)
% 0.20/0.46 % Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% 0.20/0.46 % Number of symbols : 7 ( 3 usr; 3 con; 0-5 aty)
% 0.20/0.46 % Number of variables : 12 ( 9 ^; 2 !; 1 ?; 12 :)
% 0.20/0.46 % SPC : TH0_THM_EQU_NAR
% 0.20/0.46
% 0.20/0.46 % Comments :
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 thf(eps,type,
% 0.20/0.46 eps: ( $i > $o ) > $i ).
% 0.20/0.46
% 0.20/0.46 thf(choiceax,axiom,
% 0.20/0.46 ! [P: $i > $o] :
% 0.20/0.46 ( ? [X: $i] : ( P @ X )
% 0.20/0.46 => ( P @ ( eps @ P ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(caseoo,type,
% 0.20/0.46 case: ( $o > $o ) > $i > $i > $i > $i > $i ).
% 0.20/0.46
% 0.20/0.46 thf(caseood,definition,
% 0.20/0.46 ( case
% 0.20/0.46 = ( ^ [B: $o > $o,X: $i,Y: $i,U: $i,V: $i] :
% 0.20/0.46 ( eps
% 0.20/0.46 @ ^ [Z: $i] :
% 0.20/0.46 ( ( ( B
% 0.20/0.46 = ( ^ [A: $o] : $false ) )
% 0.20/0.46 & ( Z = X ) )
% 0.20/0.46 | ( ( B = (~) )
% 0.20/0.46 & ( Z = Y ) )
% 0.20/0.46 | ( ( B
% 0.20/0.46 = ( ^ [A: $o] : A ) )
% 0.20/0.46 & ( Z = U ) )
% 0.20/0.46 | ( ( B
% 0.20/0.46 = ( ^ [A: $o] : $true ) )
% 0.20/0.46 & ( Z = V ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(f,type,
% 0.20/0.46 f: $o > $o ).
% 0.20/0.46
% 0.20/0.46 thf(conj,conjecture,
% 0.20/0.46 ! [X: $i] :
% 0.20/0.46 ( ( case @ f @ X @ X @ X @ X )
% 0.20/0.46 = X ) ).
% 0.20/0.46
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 ------------------------
% 1.49/1.25 ---- Embedded in THF ---
% 1.49/1.26 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.49/1.26 %%% Generated on Tue Feb 24 14:33:19 EST 2026
% 1.49/1.26 %%% using '$$dhol' embedding, version 1.3.0.
% 1.49/1.26 %%% Logic specification used:
% 1.49/1.26 %%% thf(spec, logic, $$dhol).
% 1.49/1.26
% 1.49/1.26 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.ogKD8WwFWg/DTF2DTF18640.p
% 1.49/1.26 thf(eps, type, eps: (($i > $o) > $i)).
% 1.49/1.26 thf(choiceax, axiom, (! [P:($i > $o)]: (((? [X:$i]: ((P @ X))) => (P @ (eps @ P)))))).
% 1.49/1.26 thf(caseoo, type, case: (($o > $o) > ($i > ($i > ($i > ($i > $i)))))).
% 1.49/1.26 thf(caseood, definition, (case = (^ [B:($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]: ($true))) & (Z = V)))))))))))).
% 1.49/1.26 thf(f, type, f: ($o > $o)).
% 1.49/1.26 thf(conj, conjecture, (! [X:$i]: (((((((case @ f) @ X) @ X) @ X) @ X) = X)))).
% 1.49/1.26 % SZS output end ListOfTHF for /export/starexec/sandbox2/tmp/tmp.ogKD8WwFWg/DTF2DTF18640.p
% 1.49/1.26 ------------------------
% 1.49/1.27 ---- Cleaned THF ---
% 1.49/1.27 thf(eps,type,
% 1.49/1.27 eps: ( $i > $o ) > $i ).
% 1.49/1.27
% 1.49/1.27 thf(choiceax,axiom,
% 1.49/1.27 ! [P: $i > $o] :
% 1.49/1.27 ( ? [X: $i] : ( P @ X )
% 1.49/1.27 => ( P @ ( eps @ P ) ) ) ).
% 1.49/1.27
% 1.49/1.27 thf(caseoo,type,
% 1.49/1.27 case: ( $o > $o ) > $i > $i > $i > $i > $i ).
% 1.49/1.27
% 1.49/1.27 thf(caseood,definition,
% 1.49/1.27 ( case
% 1.49/1.27 = ( ^ [B: $o > $o,X: $i,Y: $i,U: $i,V: $i] :
% 1.49/1.27 ( eps
% 1.49/1.27 @ ^ [Z: $i] :
% 1.49/1.27 ( ( ( B
% 1.49/1.27 = ( ^ [A: $o] : $false ) )
% 1.49/1.27 & ( Z = X ) )
% 1.49/1.27 | ( ( B = (~) )
% 1.49/1.27 & ( Z = Y ) )
% 1.49/1.27 | ( ( B
% 1.49/1.27 = ( ^ [A: $o] : A ) )
% 1.49/1.27 & ( Z = U ) )
% 1.49/1.27 | ( ( B
% 1.49/1.27 = ( ^ [A: $o] : $true ) )
% 1.49/1.27 & ( Z = V ) ) ) ) ) ) ).
% 1.49/1.27
% 1.49/1.27 thf(f,type,
% 1.49/1.27 f: $o > $o ).
% 1.49/1.27
% 1.49/1.27 thf(conj,conjecture,
% 1.49/1.27 ! [X: $i] :
% 1.49/1.27 ( ( case @ f @ X @ X @ X @ X )
% 1.49/1.27 = X ) ).
% 1.49/1.27 ------------------------
% 1.49/1.28 % (18803)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_18640 for (2999ds/183Mi)
% 1.49/1.28 % (18809)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_18640 for (2999ds/18Mi)
% 1.49/1.28 % (18806)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_18640 for (2999ds/2Mi)
% 1.49/1.28 % (18806)Instruction limit reached!
% 1.49/1.28 % (18806)------------------------------
% 1.49/1.28 % (18806)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.28 % (18806)Termination reason: Unknown
% 1.49/1.28 % (18806)Termination phase: Saturation
% 1.49/1.28
% 1.49/1.28 % (18806)Memory used [KB]: 5500
% 1.49/1.28 % (18806)Time elapsed: 0.002 s
% 1.49/1.28 % (18806)Instructions burned: 3 (million)
% 1.49/1.28 % (18806)------------------------------
% 1.49/1.28 % (18806)------------------------------
% 1.49/1.29 % (18809)Instruction limit reached!
% 1.49/1.29 % (18809)------------------------------
% 1.49/1.29 % (18809)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.29 % (18809)Termination reason: Unknown
% 1.49/1.29 % (18809)Termination phase: Saturation
% 1.49/1.29
% 1.49/1.29 % (18809)Memory used [KB]: 5628
% 1.49/1.29 % (18809)Time elapsed: 0.007 s
% 1.49/1.29 % (18809)Instructions burned: 18 (million)
% 1.49/1.29 % (18809)------------------------------
% 1.49/1.29 % (18809)------------------------------
% 1.49/1.29 % (18804)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_18640 for (2999ds/4Mi)
% 1.49/1.29 % (18805)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_18640 for (2999ds/27Mi)
% 1.49/1.29 % (18807)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_18640 for (2999ds/2Mi)
% 1.49/1.29 % (18808)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_18640 for (2999ds/275Mi)
% 1.49/1.29 % (18807)Instruction limit reached!
% 1.49/1.29 % (18807)------------------------------
% 1.49/1.29 % (18807)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.29 % (18807)Termination reason: Unknown
% 1.49/1.29 % (18807)Termination phase: Clausification
% 1.49/1.29
% 1.49/1.29 % (18807)Memory used [KB]: 895
% 1.49/1.29 % (18807)Time elapsed: 0.003 s
% 1.49/1.29 % (18807)Instructions burned: 2 (million)
% 1.49/1.29 % (18807)------------------------------
% 1.49/1.29 % (18807)------------------------------
% 1.49/1.29 % (18808)Refutation not found, incomplete strategy
% 1.49/1.29 % (18808)------------------------------
% 1.49/1.29 % (18808)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.29 % (18808)Termination reason: Refutation not found, incomplete strategy
% 1.49/1.29
% 1.49/1.29
% 1.49/1.29 % (18808)Memory used [KB]: 5500
% 1.49/1.29 % (18808)Time elapsed: 0.003 s
% 1.49/1.29 % (18808)Instructions burned: 2 (million)
% 1.49/1.29 % (18808)------------------------------
% 1.49/1.29 % (18808)------------------------------
% 1.49/1.29 % (18804)Instruction limit reached!
% 1.49/1.29 % (18804)------------------------------
% 1.49/1.29 % (18804)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.29 % (18804)Termination reason: Unknown
% 1.49/1.29 % (18804)Termination phase: Saturation
% 1.49/1.29
% 1.49/1.29 % (18804)Memory used [KB]: 5500
% 1.49/1.29 % (18804)Time elapsed: 0.005 s
% 1.49/1.29 % (18804)Instructions burned: 5 (million)
% 1.49/1.29 % (18804)------------------------------
% 1.49/1.29 % (18804)------------------------------
% 1.49/1.29 % (18810)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_18640 for (2999ds/3Mi)
% 1.49/1.29 % (18810)Instruction limit reached!
% 1.49/1.29 % (18810)------------------------------
% 1.49/1.29 % (18810)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.29 % (18810)Termination reason: Unknown
% 1.49/1.29 % (18810)Termination phase: Saturation
% 1.49/1.29
% 1.49/1.29 % (18810)Memory used [KB]: 5500
% 1.49/1.29 % (18810)Time elapsed: 0.003 s
% 1.49/1.29 % (18810)Instructions burned: 4 (million)
% 1.49/1.29 % (18810)------------------------------
% 1.49/1.29 % (18810)------------------------------
% 1.49/1.30 % (18811)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_18640 for (2999ds/37Mi)
% 1.63/1.30 % (18805)Instruction limit reached!
% 1.63/1.30 % (18805)------------------------------
% 1.63/1.30 % (18805)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.30 % (18805)Termination reason: Unknown
% 1.63/1.30 % (18805)Termination phase: Saturation
% 1.63/1.30
% 1.63/1.30 % (18805)Memory used [KB]: 5500
% 1.63/1.30 % (18805)Time elapsed: 0.016 s
% 1.63/1.30 % (18805)Instructions burned: 28 (million)
% 1.63/1.30 % (18805)------------------------------
% 1.63/1.30 % (18805)------------------------------
% 1.63/1.30 % (18815)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_18640 for (2999ds/7Mi)
% 1.63/1.31 % (18815)Instruction limit reached!
% 1.63/1.31 % (18815)------------------------------
% 1.63/1.31 % (18815)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.31 % (18815)Termination reason: Unknown
% 1.63/1.31 % (18815)Termination phase: Saturation
% 1.63/1.31
% 1.63/1.31 % (18815)Memory used [KB]: 1023
% 1.63/1.31 % (18815)Time elapsed: 0.004 s
% 1.63/1.31 % (18815)Instructions burned: 8 (million)
% 1.63/1.31 % (18815)------------------------------
% 1.63/1.31 % (18815)------------------------------
% 1.63/1.31 % (18812)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_18640 for (2999ds/15Mi)
% 1.63/1.31 % (18811)Instruction limit reached!
