%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO035^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/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 09:53:11 AM UTC 2026
% Result : Theorem 1.48s 1.29s
% Output : Refutation 1.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 4
% Syntax : Number of formulae : 37 ( 25 unt; 0 typ; 0 def)
% Number of atoms : 198 ( 79 equ; 10 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 156 ( 12 ~; 5 |; 4 &; 106 @)
% ( 0 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 49 ( 49 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 6 usr; 6 con; 0-2 aty)
% ( 8 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 73 ( 50 ^; 19 !; 4 ?; 73 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
leibeq1: $i > $i > $o ).
thf(func_def_2,type,
leibeq2: ( $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_15,type,
sK3: $i > $o ).
thf(func_def_17,type,
ph4:
!>[X0: $tType] : X0 ).
thf(f56,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f55]) ).
thf(f55,plain,
$false = $true,
inference(forward_demodulation,[status(thm)],[f54,f28]) ).
thf(f28,plain,
( $false
= ( sK3 @ sK0 ) ),
inference(binary_proxy_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
( ( ( sK3 @ sK1 )
=> ( sK3 @ sK0 ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f26]) ).
thf(f26,plain,
( $false
= ( ^ [Y0: $i > $o] :
( ( Y0 @ sK1 )
=> ( Y0 @ sK0 ) )
@ sK3 ) ),
inference(sigma_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( Y0 @ sK1 )
=> ( Y0 @ sK0 ) ) )
!= $true ),
inference(beta_eta_normalization,[status(thm)],[f19]) ).
thf(f19,plain,
( ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) )
@ sK1
@ sK0 )
!= $true ),
inference(definition_unfolding,[status(thm)],[f18,f15]) ).
thf(f15,plain,
( leibeq1
= ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( leibeq1
= ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ^ [X0: $i,X1: $i] :
! [X2: $i > $o] :
( ( X2 @ X0 )
=> ( X2 @ X1 ) ) )
= leibeq1 ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( ^ [X0: $i,X1: $i] :
! [X2: $i > $o] :
( ( X2 @ X0 )
=> ( X2 @ X1 ) ) )
= leibeq1 ),
file('/export/starexec/sandbox/tmp/tmp.jDfm4zRQMc/DTF2THF_8119.p',leibeq1) ).
thf(f18,plain,
( ( leibeq1 @ sK1 @ sK0 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ( ( leibeq1 @ sK1 @ sK0 )
!= $true )
& ( ( leibeq2
@ ^ [Y0: $i] : ( sK1 = Y0 )
@ ^ [Y0: $i] : ( sK0 = Y0 ) )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f12,f13]) ).
thf(f13,plain,
( ? [X0: $i,X1: $i] :
( ( ( leibeq1 @ X1 @ X0 )
!= $true )
& ( ( leibeq2
@ ^ [Y0: $i] : ( X1 = Y0 )
@ ^ [Y0: $i] : ( X0 = Y0 ) )
= $true ) )
=> ( ( ( leibeq1 @ sK1 @ sK0 )
!= $true )
& ( ( leibeq2
@ ^ [Y0: $i] : ( sK1 = Y0 )
@ ^ [Y0: $i] : ( sK0 = Y0 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
? [X0: $i,X1: $i] :
( ( ( leibeq1 @ X1 @ X0 )
!= $true )
& ( ( leibeq2
@ ^ [Y0: $i] : ( X1 = Y0 )
@ ^ [Y0: $i] : ( X0 = Y0 ) )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
~ ! [X0: $i,X1: $i] :
( ( ( leibeq2
@ ^ [Y0: $i] : ( X1 = Y0 )
@ ^ [Y0: $i] : ( X0 = Y0 ) )
= $true )
=> ( ( leibeq1 @ X1 @ X0 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
~ ! [X0: $i,X1: $i] :
( ( leibeq2
@ ^ [X2: $i] : ( X1 = X2 )
@ ^ [X3: $i] : ( X0 = X3 ) )
=> ( leibeq1 @ X1 @ X0 ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ! [X1: $i,X0: $i] :
( ( leibeq2
@ ^ [X3: $i] : ( X0 = X3 )
@ ^ [X3: $i] : ( X1 = X3 ) )
=> ( leibeq1 @ X0 @ X1 ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
! [X1: $i,X0: $i] :
( ( leibeq2
@ ^ [X3: $i] : ( X0 = X3 )
@ ^ [X3: $i] : ( X1 = X3 ) )
=> ( leibeq1 @ X0 @ X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.jDfm4zRQMc/DTF2THF_8119.p',conj) ).