% 1.63/1.31 % (18811)------------------------------
% 1.63/1.31 % (18811)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.31 % (18811)Termination reason: Unknown
% 1.63/1.31 % (18811)Termination phase: Saturation
% 1.63/1.31
% 1.63/1.31 % (18811)Memory used [KB]: 5756
% 1.63/1.31 % (18811)Time elapsed: 0.012 s
% 1.63/1.31 % (18811)Instructions burned: 37 (million)
% 1.63/1.31 % (18811)------------------------------
% 1.63/1.31 % (18811)------------------------------
% 1.63/1.31 % (18813)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_18640 for (2999ds/3Mi)
% 1.63/1.31 % (18814)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_18640 for (2999ds/1041Mi)
% 1.63/1.31 % (18812)Refutation not found, incomplete strategy
% 1.63/1.31 % (18812)------------------------------
% 1.63/1.31 % (18812)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.31 % (18812)Termination reason: Refutation not found, incomplete strategy
% 1.63/1.31
% 1.63/1.31
% 1.63/1.31 % (18812)Memory used [KB]: 5500
% 1.63/1.31 % (18812)Time elapsed: 0.004 s
% 1.63/1.31 % (18812)Instructions burned: 3 (million)
% 1.63/1.31 % (18812)------------------------------
% 1.63/1.31 % (18812)------------------------------
% 1.63/1.31 % (18813)Refutation not found, incomplete strategy
% 1.63/1.31 % (18813)------------------------------
% 1.63/1.31 % (18813)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.31 % (18813)Termination reason: Refutation not found, incomplete strategy
% 1.63/1.31
% 1.63/1.31
% 1.63/1.31 % (18813)Memory used [KB]: 5500
% 1.63/1.31 % (18813)Time elapsed: 0.004 s
% 1.63/1.31 % (18813)Instructions burned: 2 (million)
% 1.63/1.31 % (18813)------------------------------
% 1.63/1.31 % (18813)------------------------------
% 1.63/1.32 % (18817)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_18640 for (2999ds/3Mi)
% 1.63/1.32 % (18818)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_18640 for (2999ds/3Mi)
% 1.63/1.32 % (18818)Instruction limit reached!
% 1.63/1.32 % (18818)------------------------------
% 1.63/1.32 % (18818)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.32 % (18818)Termination reason: Unknown
% 1.63/1.32 % (18818)Termination phase: Saturation
% 1.63/1.32
% 1.63/1.32 % (18818)Memory used [KB]: 1023
% 1.63/1.32 % (18818)Time elapsed: 0.002 s
% 1.63/1.32 % (18818)Instructions burned: 3 (million)
% 1.63/1.32 % (18818)------------------------------
% 1.63/1.32 % (18818)------------------------------
% 1.63/1.32 % (18817)Instruction limit reached!
% 1.63/1.32 % (18817)------------------------------
% 1.63/1.32 % (18817)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.32 % (18817)Termination reason: Unknown
% 1.63/1.32 % (18817)Termination phase: Saturation
% 1.63/1.32
% 1.63/1.32 % (18817)Memory used [KB]: 5500
% 1.63/1.32 % (18817)Time elapsed: 0.003 s
% 1.63/1.32 % (18817)Instructions burned: 4 (million)
% 1.63/1.32 % (18817)------------------------------
% 1.63/1.32 % (18817)------------------------------
% 1.63/1.32 % (18816)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_18640 for (2999ds/16Mi)
% 1.63/1.32 % (18814)Refutation not found, incomplete strategy
% 1.63/1.32 % (18814)------------------------------
% 1.63/1.32 % (18814)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.32 % (18814)Termination reason: Refutation not found, incomplete strategy
% 1.63/1.32
% 1.63/1.32
% 1.63/1.32 % (18814)Memory used [KB]: 5628
% 1.63/1.32 % (18814)Time elapsed: 0.013 s
% 1.63/1.32 % (18814)Instructions burned: 20 (million)
% 1.63/1.32 % (18814)------------------------------
% 1.63/1.32 % (18814)------------------------------
% 1.63/1.33 % (18821)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_18640 for (2999ds/4Mi)
% 1.63/1.33 % (18822)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_18640 for (2999ds/18Mi)
% 1.63/1.33 % (18820)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_18640 for (2999ds/3Mi)
% 1.63/1.33 % (18821)Instruction limit reached!
% 1.63/1.33 % (18821)------------------------------
% 1.63/1.33 % (18821)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.33 % (18821)Termination reason: Unknown
% 1.63/1.33 % (18821)Termination phase: Saturation
% 1.63/1.33
% 1.63/1.33 % (18821)Memory used [KB]: 5500
% 1.63/1.33 % (18821)Time elapsed: 0.003 s
% 1.63/1.33 % (18821)Instructions burned: 6 (million)
% 1.63/1.33 % (18821)------------------------------
% 1.63/1.33 % (18821)------------------------------
% 1.63/1.33 % (18820)Instruction limit reached!
% 1.63/1.33 % (18820)------------------------------
% 1.63/1.33 % (18820)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.33 % (18820)Termination reason: Unknown
% 1.63/1.33 % (18820)Termination phase: Saturation
% 1.63/1.33
% 1.63/1.33 % (18820)Memory used [KB]: 5500
% 1.63/1.33 % (18820)Time elapsed: 0.004 s
% 1.63/1.33 % (18820)Instructions burned: 4 (million)
% 1.63/1.33 % (18820)------------------------------
% 1.63/1.33 % (18820)------------------------------
% 1.63/1.33 % (18816)Instruction limit reached!
% 1.63/1.33 % (18816)------------------------------
% 1.63/1.33 % (18816)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.33 % (18816)Termination reason: Unknown
% 1.63/1.33 % (18816)Termination phase: Saturation
% 1.63/1.33
% 1.63/1.33 % (18816)Memory used [KB]: 5756
% 1.63/1.33 % (18816)Time elapsed: 0.013 s
% 1.63/1.33 % (18816)Instructions burned: 16 (million)
% 1.63/1.33 % (18816)------------------------------
% 1.63/1.33 % (18816)------------------------------
% 1.63/1.33 % (18823)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_18640 for (2999ds/710Mi)
% 1.63/1.33 % (18819)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_18640 for (2999ds/7Mi)
% 1.63/1.33 % (18822)Instruction limit reached!
% 1.63/1.33 % (18822)------------------------------
% 1.63/1.33 % (18822)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.33 % (18822)Termination reason: Unknown
% 1.63/1.33 % (18822)Termination phase: Saturation
% 1.63/1.33
% 1.63/1.33 % (18822)Memory used [KB]: 5500
% 1.63/1.33 % (18822)Time elapsed: 0.008 s
% 1.63/1.33 % (18822)Instructions burned: 19 (million)
% 1.63/1.33 % (18822)------------------------------
% 1.63/1.33 % (18822)------------------------------
% 1.63/1.34 % (18824)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_18640 for (2999ds/6Mi)
% 1.63/1.34 % (18824)Instruction limit reached!
% 1.63/1.34 % (18824)------------------------------
% 1.63/1.34 % (18824)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.34 % (18824)Termination reason: Unknown
% 1.63/1.34 % (18824)Termination phase: Saturation
% 1.63/1.34
% 1.63/1.34 % (18824)Memory used [KB]: 5500
% 1.63/1.34 % (18824)Time elapsed: 0.003 s
% 1.63/1.34 % (18824)Instructions burned: 7 (million)
% 1.63/1.34 % (18824)------------------------------
% 1.63/1.34 % (18824)------------------------------
% 1.63/1.34 % (18819)Instruction limit reached!
% 1.63/1.34 % (18819)------------------------------
% 1.63/1.34 % (18819)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.34 % (18819)Termination reason: Unknown
% 1.63/1.34 % (18819)Termination phase: Saturation
% 1.63/1.34
% 1.63/1.34 % (18819)Memory used [KB]: 5500
% 1.63/1.34 % (18819)Time elapsed: 0.010 s
% 1.63/1.34 % (18819)Instructions burned: 8 (million)
% 1.63/1.34 % (18819)------------------------------
% 1.63/1.34 % (18819)------------------------------
% 1.63/1.34 % (18827)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_18640 for (2999ds/5Mi)
% 1.63/1.35 % (18827)Instruction limit reached!
% 1.63/1.35 % (18827)------------------------------
% 1.63/1.35 % (18827)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.35 % (18803)Instruction limit reached!
% 1.63/1.35 % (18803)------------------------------
% 1.63/1.35 % (18803)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.35 % (18803)Termination reason: Unknown
% 1.63/1.35 % (18803)Termination phase: Saturation
% 1.63/1.35
% 1.63/1.35 % (18803)Memory used [KB]: 6396
% 1.63/1.35 % (18803)Time elapsed: 0.067 s
% 1.63/1.35 % (18803)Instructions burned: 185 (million)
% 1.63/1.35 % (18803)------------------------------
% 1.63/1.35 % (18803)------------------------------
% 1.63/1.35 % (18827)Termination reason: Unknown
% 1.63/1.35 % (18827)Termination phase: Saturation
% 1.63/1.35
% 1.63/1.35 % (18827)Memory used [KB]: 5500
% 1.63/1.35 % (18827)Time elapsed: 0.004 s
% 1.63/1.35 % (18827)Instructions burned: 7 (million)
% 1.63/1.35 % (18827)------------------------------
% 1.63/1.35 % (18827)------------------------------
% 1.63/1.35 % (18826)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_18640 for (2999ds/21Mi)
% 1.63/1.35 % (18825)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_18640 for (2999ds/902Mi)
% 1.63/1.35 % (18825)Refutation not found, incomplete strategy
% 1.63/1.35 % (18825)------------------------------
% 1.63/1.35 % (18825)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.35 % (18825)Termination reason: Refutation not found, incomplete strategy
% 1.63/1.35
% 1.63/1.35
% 1.63/1.35 % (18828)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_18640 for (2999ds/6Mi)
% 1.63/1.35 % (18825)Memory used [KB]: 5500
% 1.63/1.35 % (18825)Time elapsed: 0.003 s
% 1.63/1.35 % (18825)Instructions burned: 2 (million)
% 1.63/1.35 % (18825)------------------------------
% 1.63/1.35 % (18825)------------------------------
% 1.63/1.35 % (18828)Refutation not found, incomplete strategy
% 1.63/1.35 % (18828)------------------------------
% 1.63/1.35 % (18828)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.35 % (18828)Termination reason: Refutation not found, incomplete strategy
% 1.63/1.35
% 1.63/1.35
% 1.63/1.35 % (18828)Memory used [KB]: 5500
% 1.63/1.35 % (18828)Time elapsed: 0.001 s
% 1.63/1.35 % (18828)Instructions burned: 1 (million)
% 1.63/1.35 % (18828)------------------------------
% 1.63/1.35 % (18828)------------------------------
% 1.63/1.36 % (18831)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_18640 for (2999ds/19Mi)
% 1.63/1.36 % (18830)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_18640 for (2999ds/779Mi)
% 1.63/1.36 % (18831)Refutation not found, incomplete strategy
% 1.63/1.36 % (18831)------------------------------
% 1.63/1.36 % (18831)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.36 % (18826)Instruction limit reached!