thf(f54,plain,
( $true
= ( sK3 @ sK0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f51]) ).
thf(f51,plain,
( ( sK1 != sK1 )
| ( $true
= ( sK3 @ sK0 ) ) ),
inference(superposition,[status(thm)],[f29,f46]) ).
thf(f46,plain,
! [X1: $i] :
( ( sK0 = X1 )
| ( sK1 != X1 ) ),
inference(equality_proxy_clausification,[status(thm)],[f45]) ).
thf(f45,plain,
! [X1: $i] :
( ( sK0 = X1 )
| ( $false
= ( sK1 = X1 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f44]) ).
thf(f44,plain,
! [X1: $i] :
( ( ( sK0 = X1 )
= $true )
| ( $false
= ( sK1 = X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f41]) ).
thf(f41,plain,
! [X1: $i] :
( ( sK1 = X1 )
= ( sK0 = X1 ) ),
inference(argument_congruence,[status(thm)],[f31]) ).
thf(f31,plain,
( ( (=) @ sK0 )
= ( (=) @ sK1 ) ),
inference(leibniz_equality_elimination,[status(thm)],[f24]) ).
thf(f24,plain,
! [X1: ( $i > $o ) > $o] :
( ( $false
= ( X1 @ ( (=) @ sK1 ) ) )
| ( ( X1 @ ( (=) @ sK0 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
! [X1: ( $i > $o ) > $o] :
( ( ( X1 @ ( (=) @ sK1 ) )
=> ( X1 @ ( (=) @ sK0 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f22]) ).
thf(f22,plain,
! [X1: ( $i > $o ) > $o] :
( ( ^ [Y0: ( $i > $o ) > $o] :
( ( Y0 @ ( (=) @ sK1 ) )
=> ( Y0 @ ( (=) @ sK0 ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
( ( !! @ ( ( $i > $o ) > $o )
@ ^ [Y0: ( $i > $o ) > $o] :
( ( Y0 @ ( (=) @ sK1 ) )
=> ( Y0 @ ( (=) @ sK0 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f20]) ).
thf(f20,plain,
( ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ ( ( $i > $o ) > $o )
@ ^ [Y2: ( $i > $o ) > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) )
@ ^ [Y0: $i] : ( sK1 = Y0 )
@ ^ [Y0: $i] : ( sK0 = Y0 ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f17,f16]) ).
thf(f16,plain,
( leibeq2
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ ( ( $i > $o ) > $o )
@ ^ [Y2: ( $i > $o ) > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( leibeq2
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ ( ( $i > $o ) > $o )
@ ^ [Y2: ( $i > $o ) > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
( leibeq2
= ( ^ [X0: $i > $o,X1: $i > $o] :
! [X2: ( $i > $o ) > $o] :
( ( X2 @ X0 )
=> ( X2 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( leibeq2
= ( ^ [X0: $i > $o,X1: $i > $o] :
! [X2: ( $i > $o ) > $o] :
( ( X2 @ X0 )
=> ( X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.jDfm4zRQMc/DTF2THF_8119.p',leibeq2) ).
thf(f17,plain,
( ( leibeq2
@ ^ [Y0: $i] : ( sK1 = Y0 )
@ ^ [Y0: $i] : ( sK0 = Y0 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f29,plain,
( ( sK3 @ sK1 )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO035^1 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n010.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 14:22:03 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.29/0.46 ---- Original DTF file ---
% 0.29/0.46 thf(spec,logic,$$dhol).
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 % File : SYO035^1 : TPTP v9.2.1. Released v3.7.0.
% 0.29/0.46 % Domain : Syntactic
% 0.29/0.46 % Problem : Higher-order unification does not always provide projection terms
% 0.29/0.46 % Version : Especial.
% 0.29/0.46 % English :
% 0.29/0.46
% 0.29/0.46 % Refs : [BB05] Benzmueller & Brown (2005), A Structured Set of Higher
% 0.29/0.46 % : [Ben09] Benzmueller (2009), Email to Geoff Sutcliffe
% 0.29/0.46 % Source : [Ben09]
% 0.29/0.46 % Names : Example 30 [BB05]
% 0.29/0.46
% 0.29/0.46 % Status : Theorem
% 0.29/0.46 % Rating : 0.00 v9.0.0, 0.10 v8.2.0, 0.31 v8.1.0, 0.27 v7.5.0, 0.00 v7.4.0, 0.22 v7.2.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.29 v6.1.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0, 0.00 v3.7.0
% 0.29/0.46 % Syntax : Number of formulae : 5 ( 2 unt; 2 typ; 2 def)
% 0.29/0.46 % Number of atoms : 8 ( 4 equ; 0 cnn)
% 0.29/0.46 % Maximal formula atoms : 4 ( 2 avg)
% 0.29/0.46 % Number of connectives : 11 ( 0 ~; 0 |; 0 &; 8 @)
% 0.29/0.46 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.29/0.46 % Maximal formula depth : 7 ( 3 avg)
% 0.29/0.46 % Number of types : 2 ( 0 usr)
% 0.29/0.46 % Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% 0.29/0.46 % Number of symbols : 3 ( 2 usr; 0 con; 2-2 aty)
% 0.29/0.46 % Number of variables : 10 ( 6 ^; 4 !; 0 ?; 10 :)
% 0.29/0.46 % SPC : TH0_THM_EQU_NAR
% 0.29/0.46
% 0.29/0.46 % Comments : Requires set comprehension, and set instantiation
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 thf(leibeq1_type,type,
% 0.29/0.46 leibeq1: $i > $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(leibeq1,definition,
% 0.29/0.46 ( leibeq1
% 0.29/0.46 = ( ^ [X: $i,Y: $i] :
% 0.29/0.46 ! [P: $i > $o] :
% 0.29/0.46 ( ( P @ X )
% 0.29/0.46 => ( P @ Y ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(leibeq2_type,type,
% 0.29/0.46 leibeq2: ( $i > $o ) > ( $i > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(leibeq2,definition,
% 0.29/0.46 ( leibeq2
% 0.29/0.46 = ( ^ [X: $i > $o,Y: $i > $o] :
% 0.29/0.46 ! [P: ( $i > $o ) > $o] :
% 0.29/0.46 ( ( P @ X )
% 0.29/0.46 => ( P @ Y ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(conj,conjecture,
% 0.29/0.46 ! [X: $i,Y: $i] :
% 0.29/0.46 ( ( leibeq2
% 0.29/0.46 @ ^ [Z: $i] : ( Z = X )
% 0.29/0.46 @ ^ [Z: $i] : ( Z = Y ) )
% 0.29/0.46 => ( leibeq1 @ X @ Y ) ) ).
% 0.29/0.46
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 ------------------------
% 1.48/1.25 ---- Embedded in THF ---
% 1.48/1.25 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.48/1.25 %%% Generated on Tue Feb 24 14:22:04 EST 2026
% 1.48/1.25 %%% using '$$dhol' embedding, version 1.3.0.
% 1.48/1.25 %%% Logic specification used:
% 1.48/1.25 %%% thf(spec, logic, $$dhol).
% 1.48/1.25
% 1.48/1.25 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.jDfm4zRQMc/DTF2DTF8119.p
% See solution above
% 1.48/1.25 ------------------------
% 1.48/1.26 ---- Cleaned THF ---
% 1.48/1.26 thf(leibeq1_type,type,
% 1.48/1.26 leibeq1: $i > $i > $o ).
% 1.48/1.26
% 1.48/1.26 thf(leibeq1,definition,
% 1.48/1.26 ( leibeq1
% 1.48/1.26 = ( ^ [X: $i,Y: $i] :
% 1.48/1.26 ! [P: $i > $o] :
% 1.48/1.26 ( ( P @ X )
% 1.48/1.26 => ( P @ Y ) ) ) ) ).
% 1.48/1.26
% 1.48/1.26 thf(leibeq2_type,type,
% 1.48/1.26 leibeq2: ( $i > $o ) > ( $i > $o ) > $o ).
% 1.48/1.26
% 1.48/1.26 thf(leibeq2,definition,
% 1.48/1.26 ( leibeq2
% 1.48/1.26 = ( ^ [X: $i > $o,Y: $i > $o] :
% 1.48/1.26 ! [P: ( $i > $o ) > $o] :
% 1.48/1.26 ( ( P @ X )
% 1.48/1.26 => ( P @ Y ) ) ) ) ).