% 1.63/1.36 % (18826)------------------------------
% 1.63/1.36 % (18826)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.36 % (18826)Termination reason: Unknown
% 1.63/1.36 % (18826)Termination phase: Saturation
% 1.63/1.36
% 1.63/1.36 % (18826)Memory used [KB]: 5628
% 1.63/1.36 % (18826)Time elapsed: 0.011 s
% 1.63/1.36 % (18826)Instructions burned: 23 (million)
% 1.63/1.36 % (18826)------------------------------
% 1.63/1.36 % (18826)------------------------------
% 1.63/1.36 % (18831)Termination reason: Refutation not found, incomplete strategy
% 1.63/1.36
% 1.63/1.36
% 1.63/1.36 % (18831)Memory used [KB]: 5500
% 1.63/1.36 % (18831)Time elapsed: 0.001 s
% 1.63/1.36 % (18831)Instructions burned: 1 (million)
% 1.63/1.36 % (18831)------------------------------
% 1.63/1.36 % (18831)------------------------------
% 1.63/1.36 % (18830)Refutation not found, incomplete strategy
% 1.63/1.36 % (18830)------------------------------
% 1.63/1.36 % (18830)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.36 % (18830)Termination reason: Refutation not found, incomplete strategy
% 1.63/1.36
% 1.63/1.36
% 1.63/1.36 % (18830)Memory used [KB]: 5500
% 1.63/1.36 % (18830)Time elapsed: 0.003 s
% 1.63/1.36 % (18830)Instructions burned: 4 (million)
% 1.63/1.36 % (18830)------------------------------
% 1.63/1.36 % (18830)------------------------------
% 1.63/1.36 % (18829)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_18640 for (2999ds/377Mi)
% 1.63/1.36 % (18833)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_18640 for (2999ds/17Mi)
% 1.63/1.37 % (18833)Instruction limit reached!
% 1.63/1.37 % (18833)------------------------------
% 1.63/1.37 % (18833)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.37 % (18833)Termination reason: Unknown
% 1.63/1.37 % (18833)Termination phase: Saturation
% 1.63/1.37
% 1.63/1.37 % (18833)Memory used [KB]: 5628
% 1.63/1.37 % (18833)Time elapsed: 0.028 s
% 1.63/1.37 % (18833)Instructions burned: 18 (million)
% 1.63/1.37 % (18833)------------------------------
% 1.63/1.37 % (18833)------------------------------
% 1.63/1.37 % (18835)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_18640 for (2999ds/30Mi)
% 1.63/1.37 % (18834)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_18640 for (2999ds/3Mi)
% 1.63/1.37 % (18832)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_18640 for (2999ds/879Mi)
% 1.63/1.37 % (18834)Instruction limit reached!
% 1.63/1.37 % (18834)------------------------------
% 1.63/1.37 % (18834)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.37 % (18834)Termination reason: Unknown
% 1.63/1.37 % (18834)Termination phase: Saturation
% 1.63/1.37
% 1.63/1.37 % (18834)Memory used [KB]: 1023
% 1.63/1.37 % (18834)Time elapsed: 0.003 s
% 1.63/1.37 % (18834)Instructions burned: 4 (million)
% 1.63/1.37 % (18834)------------------------------
% 1.63/1.37 % (18834)------------------------------
% 1.63/1.37 % (18836)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_18640 for (2999ds/127Mi)
% 1.63/1.37 % (18835)Refutation not found, incomplete strategy
% 1.63/1.37 % (18835)------------------------------
% 1.63/1.37 % (18835)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.37 % (18835)Termination reason: Refutation not found, incomplete strategy
% 1.63/1.37
% 1.63/1.37
% 1.63/1.37 % (18835)Memory used [KB]: 5500
% 1.63/1.37 % (18835)Time elapsed: 0.003 s
% 1.63/1.37 % (18835)Instructions burned: 6 (million)
% 1.63/1.37 % (18835)------------------------------
% 1.63/1.37 % (18835)------------------------------
% 1.63/1.37 % (18832)Refutation not found, incomplete strategy
% 1.63/1.37 % (18832)------------------------------
% 1.63/1.37 % (18832)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.37 % (18832)Termination reason: Refutation not found, incomplete strategy
% 1.63/1.37
% 1.63/1.37
% 1.63/1.37 % (18832)Memory used [KB]: 5500
% 1.63/1.37 % (18832)Time elapsed: 0.005 s
% 1.63/1.37 % (18832)Instructions burned: 5 (million)
% 1.63/1.37 % (18832)------------------------------
% 1.63/1.37 % (18832)------------------------------
% 1.63/1.38 % (18837)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_18640 for (2999ds/100Mi)
% 1.63/1.38 % (18837)Refutation not found, incomplete strategy
% 1.63/1.38 % (18837)------------------------------
% 1.63/1.38 % (18837)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.38 % (18837)Termination reason: Refutation not found, incomplete strategy
% 1.63/1.38
% 1.63/1.38
% 1.63/1.38 % (18837)Memory used [KB]: 5500
% 1.63/1.38 % (18837)Time elapsed: 0.002 s
% 1.63/1.38 % (18837)Instructions burned: 4 (million)
% 1.63/1.38 % (18837)------------------------------
% 1.63/1.38 % (18837)------------------------------
% 1.63/1.38 % (18838)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_18640 for (2999ds/3Mi)
% 1.63/1.38 % (18839)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_18640 for (2999ds/20Mi)
% 1.63/1.38 % (18839)Refutation not found, incomplete strategy
% 1.63/1.38 % (18839)------------------------------
% 1.63/1.38 % (18839)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.38 % (18839)Termination reason: Refutation not found, incomplete strategy
% 1.63/1.38
% 1.63/1.38
% 1.63/1.38 % (18839)Memory used [KB]: 5500
% 1.63/1.38 % (18839)Time elapsed: 0.001 s
% 1.63/1.38 % (18839)Instructions burned: 1 (million)
% 1.63/1.38 % (18839)------------------------------
% 1.63/1.38 % (18839)------------------------------
% 1.63/1.38 % (18838)Instruction limit reached!
% 1.63/1.38 % (18838)------------------------------
% 1.63/1.38 % (18838)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.38 % (18838)Termination reason: Unknown
% 1.63/1.38 % (18838)Termination phase: Saturation
% 1.63/1.38
% 1.63/1.38 % (18838)Memory used [KB]: 5500
% 1.63/1.38 % (18838)Time elapsed: 0.003 s
% 1.63/1.38 % (18838)Instructions burned: 4 (million)
% 1.63/1.38 % (18838)------------------------------
% 1.63/1.38 % (18838)------------------------------
% 1.63/1.39 % (18841)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_18640 for (2998ds/107Mi)
% 1.63/1.39 % (18841)Refutation not found, incomplete strategy
% 1.63/1.39 % (18841)------------------------------
% 1.63/1.39 % (18841)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.39 % (18841)Termination reason: Refutation not found, incomplete strategy
% 1.63/1.39
% 1.63/1.39
% 1.63/1.39 % (18841)Memory used [KB]: 5500
% 1.63/1.39 % (18841)Time elapsed: 0.001 s
% 1.63/1.39 % (18841)Instructions burned: 1 (million)
% 1.63/1.39 % (18841)------------------------------
% 1.63/1.39 % (18841)------------------------------
% 1.63/1.39 % (18842)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_18640 for (2998ds/39Mi)
% 1.63/1.39 % (18840)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_18640 for (2999ds/86Mi)
% 1.63/1.39 % (18843)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_18640 for (2998ds/448Mi)
% 1.63/1.39 % (18843)Refutation not found, incomplete strategy
% 1.63/1.39 % (18843)------------------------------
% 1.63/1.39 % (18843)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.39 % (18843)Termination reason: Refutation not found, incomplete strategy
% 1.63/1.39
% 1.63/1.39
% 1.63/1.39 % (18843)Memory used [KB]: 5500
% 1.63/1.39 % (18843)Time elapsed: 0.002 s
% 1.63/1.39 % (18843)Instructions burned: 2 (million)
% 1.63/1.39 % (18843)------------------------------
% 1.63/1.39 % (18843)------------------------------
% 1.63/1.39 % (18840)Refutation not found, incomplete strategy
% 1.63/1.39 % (18840)------------------------------
% 1.63/1.39 % (18840)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.39 % (18840)Termination reason: Refutation not found, incomplete strategy
% 1.63/1.39
% 1.63/1.39
% 1.63/1.39 % (18840)Memory used [KB]: 5500
% 1.63/1.39 % (18840)Time elapsed: 0.003 s
% 1.63/1.39 % (18840)Instructions burned: 3 (million)
% 1.63/1.39 % (18840)------------------------------
% 1.63/1.39 % (18840)------------------------------
% 1.63/1.39 % (18836)First to succeed.
% 1.63/1.40 % (18836)Refutation found. Thanks to Tanya!
% 1.63/1.40 % SZS status Theorem for DTF2THF_18640
% 1.63/1.40 % SZS output start Proof for DTF2THF_18640
% 1.63/1.40 thf(func_def_0, type, eps: ($i > $o) > $i).
% 1.63/1.40 thf(func_def_2, type, case: ($o > $o) > $i > $i > $i > $i > $i).
% 1.63/1.40 thf(func_def_4, type, f: $o > $o).
% 1.63/1.40 thf(func_def_19, type, ph2: !>[X0: $tType]:(X0)).
% 1.63/1.40 thf(func_def_20, type, sK3: $i > $i > $i).
% 1.63/1.40 thf(func_def_21, type, sK4: $i > $i).
% 1.63/1.40 thf(f953,plain,(
% 1.63/1.40 $false),
% 1.63/1.40 inference(avatar_sat_refutation,[status(thm)],[f160,f167,f187,f188,f189,f190,f204,f213,f402,f443,f517,f526,f535,f679,f712,f723,f730,f737,f749,f790,f794,f845,f864,f952])).
% 1.63/1.40 thf(f952,plain,(
% 1.63/1.40 ~spl1_1 | ~spl1_7),
% 1.63/1.40 inference(avatar_contradiction_clause,[status(thm)],[f951])).
% 1.63/1.40 thf(f951,plain,(
% 1.63/1.40 $false | (~spl1_1 | ~spl1_7)),
% 1.63/1.40 inference(trivial_inequality_removal,[status(thm)],[f950])).
% 1.63/1.40 thf(f950,plain,(
% 1.63/1.40 (sK0 != sK0) | (~spl1_1 | ~spl1_7)),
% 1.63/1.40 inference(duplicate_literal_removal,[status(thm)],[f949])).
% 1.63/1.40 thf(f949,plain,(
% 1.63/1.40 (sK0 != sK0) | (sK0 != sK0) | (sK0 != sK0) | (~spl1_1 | ~spl1_7)),
% 1.63/1.40 inference(superposition,[status(thm)],[f186,f938])).
% 1.63/1.40 thf(f938,plain,(
% 1.63/1.40 (sK0 = (sK4 @ sK0)) | ~spl1_1),
% 1.63/1.40 inference(duplicate_literal_removal,[status(thm)],[f937])).
% 1.63/1.40 thf(f937,plain,(
% 1.63/1.40 (sK0 = (sK4 @ sK0)) | (sK0 = (sK4 @ sK0)) | ~spl1_1),
% 1.63/1.40 inference(equality_resolution,[status(thm)],[f148])).
% 1.63/1.40 thf(f148,plain,(
% 1.63/1.40 ( ! [X0 : $i] : ((sK0 != X0) | ((sK4 @ X0) = X0) | (sK0 = (sK4 @ X0))) ) | ~spl1_1),
% 1.63/1.40 inference(avatar_component_clause,[status(thm)],[f147])).
% 1.63/1.40 thf(f147,definition,(
% 1.63/1.40 spl1_1 <=> ! [X0 : $i] : (((sK4 @ X0) = X0) | (sK0 != X0) | (sK0 = (sK4 @ X0)))),
% 1.63/1.40 introduced(definition,[new_symbols(naming,[spl1_1])],[avatar_definition])).
% 1.63/1.40 thf(f186,plain,(
% 1.63/1.40 ( ! [X0 : $i] : ((sK0 != (sK4 @ X0)) | ((sK4 @ X0) != X0) | (sK0 != X0)) ) | ~spl1_7),
% 1.63/1.40 inference(avatar_component_clause,[status(thm)],[f185])).