% 1.48/1.26
% 1.48/1.26 thf(conj,conjecture,
% 1.48/1.26 ! [X: $i,Y: $i] :
% 1.48/1.26 ( ( leibeq2
% 1.48/1.26 @ ^ [Z: $i] : ( Z = X )
% 1.48/1.26 @ ^ [Z: $i] : ( Z = Y ) )
% 1.48/1.26 => ( leibeq1 @ X @ Y ) ) ).
% 1.48/1.26 ------------------------
% 1.48/1.28 % (8396)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_8119 for (2999ds/2Mi)
% 1.48/1.28 % (8395)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_8119 for (2999ds/2Mi)
% 1.48/1.28 % (8395)Instruction limit reached!
% 1.48/1.28 % (8395)------------------------------
% 1.48/1.28 % (8395)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.28 % (8395)Termination reason: Unknown
% 1.48/1.28 % (8395)Termination phase: Saturation
% 1.48/1.28
% 1.48/1.28 % (8395)Memory used [KB]: 5373
% 1.48/1.28 % (8395)Time elapsed: 0.002 s
% 1.48/1.28 % (8395)Instructions burned: 2 (million)
% 1.48/1.28 % (8395)------------------------------
% 1.48/1.28 % (8395)------------------------------
% 1.48/1.28 % (8396)Instruction limit reached!
% 1.48/1.28 % (8396)------------------------------
% 1.48/1.28 % (8396)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.28 % (8396)Termination reason: Unknown
% 1.48/1.28 % (8396)Termination phase: Saturation
% 1.48/1.28
% 1.48/1.28 % (8396)Memory used [KB]: 5500
% 1.48/1.28 % (8396)Time elapsed: 0.003 s
% 1.48/1.28 % (8396)Instructions burned: 3 (million)
% 1.48/1.28 % (8396)------------------------------
% 1.48/1.28 % (8396)------------------------------
% 1.48/1.28 % (8392)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_8119 for (2999ds/183Mi)
% 1.48/1.28 % (8393)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_8119 for (2999ds/4Mi)
% 1.48/1.28 % (8394)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_8119 for (2999ds/27Mi)
% 1.48/1.28 % (8397)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_8119 for (2999ds/275Mi)
% 1.48/1.28 % (8398)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_8119 for (2999ds/18Mi)
% 1.48/1.29 % (8394)Refutation not found, incomplete strategy
% 1.48/1.29 % (8394)------------------------------
% 1.48/1.29 % (8394)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.29 % (8394)Termination reason: Refutation not found, incomplete strategy
% 1.48/1.29
% 1.48/1.29
% 1.48/1.29 % (8394)Memory used [KB]: 5500
% 1.48/1.29 % (8394)Time elapsed: 0.004 s
% 1.48/1.29 % (8394)Instructions burned: 2 (million)
% 1.48/1.29 % (8394)------------------------------
% 1.48/1.29 % (8394)------------------------------
% 1.48/1.29 % (8393)Instruction limit reached!
% 1.48/1.29 % (8393)------------------------------
% 1.48/1.29 % (8393)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.29 % (8393)Termination reason: Unknown
% 1.48/1.29 % (8393)Termination phase: Saturation
% 1.48/1.29
% 1.48/1.29 % (8393)Memory used [KB]: 5500
% 1.48/1.29 % (8393)Time elapsed: 0.005 s
% 1.48/1.29 % (8393)Instructions burned: 4 (million)
% 1.48/1.29 % (8393)------------------------------
% 1.48/1.29 % (8393)------------------------------
% 1.48/1.29 % (8397)First to succeed.
% 1.48/1.29 % (8400)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_8119 for (2999ds/37Mi)
% 1.48/1.29 % (8399)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_8119 for (2999ds/3Mi)
% 1.48/1.29 % (8398)Also succeeded, but the first one will report.
% 1.48/1.29 % (8399)Refutation not found, incomplete strategy
% 1.48/1.29 % (8399)------------------------------
% 1.48/1.29 % (8399)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.29 % (8399)Termination reason: Refutation not found, incomplete strategy
% 1.48/1.29
% 1.48/1.29
% 1.48/1.29 % (8399)Memory used [KB]: 5500
% 1.48/1.29 % (8399)Time elapsed: 0.001 s
% 1.48/1.29 % (8399)Instructions burned: 1 (million)
% 1.48/1.29 % (8399)------------------------------
% 1.48/1.29 % (8399)------------------------------
% 1.48/1.29 % (8397)Refutation found. Thanks to Tanya!
% 1.48/1.29 % SZS status Theorem for DTF2THF_8119
% 1.48/1.29 % SZS output start Proof for DTF2THF_8119
% 1.48/1.29 thf(func_def_0, type, leibeq1: $i > $i > $o).
% 1.48/1.29 thf(func_def_2, type, leibeq2: ($i > $o) > ($i > $o) > $o).
% 1.48/1.29 thf(func_def_15, type, sK3: $i > $o).
% 1.48/1.29 thf(func_def_17, type, ph4: !>[X0: $tType]:(X0)).
% 1.48/1.29 thf(f56,plain,(
% 1.48/1.29 $false),
% 1.48/1.29 inference(trivial_inequality_removal,[status(thm)],[f55])).
% 1.48/1.29 thf(f55,plain,(
% 1.48/1.29 ($false = $true)),
% 1.48/1.29 inference(forward_demodulation,[status(thm)],[f54,f28])).
% 1.48/1.29 thf(f28,plain,(
% 1.48/1.29 ($false = (sK3 @ sK0))),
% 1.48/1.29 inference(binary_proxy_clausification,[status(thm)],[f27])).
% 1.48/1.29 thf(f27,plain,(
% 1.48/1.29 (((sK3 @ sK1) => (sK3 @ sK0)) = $false)),
% 1.48/1.29 inference(beta_eta_normalization,[status(thm)],[f26])).
% 1.48/1.29 thf(f26,plain,(
% 1.48/1.29 ($false = ((^[Y0 : $i > $o]: ((Y0 @ sK1) => (Y0 @ sK0))) @ sK3))),
% 1.48/1.29 inference(sigma_clausification,[status(thm)],[f25])).
% 1.48/1.29 thf(f25,plain,(
% 1.48/1.29 ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((Y0 @ sK1) => (Y0 @ sK0)))) != $true)),
% 1.48/1.29 inference(beta_eta_normalization,[status(thm)],[f19])).
% 1.48/1.29 thf(f19,plain,(
% 1.48/1.29 (((^[Y0 : $i]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))) @ sK1 @ sK0) != $true)),
% 1.48/1.29 inference(definition_unfolding,[status(thm)],[f18,f15])).
% 1.48/1.29 thf(f15,plain,(
% 1.48/1.29 (leibeq1 = (^[Y0 : $i]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))))),
% 1.48/1.29 inference(cnf_transformation,[status(thm)],[f7])).
% 1.48/1.29 thf(f7,plain,(
% 1.48/1.29 (leibeq1 = (^[Y0 : $i]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))))),
% 1.48/1.29 inference(fool_elimination,[status(thm)],[f6])).
% 1.48/1.29 thf(f6,plain,(
% 1.48/1.29 ((^[X0 : $i, X1 : $i] : (! [X2 : $i > $o] : ((X2 @ X0) => (X2 @ X1)))) = leibeq1)),
% 1.48/1.29 inference(rectify,[status(thm)],[f1])).
% 1.48/1.29 thf(f1,axiom,(
% 1.48/1.29 ((^[X0 : $i, X1 : $i] : (! [X2 : $i > $o] : ((X2 @ X0) => (X2 @ X1)))) = leibeq1)),
% 1.48/1.29 file('/export/starexec/sandbox/tmp/tmp.jDfm4zRQMc/DTF2THF_8119.p',leibeq1)).
% 1.48/1.29 thf(f18,plain,(
% 1.48/1.29 ((leibeq1 @ sK1 @ sK0) != $true)),
% 1.48/1.29 inference(cnf_transformation,[status(thm)],[f14])).
% 1.48/1.29 thf(f14,plain,(
% 1.48/1.29 ((leibeq1 @ sK1 @ sK0) != $true) & ((leibeq2 @ (^[Y0 : $i]: (sK1 = Y0)) @ (^[Y0 : $i]: (sK0 = Y0))) = $true)),
% 1.48/1.29 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f12,f13])).