% 1.63/1.40 thf(f185,definition,(
% 1.63/1.40 spl1_7 <=> ! [X0 : $i] : ((sK0 != X0) | ((sK4 @ X0) != X0) | (sK0 != (sK4 @ X0)))),
% 1.63/1.40 introduced(definition,[new_symbols(naming,[spl1_7])],[avatar_definition])).
% 1.63/1.40 thf(f864,plain,(
% 1.63/1.40 spl1_10 | spl1_9),
% 1.63/1.40 inference(avatar_split_clause,[status(thm)],[f863,f201,f206])).
% 1.63/1.40 thf(f206,definition,(
% 1.63/1.40 spl1_10 <=> ($true = sK5)),
% 1.63/1.40 introduced(definition,[new_symbols(naming,[spl1_10])],[avatar_definition])).
% 1.63/1.40 thf(f201,definition,(
% 1.63/1.40 spl1_9 <=> ($false = sK5)),
% 1.63/1.40 introduced(definition,[new_symbols(naming,[spl1_9])],[avatar_definition])).
% 1.63/1.40 thf(f863,plain,(
% 1.63/1.40 ($true = sK5) | spl1_9),
% 1.63/1.40 inference(beta_eta_normalization,[status(thm)],[f862])).
% 1.63/1.40 thf(f862,plain,(
% 1.63/1.40 ( ! [X0 : $i] : ((((^[Y0 : $i]: (sK5)) @ X0) = $true)) ) | spl1_9),
% 1.63/1.40 inference(trivial_inequality_removal,[status(thm)],[f860])).
% 1.63/1.40 thf(f860,plain,(
% 1.63/1.40 ( ! [X0 : $i] : ((((^[Y0 : $i]: (sK5)) @ X0) = $true) | ($false != $false)) ) | spl1_9),
% 1.63/1.40 inference(superposition,[status(thm)],[f202,f28])).
% 1.63/1.40 thf(f28,plain,(
% 1.63/1.40 ( ! [X1 : $i,X4 : $i > $o] : (((X4 @ (eps @ (^[Y0 : $i]: (~ (X4 @ Y0))))) = $false) | ((X4 @ X1) = $true)) )),
% 1.63/1.40 inference(not_proxy_clausification,[status(thm)],[f27])).
% 1.63/1.40 thf(f27,plain,(
% 1.63/1.40 ( ! [X1 : $i,X4 : $i > $o] : (((X4 @ (eps @ (^[Y0 : $i]: (~ (X4 @ Y0))))) = $false) | ((~ (X4 @ X1)) != $true)) )),
% 1.63/1.40 inference(not_proxy_clausification,[status(thm)],[f26])).
% 1.63/1.40 thf(f26,plain,(
% 1.63/1.40 ( ! [X1 : $i,X4 : $i > $o] : (($true = (~ (X4 @ (eps @ (^[Y0 : $i]: (~ (X4 @ Y0))))))) | ((~ (X4 @ X1)) != $true)) )),
% 1.63/1.40 inference(beta_eta_normalization,[status(thm)],[f23])).
% 1.63/1.40 thf(f23,plain,(
% 1.63/1.40 ( ! [X1 : $i,X4 : $i > $o] : ((((^[Y0 : $i]: (~ (X4 @ Y0))) @ X1) != $true) | (((^[Y0 : $i]: (~ (X4 @ Y0))) @ (eps @ (^[Y0 : $i]: (~ (X4 @ Y0))))) = $true)) )),
% 1.63/1.40 inference(primitive_instantiation,[status(thm)],[f17])).
% 1.63/1.40 thf(f17,plain,(
% 1.63/1.40 ( ! [X0 : $i > $o,X1 : $i] : (((X0 @ X1) != $true) | ((X0 @ (eps @ X0)) = $true)) )),
% 1.63/1.40 inference(cnf_transformation,[status(thm)],[f11])).
% 1.63/1.40 thf(f11,plain,(
% 1.63/1.40 ! [X0 : $i > $o] : (! [X1 : $i] : ((X0 @ X1) != $true) | ((X0 @ (eps @ X0)) = $true))),
% 1.63/1.40 inference(ennf_transformation,[status(thm)],[f9])).
% 1.63/1.40 thf(f9,plain,(
% 1.63/1.40 ! [X0 : $i > $o] : (? [X1 : $i] : ((X0 @ X1) = $true) => ((X0 @ (eps @ X0)) = $true))),
% 1.63/1.40 inference(fool_elimination,[status(thm)],[f8])).
% 1.63/1.40 thf(f8,plain,(
% 1.63/1.40 ! [X0 : $i > $o] : (? [X1 : $i] : (X0 @ X1) => (X0 @ (eps @ X0)))),
% 1.63/1.40 inference(rectify,[status(thm)],[f1])).
% 1.63/1.40 thf(f1,axiom,(
% 1.63/1.40 ! [X0 : $i > $o] : (? [X1 : $i] : (X0 @ X1) => (X0 @ (eps @ X0)))),
% 1.63/1.40 file('/export/starexec/sandbox2/tmp/tmp.ogKD8WwFWg/DTF2THF_18640.p',choiceax)).
% 1.63/1.40 thf(f202,plain,(
% 1.63/1.40 ($false != sK5) | spl1_9),
% 1.63/1.40 inference(avatar_component_clause,[status(thm)],[f201])).
% 1.63/1.40 thf(f845,plain,(
% 1.63/1.40 ~spl1_32 | ~spl1_34 | ~spl1_40),
% 1.63/1.40 inference(avatar_contradiction_clause,[status(thm)],[f844])).
% 1.63/1.40 thf(f844,plain,(
% 1.63/1.40 $false | (~spl1_32 | ~spl1_34 | ~spl1_40)),
% 1.63/1.40 inference(trivial_inequality_removal,[status(thm)],[f843])).
% 1.63/1.40 thf(f843,plain,(
% 1.63/1.40 ($true = $false) | (~spl1_32 | ~spl1_34 | ~spl1_40)),
% 1.63/1.40 inference(forward_demodulation,[status(thm)],[f747,f673])).
% 1.63/1.40 thf(f673,plain,(
% 1.63/1.40 ((f @ $false) = $false) | ~spl1_40),
% 1.63/1.40 inference(avatar_component_clause,[status(thm)],[f672])).
% 1.63/1.40 thf(f672,definition,(
% 1.63/1.40 spl1_40 <=> ((f @ $false) = $false)),
% 1.63/1.40 introduced(definition,[new_symbols(naming,[spl1_40])],[avatar_definition])).
% 1.63/1.40 thf(f747,plain,(
% 1.63/1.40 ((f @ $false) = $true) | (~spl1_32 | ~spl1_34)),
% 1.63/1.40 inference(forward_demodulation,[status(thm)],[f512,f521])).
% 1.63/1.40 thf(f521,plain,(
% 1.63/1.40 ($false = sK19) | ~spl1_34),
% 1.63/1.40 inference(avatar_component_clause,[status(thm)],[f519])).
% 1.63/1.40 thf(f519,definition,(
% 1.63/1.40 spl1_34 <=> ($false = sK19)),
% 1.63/1.40 introduced(definition,[new_symbols(naming,[spl1_34])],[avatar_definition])).
% 1.63/1.40 thf(f512,plain,(
% 1.63/1.40 ($true = (f @ sK19)) | ~spl1_32),
% 1.63/1.40 inference(avatar_component_clause,[status(thm)],[f510])).
% 1.63/1.40 thf(f510,definition,(
% 1.63/1.40 spl1_32 <=> ($true = (f @ sK19))),
% 1.63/1.40 introduced(definition,[new_symbols(naming,[spl1_32])],[avatar_definition])).
% 1.63/1.40 thf(f794,plain,(
% 1.63/1.40 spl1_40 | ~spl1_9 | ~spl1_11),
% 1.63/1.40 inference(avatar_split_clause,[status(thm)],[f793,f210,f201,f672])).
% 1.63/1.40 thf(f210,definition,(
% 1.63/1.40 spl1_11 <=> ((f @ sK5) = $false)),
% 1.63/1.40 introduced(definition,[new_symbols(naming,[spl1_11])],[avatar_definition])).
% 1.63/1.40 thf(f793,plain,(
% 1.63/1.40 ((f @ $false) = $false) | (~spl1_9 | ~spl1_11)),
% 1.63/1.40 inference(forward_demodulation,[status(thm)],[f212,f203])).
% 1.63/1.40 thf(f203,plain,(
% 1.63/1.40 ($false = sK5) | ~spl1_9),
% 1.63/1.40 inference(avatar_component_clause,[status(thm)],[f201])).
% 1.63/1.40 thf(f212,plain,(
% 1.63/1.40 ((f @ sK5) = $false) | ~spl1_11),
% 1.63/1.40 inference(avatar_component_clause,[status(thm)],[f210])).
% 1.63/1.40 thf(f790,plain,(
% 1.63/1.40 ~spl1_9 | ~spl1_10),
% 1.63/1.40 inference(avatar_contradiction_clause,[status(thm)],[f789])).
% 1.63/1.40 thf(f789,plain,(
% 1.63/1.40 $false | (~spl1_9 | ~spl1_10)),
% 1.63/1.40 inference(trivial_inequality_removal,[status(thm)],[f780])).
% 1.63/1.40 thf(f780,plain,(
% 1.63/1.40 ($true = $false) | (~spl1_9 | ~spl1_10)),
% 1.63/1.40 inference(backward_demodulation,[status(thm)],[f208,f203])).
% 1.63/1.40 thf(f208,plain,(
% 1.63/1.40 ($true = sK5) | ~spl1_10),
% 1.63/1.40 inference(avatar_component_clause,[status(thm)],[f206])).
% 1.63/1.40 thf(f749,plain,(
% 1.63/1.40 spl1_2 | ~spl1_8 | ~spl1_10 | ~spl1_32 | ~spl1_34),
% 1.63/1.40 inference(avatar_contradiction_clause,[status(thm)],[f748])).
% 1.63/1.40 thf(f748,plain,(
% 1.63/1.40 $false | (spl1_2 | ~spl1_8 | ~spl1_10 | ~spl1_32 | ~spl1_34)),
% 1.63/1.40 inference(subsumption_resolution,[status(thm)],[f747,f696])).
% 1.63/1.40 thf(f696,plain,(
% 1.63/1.40 ((f @ $false) != $true) | (spl1_2 | ~spl1_8 | ~spl1_10)),
% 1.63/1.40 inference(backward_demodulation,[status(thm)],[f497,f662])).
% 1.63/1.40 thf(f662,plain,(
% 1.63/1.40 (sK17 = $false) | (spl1_2 | ~spl1_8 | ~spl1_10)),
% 1.63/1.40 inference(subsumption_resolution,[status(thm)],[f604,f276])).
% 1.63/1.40 thf(f276,plain,(
% 1.63/1.40 ($true = (f @ $true)) | (~spl1_8 | ~spl1_10)),
% 1.63/1.40 inference(forward_demodulation,[status(thm)],[f199,f208])).
% 1.63/1.40 thf(f199,plain,(
% 1.63/1.40 ((f @ sK5) = $true) | ~spl1_8),
% 1.63/1.40 inference(avatar_component_clause,[status(thm)],[f197])).
% 1.63/1.40 thf(f197,definition,(
% 1.63/1.40 spl1_8 <=> ((f @ sK5) = $true)),
% 1.63/1.40 introduced(definition,[new_symbols(naming,[spl1_8])],[avatar_definition])).
% 1.63/1.40 thf(f604,plain,(
% 1.63/1.40 (sK17 = $false) | ($true != (f @ $true)) | spl1_2),
% 1.63/1.40 inference(beta_eta_normalization,[status(thm)],[f570])).
% 1.63/1.40 thf(f570,plain,(
% 1.63/1.40 ($true != (f @ $true)) | (((^[Y0 : $i]: (sK17)) @ (eps @ (^[Y0 : $i]: (~ ((^[Y1 : $i]: (sK17)) @ Y0))))) = $false) | spl1_2),
% 1.63/1.40 inference(superposition,[status(thm)],[f497,f28])).
% 1.63/1.40 thf(f497,plain,(
% 1.63/1.40 ((f @ sK17) != $true) | spl1_2),
% 1.63/1.40 inference(beta_eta_normalization,[status(thm)],[f496])).
% 1.63/1.40 thf(f496,plain,(
% 1.63/1.40 ((f @ sK17) != ((^[Y0 : $o]: ($true)) @ sK17)) | spl1_2),
% 1.63/1.40 inference(negative_extensionality,[status(thm)],[f151])).
% 1.63/1.40 thf(f151,plain,(
% 1.63/1.40 (f != (^[Y0 : $o]: ($true))) | spl1_2),
% 1.63/1.40 inference(avatar_component_clause,[status(thm)],[f150])).
% 1.63/1.40 thf(f150,definition,(
% 1.63/1.40 spl1_2 <=> (f = (^[Y0 : $o]: ($true)))),
% 1.63/1.40 introduced(definition,[new_symbols(naming,[spl1_2])],[avatar_definition])).
% 1.63/1.40 thf(f737,plain,(
% 1.63/1.40 spl1_34 | spl1_33),
% 1.63/1.40 inference(avatar_split_clause,[status(thm)],[f735,f514,f519])).
% 1.63/1.40 thf(f514,definition,(
% 1.63/1.40 spl1_33 <=> ($true = sK19)),
% 1.63/1.40 introduced(definition,[new_symbols(naming,[spl1_33])],[avatar_definition])).
% 1.63/1.40 thf(f735,plain,(
% 1.63/1.40 ($false = sK19) | spl1_33),
% 1.63/1.40 inference(beta_eta_normalization,[status(thm)],[f734])).
% 1.63/1.40 thf(f734,plain,(
% 1.63/1.40 ($false = ((^[Y0 : $i]: (sK19)) @ (eps @ (^[Y0 : $i]: (~ ((^[Y1 : $i]: (sK19)) @ Y0)))))) | spl1_33),
% 1.63/1.40 inference(trivial_inequality_removal,[status(thm)],[f732])).
% 1.63/1.40 thf(f732,plain,(
% 1.63/1.40 ($false = ((^[Y0 : $i]: (sK19)) @ (eps @ (^[Y0 : $i]: (~ ((^[Y1 : $i]: (sK19)) @ Y0)))))) | ($true != $true) | spl1_33),
% 1.63/1.40 inference(superposition,[status(thm)],[f515,f28])).
% 1.63/1.40 thf(f515,plain,(
% 1.63/1.40 ($true != sK19) | spl1_33),
% 1.63/1.40 inference(avatar_component_clause,[status(thm)],[f514])).
% 1.63/1.40 thf(f730,plain,(
% 1.63/1.40 spl1_37 | ~spl1_33 | ~spl1_35),
% 1.63/1.40 inference(avatar_split_clause,[status(thm)],[f729,f523,f514,f658])).
% 1.63/1.40 thf(f658,definition,(
% 1.63/1.40 spl1_37 <=> ($false = (f @ $true))),
% 1.63/1.40 introduced(definition,[new_symbols(naming,[spl1_37])],[avatar_definition])).
% 1.63/1.40 thf(f523,definition,(
% 1.63/1.40 spl1_35 <=> ($false = (f @ sK19))),
% 1.63/1.40 introduced(definition,[new_symbols(naming,[spl1_35])],[avatar_definition])).
% 1.63/1.40 thf(f729,plain,(
% 1.63/1.40 ($false = (f @ $true)) | (~spl1_33 | ~spl1_35)),
% 1.63/1.40 inference(forward_demodulation,[status(thm)],[f525,f516])).
% 1.63/1.40 thf(f516,plain,(
% 1.63/1.40 ($true = sK19) | ~spl1_33),
% 1.63/1.40 inference(avatar_component_clause,[status(thm)],[f514])).
% 1.63/1.40 thf(f525,plain,(
% 1.63/1.40 ($false = (f @ sK19)) | ~spl1_35),
% 1.63/1.40 inference(avatar_component_clause,[status(thm)],[f523])).
% 1.63/1.40 thf(f723,plain,(
% 1.63/1.40 ~spl1_37 | spl1_5 | ~spl1_41),
% 1.63/1.40 inference(avatar_split_clause,[status(thm)],[f713,f676,f170,f658])).
% 1.63/1.40 thf(f170,definition,(
% 1.63/1.40 spl1_5 <=> (f = (^[Y0 : $o]: ($false)))),
% 1.63/1.40 introduced(definition,[new_symbols(naming,[spl1_5])],[avatar_definition])).
% 1.63/1.40 thf(f676,definition,(
% 1.63/1.40 spl1_41 <=> ($true = sK18)),
% 1.63/1.40 introduced(definition,[new_symbols(naming,[spl1_41])],[avatar_definition])).
% 1.63/1.40 thf(f713,plain,(
% 1.63/1.40 ($false != (f @ $true)) | (spl1_5 | ~spl1_41)),
% 1.63/1.40 inference(backward_demodulation,[status(thm)],[f501,f678])).
% 1.63/1.40 thf(f678,plain,(
% 1.63/1.40 ($true = sK18) | ~spl1_41),
% 1.63/1.40 inference(avatar_component_clause,[status(thm)],[f676])).
% 1.63/1.40 thf(f501,plain,(
% 1.63/1.40 ((f @ sK18) != $false) | spl1_5),
% 1.63/1.40 inference(beta_eta_normalization,[status(thm)],[f500])).
% 1.63/1.40 thf(f500,plain,(
% 1.63/1.40 (((^[Y0 : $o]: ($false)) @ sK18) != (f @ sK18)) | spl1_5),
% 1.63/1.40 inference(negative_extensionality,[status(thm)],[f171])).
% 1.63/1.40 thf(f171,plain,(
% 1.63/1.40 (f != (^[Y0 : $o]: ($false))) | spl1_5),
% 1.63/1.40 inference(avatar_component_clause,[status(thm)],[f170])).
% 1.63/1.40 thf(f712,plain,(
% 1.63/1.40 spl1_40 | spl1_2 | ~spl1_8 | ~spl1_10),
% 1.63/1.40 inference(avatar_split_clause,[status(thm)],[f710,f206,f197,f150,f672])).
% 1.63/1.40 thf(f710,plain,(
% 1.63/1.40 ((f @ $false) = $false) | (spl1_2 | ~spl1_8 | ~spl1_10)),
% 1.63/1.40 inference(beta_eta_normalization,[status(thm)],[f709])).
% 1.63/1.40 thf(f709,plain,(
% 1.63/1.40 (((^[Y0 : $i]: (f @ ((^[Y1 : $i]: ($false)) @ Y0))) @ (eps @ (^[Y0 : $i]: (~ ((^[Y1 : $i]: (f @ ((^[Y2 : $i]: ($false)) @ Y1))) @ Y0))))) = $false) | (spl1_2 | ~spl1_8 | ~spl1_10)),
% 1.63/1.40 inference(trivial_inequality_removal,[status(thm)],[f706])).
% 1.63/1.40 thf(f706,plain,(
% 1.63/1.40 (((^[Y0 : $i]: (f @ ((^[Y1 : $i]: ($false)) @ Y0))) @ (eps @ (^[Y0 : $i]: (~ ((^[Y1 : $i]: (f @ ((^[Y2 : $i]: ($false)) @ Y1))) @ Y0))))) = $false) | ($true != $true) | (spl1_2 | ~spl1_8 | ~spl1_10)),
% 1.63/1.40 inference(superposition,[status(thm)],[f696,f28])).
% 1.63/1.40 thf(f679,plain,(
% 1.63/1.40 ~spl1_40 | spl1_41 | spl1_5),
% 1.63/1.40 inference(avatar_split_clause,[status(thm)],[f579,f170,f676,f672])).
% 1.63/1.40 thf(f579,plain,(
% 1.63/1.40 ($true = sK18) | ((f @ $false) != $false) | spl1_5),
% 1.63/1.40 inference(beta_eta_normalization,[status(thm)],[f561])).
% 1.63/1.40 thf(f561,plain,(
% 1.63/1.40 ( ! [X0 : $i] : ((((^[Y0 : $i]: (sK18)) @ X0) = $true) | ((f @ $false) != $false)) ) | spl1_5),
% 1.63/1.40 inference(superposition,[status(thm)],[f501,f28])).
% 1.63/1.40 thf(f535,plain,(
% 1.63/1.40 ~spl1_33 | ~spl1_34),
% 1.63/1.40 inference(avatar_contradiction_clause,[status(thm)],[f534])).
% 1.63/1.40 thf(f534,plain,(
% 1.63/1.40 $false | (~spl1_33 | ~spl1_34)),
% 1.63/1.40 inference(trivial_inequality_removal,[status(thm)],[f531])).
% 1.63/1.40 thf(f531,plain,(
% 1.63/1.40 ($true = $false) | (~spl1_33 | ~spl1_34)),
% 1.63/1.40 inference(backward_demodulation,[status(thm)],[f516,f521])).
% 1.63/1.40 thf(f526,plain,(
% 1.63/1.40 spl1_34 | spl1_35 | spl1_4),
% 1.63/1.40 inference(avatar_split_clause,[status(thm)],[f508,f162,f523,f519])).
% 1.63/1.40 thf(f162,definition,(
% 1.63/1.40 spl1_4 <=> (f = (^[Y0 : $o]: (Y0)))),
% 1.63/1.40 introduced(definition,[new_symbols(naming,[spl1_4])],[avatar_definition])).
% 1.63/1.40 thf(f508,plain,(
% 1.63/1.40 ($false = (f @ sK19)) | ($false = sK19) | spl1_4),
% 1.63/1.40 inference(binary_proxy_clausification,[status(thm)],[f506])).
% 1.63/1.40 thf(f506,plain,(
% 1.63/1.40 (sK19 != (f @ sK19)) | spl1_4),
% 1.63/1.40 inference(beta_eta_normalization,[status(thm)],[f505])).
% 1.63/1.40 thf(f505,plain,(
% 1.63/1.40 (((^[Y0 : $o]: (Y0)) @ sK19) != (f @ sK19)) | spl1_4),
% 1.63/1.40 inference(negative_extensionality,[status(thm)],[f163])).
% 1.63/1.40 thf(f163,plain,(
% 1.63/1.40 (f != (^[Y0 : $o]: (Y0))) | spl1_4),
% 1.63/1.40 inference(avatar_component_clause,[status(thm)],[f162])).
% 1.63/1.40 thf(f517,plain,(
% 1.63/1.40 spl1_32 | spl1_33 | spl1_4),
% 1.63/1.40 inference(avatar_split_clause,[status(thm)],[f507,f162,f514,f510])).
% 1.63/1.40 thf(f507,plain,(
% 1.63/1.40 ($true = (f @ sK19)) | ($true = sK19) | spl1_4),
% 1.63/1.40 inference(binary_proxy_clausification,[status(thm)],[f506])).
% 1.63/1.40 thf(f443,plain,(
% 1.63/1.40 spl1_18 | ~spl1_3 | ~spl1_4),
% 1.63/1.40 inference(avatar_split_clause,[status(thm)],[f438,f162,f156,f340])).