% 1.48/1.29 thf(f13,plain,(
% 1.48/1.29 ? [X0 : $i,X1 : $i] : (((leibeq1 @ X1 @ X0) != $true) & ((leibeq2 @ (^[Y0 : $i]: (X1 = Y0)) @ (^[Y0 : $i]: (X0 = Y0))) = $true)) => (((leibeq1 @ sK1 @ sK0) != $true) & ((leibeq2 @ (^[Y0 : $i]: (sK1 = Y0)) @ (^[Y0 : $i]: (sK0 = Y0))) = $true))),
% 1.48/1.29 introduced(definition,[],[choice_axiom])).
% 1.48/1.29 thf(f12,plain,(
% 1.48/1.29 ? [X0 : $i,X1 : $i] : (((leibeq1 @ X1 @ X0) != $true) & ((leibeq2 @ (^[Y0 : $i]: (X1 = Y0)) @ (^[Y0 : $i]: (X0 = Y0))) = $true))),
% 1.48/1.29 inference(ennf_transformation,[status(thm)],[f11])).
% 1.48/1.29 thf(f11,plain,(
% 1.48/1.29 ~! [X0 : $i,X1 : $i] : (((leibeq2 @ (^[Y0 : $i]: (X1 = Y0)) @ (^[Y0 : $i]: (X0 = Y0))) = $true) => ((leibeq1 @ X1 @ X0) = $true))),
% 1.48/1.29 inference(fool_elimination,[status(thm)],[f10])).
% 1.48/1.29 thf(f10,plain,(
% 1.48/1.29 ~! [X0 : $i,X1 : $i] : ((leibeq2 @ (^[X2 : $i] : ((X1 = X2))) @ (^[X3 : $i] : ((X0 = X3)))) => (leibeq1 @ X1 @ X0))),
% 1.48/1.29 inference(rectify,[status(thm)],[f4])).
% 1.48/1.29 thf(f4,negated_conjecture,(
% 1.48/1.29 ~! [X1 : $i,X0 : $i] : ((leibeq2 @ (^[X3 : $i] : ((X0 = X3))) @ (^[X3 : $i] : ((X1 = X3)))) => (leibeq1 @ X0 @ X1))),
% 1.48/1.29 inference(negated_conjecture,[status(cth)],[f3])).
% 1.48/1.29 thf(f3,conjecture,(
% 1.48/1.29 ! [X1 : $i,X0 : $i] : ((leibeq2 @ (^[X3 : $i] : ((X0 = X3))) @ (^[X3 : $i] : ((X1 = X3)))) => (leibeq1 @ X0 @ X1))),
% 1.48/1.29 file('/export/starexec/sandbox/tmp/tmp.jDfm4zRQMc/DTF2THF_8119.p',conj)).
% 1.48/1.29 thf(f54,plain,(
% 1.48/1.29 ($true = (sK3 @ sK0))),
% 1.48/1.29 inference(trivial_inequality_removal,[status(thm)],[f51])).
% 1.48/1.29 thf(f51,plain,(
% 1.48/1.29 (sK1 != sK1) | ($true = (sK3 @ sK0))),
% 1.48/1.29 inference(superposition,[status(thm)],[f29,f46])).
% 1.48/1.29 thf(f46,plain,(
% 1.48/1.29 ( ! [X1 : $i] : ((sK0 = X1) | (sK1 != X1)) )),
% 1.48/1.29 inference(equality_proxy_clausification,[status(thm)],[f45])).
% 1.48/1.29 thf(f45,plain,(
% 1.48/1.29 ( ! [X1 : $i] : ((sK0 = X1) | ($false = (sK1 = X1))) )),
% 1.48/1.29 inference(equality_proxy_clausification,[status(thm)],[f44])).
% 1.48/1.29 thf(f44,plain,(
% 1.48/1.29 ( ! [X1 : $i] : (((sK0 = X1) = $true) | ($false = (sK1 = X1))) )),
% 1.48/1.29 inference(binary_proxy_clausification,[status(thm)],[f41])).
% 1.48/1.29 thf(f41,plain,(
% 1.48/1.29 ( ! [X1 : $i] : (((sK1 = X1) = (sK0 = X1))) )),
% 1.48/1.29 inference(argument_congruence,[status(thm)],[f31])).