% 1.63/1.40 thf(f340,definition,(
% 1.63/1.40 spl1_18 <=> ! [X0 : $o] : ($true = X0)),
% 1.63/1.40 introduced(definition,[new_symbols(naming,[spl1_18])],[avatar_definition])).
% 1.63/1.40 thf(f156,definition,(
% 1.63/1.40 spl1_3 <=> (~ = f)),
% 1.63/1.40 introduced(definition,[new_symbols(naming,[spl1_3])],[avatar_definition])).
% 1.63/1.40 thf(f438,plain,(
% 1.63/1.40 ( ! [X1 : $o] : (($true = X1)) ) | (~spl1_3 | ~spl1_4)),
% 1.63/1.40 inference(duplicate_literal_removal,[status(thm)],[f437])).
% 1.63/1.40 thf(f437,plain,(
% 1.63/1.40 ( ! [X1 : $o] : (($true = X1) | ($true = X1)) ) | (~spl1_3 | ~spl1_4)),
% 1.63/1.40 inference(not_proxy_clausification,[status(thm)],[f436])).
% 1.63/1.40 thf(f436,plain,(
% 1.63/1.40 ( ! [X1 : $o] : (($true = X1) | ((~ X1) = $false)) ) | (~spl1_3 | ~spl1_4)),
% 1.63/1.40 inference(binary_proxy_clausification,[status(thm)],[f434])).
% 1.63/1.40 thf(f434,plain,(
% 1.63/1.40 ( ! [X1 : $o] : (((~ X1) = X1)) ) | (~spl1_3 | ~spl1_4)),
% 1.63/1.40 inference(beta_eta_normalization,[status(thm)],[f430])).
% 1.63/1.40 thf(f430,plain,(
% 1.63/1.40 ( ! [X1 : $o] : (((~ X1) = ((^[Y0 : $o]: (Y0)) @ X1))) ) | (~spl1_3 | ~spl1_4)),
% 1.63/1.40 inference(argument_congruence,[status(thm)],[f429])).
% 1.63/1.40 thf(f429,plain,(
% 1.63/1.40 (~ = (^[Y0 : $o]: (Y0))) | (~spl1_3 | ~spl1_4)),
% 1.63/1.40 inference(forward_demodulation,[status(thm)],[f164,f158])).
% 1.63/1.40 thf(f158,plain,(
% 1.63/1.40 (~ = f) | ~spl1_3),
% 1.63/1.40 inference(avatar_component_clause,[status(thm)],[f156])).
% 1.63/1.40 thf(f164,plain,(
% 1.63/1.40 (f = (^[Y0 : $o]: (Y0))) | ~spl1_4),
% 1.63/1.40 inference(avatar_component_clause,[status(thm)],[f162])).
% 1.63/1.40 thf(f402,plain,(
% 1.63/1.40 ~spl1_18),
% 1.63/1.40 inference(avatar_contradiction_clause,[status(thm)],[f401])).
% 1.63/1.40 thf(f401,plain,(
% 1.63/1.40 $false | ~spl1_18),
% 1.63/1.40 inference(equality_resolution,[status(thm)],[f380])).
% 1.63/1.40 thf(f380,plain,(
% 1.63/1.40 ( ! [X0 : $o] : (($false != X0)) ) | ~spl1_18),
% 1.63/1.40 inference(superposition,[status(thm)],[f5,f341])).
% 1.63/1.40 thf(f341,plain,(
% 1.63/1.40 ( ! [X0 : $o] : (($true = X0)) ) | ~spl1_18),
% 1.63/1.40 inference(avatar_component_clause,[status(thm)],[f340])).
% 1.63/1.40 thf(f5,plain,(
% 1.63/1.40 ($true != $false)),
% 1.63/1.40 introduced(definition,[],[fool_axiom])).
% 1.63/1.40 thf(f213,plain,(
% 1.63/1.40 spl1_10 | spl1_11 | spl1_3),
% 1.63/1.40 inference(avatar_split_clause,[status(thm)],[f194,f156,f210,f206])).
% 1.63/1.40 thf(f194,plain,(
% 1.63/1.40 ($true = sK5) | ((f @ sK5) = $false) | spl1_3),
% 1.63/1.40 inference(not_proxy_clausification,[status(thm)],[f193])).
% 1.63/1.40 thf(f193,plain,(
% 1.63/1.40 ($false = (~ sK5)) | ((f @ sK5) = $false) | spl1_3),
% 1.63/1.40 inference(binary_proxy_clausification,[status(thm)],[f191])).
% 1.63/1.40 thf(f191,plain,(
% 1.63/1.40 ((f @ sK5) != (~ sK5)) | spl1_3),
% 1.63/1.40 inference(negative_extensionality,[status(thm)],[f157])).
% 1.63/1.40 thf(f157,plain,(
% 1.63/1.40 (~ != f) | spl1_3),
% 1.63/1.40 inference(avatar_component_clause,[status(thm)],[f156])).
% 1.63/1.40 thf(f204,plain,(
% 1.63/1.40 spl1_8 | spl1_9 | spl1_3),
% 1.63/1.40 inference(avatar_split_clause,[status(thm)],[f195,f156,f201,f197])).
% 1.63/1.40 thf(f195,plain,(
% 1.63/1.40 ((f @ sK5) = $true) | ($false = sK5) | spl1_3),
% 1.63/1.40 inference(not_proxy_clausification,[status(thm)],[f192])).
% 1.63/1.40 thf(f192,plain,(
% 1.63/1.40 ((f @ sK5) = $true) | ($true = (~ sK5)) | spl1_3),
% 1.63/1.40 inference(binary_proxy_clausification,[status(thm)],[f191])).
% 1.63/1.40 thf(f190,plain,(
% 1.63/1.40 spl1_7 | ~spl1_3),
% 1.63/1.40 inference(avatar_split_clause,[status(thm)],[f53,f156,f185])).
% 1.63/1.40 thf(f53,plain,(
% 1.63/1.40 ( ! [X0 : $i] : (((sK4 @ X0) != X0) | (sK0 != X0) | (~ != f) | (sK0 != (sK4 @ X0))) )),
% 1.63/1.40 inference(equality_proxy_clausification,[status(thm)],[f52])).
% 1.63/1.40 thf(f52,plain,(
% 1.63/1.40 ( ! [X0 : $i] : (((~ = f) = $false) | (sK0 != X0) | ((sK4 @ X0) != X0) | (sK0 != (sK4 @ X0))) )),
% 1.63/1.40 inference(equality_proxy_clausification,[status(thm)],[f51])).
% 1.63/1.40 thf(f51,plain,(
% 1.63/1.40 ( ! [X0 : $i] : (((sK0 = (sK4 @ X0)) = $false) | ((~ = f) = $false) | (sK0 != X0) | ((sK4 @ X0) != X0)) )),
% 1.63/1.40 inference(binary_proxy_clausification,[status(thm)],[f50])).
% 1.63/1.40 thf(f50,plain,(
% 1.63/1.40 ( ! [X0 : $i] : ((((~ = f) & (sK0 = (sK4 @ X0))) = $false) | ((sK4 @ X0) != X0) | (sK0 != X0)) )),
% 1.63/1.40 inference(binary_proxy_clausification,[status(thm)],[f48])).
% 1.63/1.40 thf(f48,plain,(
% 1.63/1.40 ( ! [X0 : $i] : ((sK0 != X0) | ((sK4 @ X0) != X0) | ((((~ = f) & (sK0 = (sK4 @ X0))) | (((^[Y0 : $o]: (Y0)) = f) & (sK0 = (sK4 @ X0)))) = $false)) )),
% 1.63/1.40 inference(binary_proxy_clausification,[status(thm)],[f46])).
% 1.63/1.40 thf(f46,plain,(
% 1.63/1.40 ( ! [X0 : $i] : (((sK4 @ X0) != X0) | (sK0 != X0) | (((((~ = f) & (sK0 = (sK4 @ X0))) | (((^[Y0 : $o]: (Y0)) = f) & (sK0 = (sK4 @ X0)))) | ((sK0 = (sK4 @ X0)) & (f = (^[Y0 : $o]: ($true))))) = $false)) )),
% 1.63/1.40 inference(equality_proxy_clausification,[status(thm)],[f45])).
% 1.63/1.40 thf(f45,plain,(
% 1.63/1.40 ( ! [X0 : $i] : (((X0 = (sK4 @ X0)) = $false) | (((((~ = f) & (sK0 = (sK4 @ X0))) | (((^[Y0 : $o]: (Y0)) = f) & (sK0 = (sK4 @ X0)))) | ((sK0 = (sK4 @ X0)) & (f = (^[Y0 : $o]: ($true))))) = $false) | (sK0 != X0)) )),
% 1.63/1.40 inference(binary_proxy_clausification,[status(thm)],[f43])).
% 1.63/1.40 thf(f43,plain,(
% 1.63/1.40 ( ! [X0 : $i] : (((((((~ = f) & (sK0 = (sK4 @ X0))) | (((^[Y0 : $o]: (Y0)) = f) & (sK0 = (sK4 @ X0)))) | ((sK0 = (sK4 @ X0)) & (f = (^[Y0 : $o]: ($true))))) | ((f = (^[Y0 : $o]: ($false))) & (sK0 = (sK4 @ X0)))) = $false) | ((X0 = (sK4 @ X0)) = $false) | (sK0 != X0)) )),
% 1.63/1.40 inference(binary_proxy_clausification,[status(thm)],[f41])).
% 1.63/1.40 thf(f41,plain,(
% 1.63/1.40 ( ! [X0 : $i] : (((X0 = (sK4 @ X0)) != (((((~ = f) & (sK0 = (sK4 @ X0))) | (((^[Y0 : $o]: (Y0)) = f) & (sK0 = (sK4 @ X0)))) | ((sK0 = (sK4 @ X0)) & (f = (^[Y0 : $o]: ($true))))) | ((f = (^[Y0 : $o]: ($false))) & (sK0 = (sK4 @ X0))))) | (sK0 != X0)) )),
% 1.63/1.40 inference(beta_eta_normalization,[status(thm)],[f40])).
% 1.63/1.40 thf(f40,plain,(
% 1.63/1.40 ( ! [X0 : $i] : ((sK0 != X0) | ((X0 = (sK4 @ X0)) != ((^[Y0 : $i]: (((((~ = f) & (sK0 = Y0)) | (((^[Y1 : $o]: (Y1)) = f) & (sK0 = Y0))) | ((sK0 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((f = (^[Y1 : $o]: ($false))) & (sK0 = Y0)))) @ (sK4 @ X0)))) )),
% 1.63/1.40 inference(negative_extensionality,[status(thm)],[f32])).
% 1.63/1.40 thf(f32,plain,(
% 1.63/1.40 ( ! [X0 : $i] : (((= @ X0) != (^[Y0 : $i]: (((((~ = f) & (sK0 = Y0)) | (((^[Y1 : $o]: (Y1)) = f) & (sK0 = Y0))) | ((sK0 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((f = (^[Y1 : $o]: ($false))) & (sK0 = Y0))))) | (sK0 != X0)) )),
% 1.63/1.40 inference(constrained_superposition,[status(thm)],[f19,f20])).
% 1.63/1.40 thf(f20,plain,(
% 1.63/1.40 ( ! [X0 : $i] : (((eps @ (= @ X0)) = X0)) )),
% 1.63/1.40 inference(leibniz_equality_elimination,[status(thm)],[f17])).
% 1.63/1.40 thf(f19,plain,(
% 1.63/1.40 ((eps @ (^[Y0 : $i]: (((((~ = f) & (sK0 = Y0)) | (((^[Y1 : $o]: (Y1)) = f) & (sK0 = Y0))) | ((sK0 = Y0) & (f = (^[Y1 : $o]: ($true))))) | ((f = (^[Y1 : $o]: ($false))) & (sK0 = Y0))))) != sK0)),
% 1.63/1.40 inference(beta_eta_normalization,[status(thm)],[f18])).
% 1.63/1.40 thf(f18,plain,(
% 1.63/1.40 (sK0 != ((^[Y0 : $o > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((((~ = Y0) & (Y2 = Y5)) | (((^[Y6 : $o]: (Y6)) = Y0) & (Y3 = Y5))) | ((Y4 = Y5) & (Y0 = (^[Y6 : $o]: ($true))))) | ((Y0 = (^[Y6 : $o]: ($false))) & (Y1 = Y5)))))))))))))) @ f @ sK0 @ sK0 @ sK0 @ sK0))),
% 1.63/1.40 inference(definition_unfolding,[status(thm)],[f16,f15])).
% 1.63/1.40 thf(f15,plain,(
% 1.63/1.40 (case = (^[Y0 : $o > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((((~ = Y0) & (Y2 = Y5)) | (((^[Y6 : $o]: (Y6)) = Y0) & (Y3 = Y5))) | ((Y4 = Y5) & (Y0 = (^[Y6 : $o]: ($true))))) | ((Y0 = (^[Y6 : $o]: ($false))) & (Y1 = Y5)))))))))))))))),
% 1.63/1.40 inference(cnf_transformation,[status(thm)],[f7])).
% 1.63/1.40 thf(f7,plain,(
% 1.63/1.40 (case = (^[Y0 : $o > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((((~ = Y0) & (Y2 = Y5)) | (((^[Y6 : $o]: (Y6)) = Y0) & (Y3 = Y5))) | ((Y4 = Y5) & (Y0 = (^[Y6 : $o]: ($true))))) | ((Y0 = (^[Y6 : $o]: ($false))) & (Y1 = Y5)))))))))))))))),
% 1.63/1.40 inference(fool_elimination,[status(thm)],[f6])).
% 1.63/1.40 thf(f6,plain,(
% 1.63/1.40 ((^[X0 : $o > $o, X1 : $i, X2 : $i, X3 : $i, X4 : $i] : (eps @ (^[X5 : $i] : (((X1 = X5) & (X0 = (^[X6 : $o] : ($false)))) | ((X0 = (^[X7 : $o] : ($true))) & (X4 = X5)) | ((X3 = X5) & ((^[X8 : $o] : (X8)) = X0)) | ((X2 = X5) & (~ = X0)))))) = case)),
% 1.63/1.40 inference(rectify,[status(thm)],[f2])).
% 1.63/1.40 thf(f2,axiom,(
% 1.63/1.40 ((^[X2 : $o > $o, X1 : $i, X3 : $i, X4 : $i, X5 : $i] : (eps @ (^[X6 : $i] : (((X1 = X6) & (X2 = (^[X7 : $o] : ($false)))) | ((X2 = (^[X7 : $o] : ($true))) & (X5 = X6)) | ((X4 = X6) & ((^[X7 : $o] : (X7)) = X2)) | ((X3 = X6) & (~ = X2)))))) = case)),
% 1.63/1.40 file('/export/starexec/sandbox2/tmp/tmp.ogKD8WwFWg/DTF2THF_18640.p',caseood)).
% 1.63/1.40 thf(f16,plain,(
% 1.63/1.40 ((case @ f @ sK0 @ sK0 @ sK0 @ sK0) != sK0)),
% 1.63/1.40 inference(cnf_transformation,[status(thm)],[f14])).
% 1.63/1.40 thf(f14,plain,(
% 1.63/1.40 ((case @ f @ sK0 @ sK0 @ sK0 @ sK0) != sK0)),
% 1.63/1.40 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f12,f13])).
% 1.63/1.40 thf(f13,plain,(
% 1.63/1.40 ? [X0 : $i] : ((case @ f @ X0 @ X0 @ X0 @ X0) != X0) => ((case @ f @ sK0 @ sK0 @ sK0 @ sK0) != sK0)),
% 1.63/1.40 introduced(definition,[],[choice_axiom])).
% 1.63/1.40 thf(f12,plain,(
% 1.63/1.40 ? [X0 : $i] : ((case @ f @ X0 @ X0 @ X0 @ X0) != X0)),
% 1.63/1.40 inference(ennf_transformation,[status(thm)],[f10])).
% 1.63/1.40 thf(f10,plain,(
% 1.63/1.40 ~! [X0 : $i] : ((case @ f @ X0 @ X0 @ X0 @ X0) = X0)),
% 1.63/1.40 inference(rectify,[status(thm)],[f4])).
% 1.63/1.40 thf(f4,negated_conjecture,(
% 1.63/1.40 ~! [X1 : $i] : ((case @ f @ X1 @ X1 @ X1 @ X1) = X1)),
% 1.63/1.40 inference(negated_conjecture,[status(cth)],[f3])).
% 1.63/1.40 thf(f3,conjecture,(
% 1.63/1.40 ! [X1 : $i] : ((case @ f @ X1 @ X1 @ X1 @ X1) = X1)),
% 1.63/1.40 file('/export/starexec/sandbox2/tmp/tmp.ogKD8WwFWg/DTF2THF_18640.p',conj)).
% 1.63/1.40 thf(f189,plain,(
% 1.63/1.40 spl1_7 | ~spl1_4),
% 1.63/1.40 inference(avatar_split_clause,[status(thm)],[f56,f162,f185])).
% 1.63/1.40 thf(f56,plain,(
% 1.63/1.40 ( ! [X0 : $i] : ((sK0 != X0) | (sK0 != (sK4 @ X0)) | (f != (^[Y0 : $o]: (Y0))) | ((sK4 @ X0) != X0)) )),
% 1.63/1.40 inference(equality_proxy_clausification,[status(thm)],[f55])).
% 1.63/1.40 thf(f55,plain,(
% 1.63/1.40 ( ! [X0 : $i] : ((((^[Y0 : $o]: (Y0)) = f) = $false) | (sK0 != (sK4 @ X0)) | (sK0 != X0) | ((sK4 @ X0) != X0)) )),
% 1.63/1.40 inference(equality_proxy_clausification,[status(thm)],[f54])).
% 1.63/1.40 thf(f54,plain,(
% 1.63/1.40 ( ! [X0 : $i] : (((sK4 @ X0) != X0) | (sK0 != X0) | ((sK0 = (sK4 @ X0)) = $false) | (((^[Y0 : $o]: (Y0)) = f) = $false)) )),
% 1.63/1.40 inference(binary_proxy_clausification,[status(thm)],[f49])).
% 1.63/1.40 thf(f49,plain,(
% 1.63/1.40 ( ! [X0 : $i] : (((((^[Y0 : $o]: (Y0)) = f) & (sK0 = (sK4 @ X0))) = $false) | (sK0 != X0) | ((sK4 @ X0) != X0)) )),
% 1.63/1.40 inference(binary_proxy_clausification,[status(thm)],[f48])).
% 1.63/1.40 thf(f188,plain,(
% 1.63/1.40 ~spl1_2 | spl1_7),
% 1.63/1.40 inference(avatar_split_clause,[status(thm)],[f59,f185,f150])).
% 1.63/1.40 thf(f59,plain,(
% 1.63/1.40 ( ! [X0 : $i] : ((sK0 != X0) | (sK0 != (sK4 @ X0)) | (f != (^[Y0 : $o]: ($true))) | ((sK4 @ X0) != X0)) )),
% 1.63/1.40 inference(equality_proxy_clausification,[status(thm)],[f58])).
% 1.63/1.40 thf(f58,plain,(
% 1.63/1.40 ( ! [X0 : $i] : (((sK4 @ X0) != X0) | (sK0 != X0) | (f != (^[Y0 : $o]: ($true))) | ((sK0 = (sK4 @ X0)) = $false)) )),
% 1.63/1.40 inference(equality_proxy_clausification,[status(thm)],[f57])).
% 1.63/1.40 thf(f57,plain,(
% 1.63/1.40 ( ! [X0 : $i] : (((sK4 @ X0) != X0) | ((f = (^[Y0 : $o]: ($true))) = $false) | (sK0 != X0) | ((sK0 = (sK4 @ X0)) = $false)) )),
% 1.63/1.40 inference(binary_proxy_clausification,[status(thm)],[f47])).
% 1.63/1.40 thf(f47,plain,(
% 1.63/1.40 ( ! [X0 : $i] : ((sK0 != X0) | ($false = ((sK0 = (sK4 @ X0)) & (f = (^[Y0 : $o]: ($true))))) | ((sK4 @ X0) != X0)) )),
% 1.63/1.40 inference(binary_proxy_clausification,[status(thm)],[f46])).
% 1.63/1.40 thf(f187,plain,(
% 1.63/1.40 spl1_7 | ~spl1_5),
% 1.63/1.40 inference(avatar_split_clause,[status(thm)],[f63,f170,f185])).
% 1.63/1.40 thf(f63,plain,(
% 1.63/1.40 ( ! [X0 : $i] : ((sK0 != X0) | (sK0 != (sK4 @ X0)) | (f != (^[Y0 : $o]: ($false))) | ((sK4 @ X0) != X0)) )),
% 1.63/1.40 inference(equality_proxy_clausification,[status(thm)],[f62])).
% 1.63/1.40 thf(f62,plain,(
% 1.63/1.40 ( ! [X0 : $i] : (((sK0 = (sK4 @ X0)) = $false) | (f != (^[Y0 : $o]: ($false))) | ((sK4 @ X0) != X0) | (sK0 != X0)) )),
% 1.63/1.40 inference(equality_proxy_clausification,[status(thm)],[f61])).
% 1.63/1.40 thf(f61,plain,(
% 1.63/1.40 ( ! [X0 : $i] : ((sK0 != X0) | ((sK4 @ X0) != X0) | ((f = (^[Y0 : $o]: ($false))) = $false) | ((sK0 = (sK4 @ X0)) = $false)) )),
% 1.63/1.40 inference(binary_proxy_clausification,[status(thm)],[f60])).
% 1.63/1.40 thf(f60,plain,(
% 1.63/1.40 ( ! [X0 : $i] : (((sK4 @ X0) != X0) | (((f = (^[Y0 : $o]: ($false))) & (sK0 = (sK4 @ X0))) = $false) | (sK0 != X0)) )),
% 1.63/1.40 inference(equality_proxy_clausification,[status(thm)],[f44])).
% 1.63/1.40 thf(f44,plain,(
% 1.63/1.40 ( ! [X0 : $i] : (((X0 = (sK4 @ X0)) = $false) | (sK0 != X0) | (((f = (^[Y0 : $o]: ($false))) & (sK0 = (sK4 @ X0))) = $false)) )),
% 1.63/1.40 inference(binary_proxy_clausification,[status(thm)],[f43])).
% 1.63/1.40 thf(f167,plain,(
% 1.63/1.40 spl1_4 | spl1_1),
% 1.63/1.40 inference(avatar_split_clause,[status(thm)],[f119,f147,f162])).
% 1.63/1.40 thf(f119,plain,(
% 1.63/1.40 ( ! [X0 : $i] : (((sK4 @ X0) = X0) | (sK0 != X0) | (sK0 = (sK4 @ X0)) | (f = (^[Y0 : $o]: (Y0)))) )),
% 1.63/1.40 inference(duplicate_literal_removal,[status(thm)],[f118])).
% 1.63/1.40 thf(f118,plain,(
% 1.63/1.40 ( ! [X0 : $i] : ((sK0 = (sK4 @ X0)) | (sK0 != X0) | (sK0 = (sK4 @ X0)) | ((sK4 @ X0) = X0) | (f = (^[Y0 : $o]: (Y0)))) )),
% 1.63/1.40 inference(equality_proxy_clausification,[status(thm)],[f117])).