% 1.48/1.29 thf(f31,plain,(
% 1.48/1.29 ((= @ sK0) = (= @ sK1))),
% 1.48/1.29 inference(leibniz_equality_elimination,[status(thm)],[f24])).
% 1.48/1.29 thf(f24,plain,(
% 1.48/1.29 ( ! [X1 : ($i > $o) > $o] : (($false = (X1 @ (= @ sK1))) | ((X1 @ (= @ sK0)) = $true)) )),
% 1.48/1.29 inference(binary_proxy_clausification,[status(thm)],[f23])).
% 1.48/1.29 thf(f23,plain,(
% 1.48/1.29 ( ! [X1 : ($i > $o) > $o] : ((((X1 @ (= @ sK1)) => (X1 @ (= @ sK0))) = $true)) )),
% 1.48/1.29 inference(beta_eta_normalization,[status(thm)],[f22])).
% 1.48/1.29 thf(f22,plain,(
% 1.48/1.29 ( ! [X1 : ($i > $o) > $o] : ((((^[Y0 : ($i > $o) > $o]: ((Y0 @ (= @ sK1)) => (Y0 @ (= @ sK0)))) @ X1) = $true)) )),
% 1.48/1.29 inference(pi_clausification,[status(thm)],[f21])).
% 1.48/1.29 thf(f21,plain,(
% 1.48/1.29 ((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((Y0 @ (= @ sK1)) => (Y0 @ (= @ sK0))))) = $true)),
% 1.48/1.29 inference(beta_eta_normalization,[status(thm)],[f20])).
% 1.48/1.29 thf(f20,plain,(
% 1.48/1.29 (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))) @ (^[Y0 : $i]: (sK1 = Y0)) @ (^[Y0 : $i]: (sK0 = Y0))) = $true)),
% 1.48/1.29 inference(definition_unfolding,[status(thm)],[f17,f16])).
% 1.48/1.29 thf(f16,plain,(
% 1.48/1.29 (leibeq2 = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))))),
% 1.48/1.29 inference(cnf_transformation,[status(thm)],[f9])).
% 1.48/1.29 thf(f9,plain,(
% 1.48/1.29 (leibeq2 = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))))),
% 1.48/1.29 inference(fool_elimination,[status(thm)],[f8])).
% 1.48/1.29 thf(f8,plain,(
% 1.48/1.29 (leibeq2 = (^[X0 : $i > $o, X1 : $i > $o] : (! [X2 : ($i > $o) > $o] : ((X2 @ X0) => (X2 @ X1)))))),
% 1.48/1.29 inference(rectify,[status(thm)],[f2])).
% 1.48/1.29 thf(f2,axiom,(
% 1.48/1.29 (leibeq2 = (^[X0 : $i > $o, X1 : $i > $o] : (! [X2 : ($i > $o) > $o] : ((X2 @ X0) => (X2 @ X1)))))),
% 1.48/1.29 file('/export/starexec/sandbox/tmp/tmp.jDfm4zRQMc/DTF2THF_8119.p',leibeq2)).
% 1.48/1.29 thf(f17,plain,(
% 1.48/1.29 ((leibeq2 @ (^[Y0 : $i]: (sK1 = Y0)) @ (^[Y0 : $i]: (sK0 = Y0))) = $true)),
% 1.48/1.29 inference(cnf_transformation,[status(thm)],[f14])).
% 1.48/1.29 thf(f29,plain,(
% 1.48/1.29 ((sK3 @ sK1) = $true)),
% 1.48/1.29 inference(binary_proxy_clausification,[status(thm)],[f27])).
% 1.48/1.29 % SZS output end Proof for DTF2THF_8119
% 1.48/1.29 % (8397)------------------------------
% 1.48/1.29 % (8397)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.29 % (8397)Termination reason: Refutation
% 1.48/1.29
% 1.48/1.29 % (8397)Memory used [KB]: 5500
% 1.48/1.29 % (8397)Time elapsed: 0.006 s
% 1.48/1.29 % (8397)Instructions burned: 4 (million)
% 1.48/1.29 % (8397)------------------------------
% 1.48/1.29 % (8397)------------------------------
% 1.48/1.29 % (8391)Success in time 0.022 s
%------------------------------------------------------------------------------