% 1.63/1.40 thf(f117,plain,(
% 1.63/1.40 ( ! [X0 : $i] : ((sK0 != X0) | ((sK0 = (sK4 @ X0)) = $true) | (sK0 = (sK4 @ X0)) | (f = (^[Y0 : $o]: (Y0))) | ((sK4 @ X0) = X0)) )),
% 1.63/1.40 inference(duplicate_literal_removal,[status(thm)],[f112])).
% 1.63/1.40 thf(f112,plain,(
% 1.63/1.40 ( ! [X0 : $i] : ((f = (^[Y0 : $o]: (Y0))) | (sK0 != X0) | ((sK0 = (sK4 @ X0)) = $true) | ((sK4 @ X0) = X0) | (sK0 = (sK4 @ X0)) | ((sK0 = (sK4 @ X0)) = $true)) )),
% 1.63/1.40 inference(binary_proxy_clausification,[status(thm)],[f111])).
% 1.63/1.40 thf(f111,plain,(
% 1.63/1.40 ( ! [X0 : $i] : ((sK0 = (sK4 @ X0)) | (f = (^[Y0 : $o]: (Y0))) | (sK0 != X0) | ($true = ((~ = f) & (sK0 = (sK4 @ X0)))) | ((sK0 = (sK4 @ X0)) = $true) | ((sK4 @ X0) = X0)) )),
% 1.63/1.40 inference(binary_proxy_clausification,[status(thm)],[f109])).
% 1.63/1.40 thf(f109,plain,(
% 1.63/1.40 ( ! [X0 : $i] : ((sK0 = (sK4 @ X0)) | (f = (^[Y0 : $o]: (Y0))) | ($true = ((sK0 = (sK4 @ X0)) & (f = (^[Y0 : $o]: ($true))))) | ((sK4 @ X0) = X0) | (sK0 != X0) | ($true = ((~ = f) & (sK0 = (sK4 @ X0))))) )),
% 1.63/1.40 inference(equality_proxy_clausification,[status(thm)],[f108])).
% 1.63/1.40 thf(f108,plain,(
% 1.63/1.40 ( ! [X0 : $i] : (((sK4 @ X0) = X0) | ($true = ((^[Y0 : $o]: (Y0)) = f)) | ($true = ((sK0 = (sK4 @ X0)) & (f = (^[Y0 : $o]: ($true))))) | (sK0 != X0) | ($true = ((~ = f) & (sK0 = (sK4 @ X0)))) | (sK0 = (sK4 @ X0))) )),
% 1.63/1.40 inference(binary_proxy_clausification,[status(thm)],[f106])).
% 1.63/1.40 thf(f106,plain,(
% 1.63/1.40 ( ! [X0 : $i] : (((((^[Y0 : $o]: (Y0)) = f) & (sK0 = (sK4 @ X0))) = $true) | ($true = ((~ = f) & (sK0 = (sK4 @ X0)))) | (sK0 = (sK4 @ X0)) | ((sK4 @ X0) = X0) | ($true = ((sK0 = (sK4 @ X0)) & (f = (^[Y0 : $o]: ($true))))) | (sK0 != X0)) )),
% 1.63/1.40 inference(equality_proxy_clausification,[status(thm)],[f105])).
% 1.63/1.40 thf(f105,plain,(
% 1.63/1.40 ( ! [X0 : $i] : (((sK0 = (sK4 @ X0)) = $true) | ($true = ((~ = f) & (sK0 = (sK4 @ X0)))) | (sK0 != X0) | ((((^[Y0 : $o]: (Y0)) = f) & (sK0 = (sK4 @ X0))) = $true) | ((sK4 @ X0) = X0) | ($true = ((sK0 = (sK4 @ X0)) & (f = (^[Y0 : $o]: ($true)))))) )),
% 1.63/1.40 inference(binary_proxy_clausification,[status(thm)],[f104])).
% 1.63/1.40 thf(f104,plain,(
% 1.63/1.40 ( ! [X0 : $i] : ((sK0 != X0) | ((((~ = f) & (sK0 = (sK4 @ X0))) | (((^[Y0 : $o]: (Y0)) = f) & (sK0 = (sK4 @ X0)))) = $true) | ((sK4 @ X0) = X0) | ($true = ((sK0 = (sK4 @ X0)) & (f = (^[Y0 : $o]: ($true))))) | ((sK0 = (sK4 @ X0)) = $true)) )),
% 1.63/1.40 inference(binary_proxy_clausification,[status(thm)],[f66])).
% 1.63/1.40 thf(f66,plain,(
% 1.63/1.40 ( ! [X0 : $i] : ((((((~ = f) & (sK0 = (sK4 @ X0))) | (((^[Y0 : $o]: (Y0)) = f) & (sK0 = (sK4 @ X0)))) | ((sK0 = (sK4 @ X0)) & (f = (^[Y0 : $o]: ($true))))) = $true) | ((sK0 = (sK4 @ X0)) = $true) | ((sK4 @ X0) = X0) | (sK0 != X0)) )),
% 1.63/1.40 inference(binary_proxy_clausification,[status(thm)],[f65])).
% 1.63/1.40 thf(f65,plain,(
% 1.63/1.40 ( ! [X0 : $i] : (($true = ((f = (^[Y0 : $o]: ($false))) & (sK0 = (sK4 @ X0)))) | (((((~ = f) & (sK0 = (sK4 @ X0))) | (((^[Y0 : $o]: (Y0)) = f) & (sK0 = (sK4 @ X0)))) | ((sK0 = (sK4 @ X0)) & (f = (^[Y0 : $o]: ($true))))) = $true) | ((sK4 @ X0) = X0) | (sK0 != X0)) )),
% 1.63/1.40 inference(equality_proxy_clausification,[status(thm)],[f64])).
% 1.63/1.40 thf(f64,plain,(
% 1.63/1.40 ( ! [X0 : $i] : ((sK0 != X0) | ((X0 = (sK4 @ X0)) = $true) | ($true = ((f = (^[Y0 : $o]: ($false))) & (sK0 = (sK4 @ X0)))) | (((((~ = f) & (sK0 = (sK4 @ X0))) | (((^[Y0 : $o]: (Y0)) = f) & (sK0 = (sK4 @ X0)))) | ((sK0 = (sK4 @ X0)) & (f = (^[Y0 : $o]: ($true))))) = $true)) )),
% 1.63/1.40 inference(binary_proxy_clausification,[status(thm)],[f42])).
% 1.63/1.40 thf(f42,plain,(
% 1.63/1.40 ( ! [X0 : $i] : (((((((~ = f) & (sK0 = (sK4 @ X0))) | (((^[Y0 : $o]: (Y0)) = f) & (sK0 = (sK4 @ X0)))) | ((sK0 = (sK4 @ X0)) & (f = (^[Y0 : $o]: ($true))))) | ((f = (^[Y0 : $o]: ($false))) & (sK0 = (sK4 @ X0)))) = $true) | ((X0 = (sK4 @ X0)) = $true) | (sK0 != X0)) )),
% 1.63/1.40 inference(binary_proxy_clausification,[status(thm)],[f41])).
% 1.63/1.40 thf(f160,plain,(
% 1.63/1.40 spl1_3 | spl1_1),
% 1.63/1.40 inference(avatar_split_clause,[status(thm)],[f135,f147,f156])).
% 1.63/1.40 thf(f135,plain,(
% 1.63/1.40 ( ! [X0 : $i] : (((sK4 @ X0) = X0) | (sK0 != X0) | (~ = f) | (sK0 = (sK4 @ X0))) )),
% 1.63/1.40 inference(duplicate_literal_removal,[status(thm)],[f134])).
% 1.63/1.40 thf(f134,plain,(
% 1.63/1.40 ( ! [X0 : $i] : ((~ = f) | (sK0 != X0) | (sK0 = (sK4 @ X0)) | ((sK4 @ X0) = X0) | (sK0 = (sK4 @ X0))) )),
% 1.63/1.40 inference(equality_proxy_clausification,[status(thm)],[f133])).
% 1.63/1.40 thf(f133,plain,(
% 1.63/1.40 ( ! [X0 : $i] : ((~ = f) | (sK0 != X0) | ((sK0 = (sK4 @ X0)) = $true) | (sK0 = (sK4 @ X0)) | ((sK4 @ X0) = X0)) )),
% 1.63/1.40 inference(binary_proxy_clausification,[status(thm)],[f131])).
% 1.63/1.40 thf(f131,plain,(
% 1.63/1.40 ( ! [X0 : $i] : (($true = ((sK0 = (sK4 @ X0)) & (f = (^[Y0 : $o]: ($true))))) | (sK0 = (sK4 @ X0)) | (~ = f) | (sK0 != X0) | ((sK4 @ X0) = X0)) )),
% 1.63/1.40 inference(equality_proxy_clausification,[status(thm)],[f130])).
% 1.63/1.40 thf(f130,plain,(
% 1.63/1.40 ( ! [X0 : $i] : (((~ = f) = $true) | (sK0 = (sK4 @ X0)) | (sK0 != X0) | ($true = ((sK0 = (sK4 @ X0)) & (f = (^[Y0 : $o]: ($true))))) | ((sK4 @ X0) = X0)) )),
% 1.63/1.40 inference(duplicate_literal_removal,[status(thm)],[f129])).
% 1.63/1.40 thf(f129,plain,(
% 1.63/1.40 ( ! [X0 : $i] : (($true = ((sK0 = (sK4 @ X0)) & (f = (^[Y0 : $o]: ($true))))) | (sK0 = (sK4 @ X0)) | ((sK4 @ X0) = X0) | ((~ = f) = $true) | (sK0 = (sK4 @ X0)) | (sK0 != X0)) )),
% 1.63/1.40 inference(equality_proxy_clausification,[status(thm)],[f128])).
% 1.63/1.40 thf(f128,plain,(
% 1.63/1.40 ( ! [X0 : $i] : (((sK0 = (sK4 @ X0)) = $true) | ((sK4 @ X0) = X0) | ($true = ((sK0 = (sK4 @ X0)) & (f = (^[Y0 : $o]: ($true))))) | (sK0 != X0) | ((~ = f) = $true) | (sK0 = (sK4 @ X0))) )),
% 1.63/1.40 inference(binary_proxy_clausification,[status(thm)],[f107])).
% 1.63/1.40 thf(f107,plain,(
% 1.63/1.40 ( ! [X0 : $i] : (((sK4 @ X0) = X0) | ($true = ((~ = f) & (sK0 = (sK4 @ X0)))) | ((sK0 = (sK4 @ X0)) = $true) | (sK0 = (sK4 @ X0)) | ($true = ((sK0 = (sK4 @ X0)) & (f = (^[Y0 : $o]: ($true))))) | (sK0 != X0)) )),
% 1.63/1.40 inference(binary_proxy_clausification,[status(thm)],[f106])).
% 1.63/1.40 % SZS output end Proof for DTF2THF_18640
% 1.63/1.40 % (18836)------------------------------
% 1.63/1.40 % (18836)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.40 % (18836)Termination reason: Refutation
% 1.63/1.40
% 1.63/1.40 % (18836)Memory used [KB]: 5884
% 1.63/1.40 % (18836)Time elapsed: 0.050 s
% 1.63/1.40 % (18836)Instructions burned: 59 (million)
% 1.63/1.40 % (18836)------------------------------
% 1.63/1.40 % (18836)------------------------------
% 1.63/1.40 % (18802)Success in time 0.126 s
%------------------------------------------------------------------------------