%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO221^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n016.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 09:53:42 AM UTC 2026
% Result : Theorem 1.54s 1.37s
% Output : Refutation 1.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 2
% Syntax : Number of formulae : 24 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 217 ( 82 equ; 2 cnn)
% Maximal formula atoms : 6 ( 9 avg)
% Number of connectives : 181 ( 44 ~; 27 |; 29 &; 70 @)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 5 usr; 5 con; 0-2 aty)
% Number of variables : 45 ( 0 ^; 31 !; 14 ?; 45 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_1,type,
cP: $i > $o ).
thf(func_def_6,type,
sK0: ( $i > $o ) > $i ).
thf(func_def_12,type,
ph2:
!>[X0: $tType] : X0 ).
thf(f64,plain,
$false,
inference(equality_resolution,[status(thm)],[f61]) ).
thf(f61,plain,
! [X0: $i] : ( a != X0 ),
inference(subsumption_resolution,[status(thm)],[f60,f12]) ).
thf(f12,plain,
a != b,
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: $i > $o] :
( ( ( cP @ a )
= $true )
& ( ( ( X0 @ b )
= $true )
| ( ( $true
= ( X0 @ ( sK0 @ X0 ) ) )
& ( $true
!= ( cP @ ( sK0 @ X0 ) ) ) )
| ! [X2: $i] :
( ( X0 @ X2 )
!= $true ) )
& ( a != b ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f9,f10]) ).
thf(f10,plain,
! [X0: $i > $o] :
( ? [X1: $i] :
( ( ( X0 @ X1 )
= $true )
& ( ( cP @ X1 )
!= $true ) )
=> ( ( $true
= ( X0 @ ( sK0 @ X0 ) ) )
& ( $true
!= ( cP @ ( sK0 @ X0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
! [X0: $i > $o] :
( ( ( cP @ a )
= $true )
& ( ( ( X0 @ b )
= $true )
| ? [X1: $i] :
( ( ( X0 @ X1 )
= $true )
& ( ( cP @ X1 )
!= $true ) )
| ! [X2: $i] :
( ( X0 @ X2 )
!= $true ) )
& ( a != b ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: $i > $o] :
( ( ( cP @ a )
= $true )
& ( ( ( X0 @ b )
= $true )
| ? [X2: $i] :
( ( ( X0 @ X2 )
= $true )
& ( $true
!= ( cP @ X2 ) ) )
| ! [X1: $i] :
( ( X0 @ X1 )
!= $true ) )
& ( a != b ) ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
! [X0: $i > $o] :
( ( ( ( X0 @ b )
= $true )
| ? [X2: $i] :
( ( ( X0 @ X2 )
= $true )
& ( $true
!= ( cP @ X2 ) ) )
| ! [X1: $i] :
( ( X0 @ X1 )
!= $true ) )
& ( a != b )
& ( ( cP @ a )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ? [X0: $i > $o] :
( ( ( a != b )
& ( ( cP @ a )
= $true ) )
=> ( ? [X1: $i] :
( ( X0 @ X1 )
= $true )
& ! [X2: $i] :
( ( ( X0 @ X2 )
= $true )
=> ( $true
= ( cP @ X2 ) ) )
& ( ( X0 @ b )
!= $true ) ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
~ ? [X0: $i > $o] :
( ( ( a != b )
& ( ( cP @ a )
= $true ) )
=> ( ? [X1: $i] :
( ( X0 @ X1 )
= $true )
& ( ( X0 @ b )
!= $true )
& ! [X2: $i] :
( ( ( X0 @ X2 )
= $true )
=> ( $true
= ( cP @ X2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ? [X0: $i > $o] :
( ( ( cP @ a )
& ( a != b ) )
=> ( ? [X1: $i] : ( X0 @ X1 )
& ~ ( X0 @ b )
& ! [X2: $i] :
( ( X0 @ X2 )
=> ( cP @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ? [X0: $i > $o] :
( ( ( cP @ a )
& ( a != b ) )
=> ( ? [X2: $i] : ( X0 @ X2 )
& ~ ( X0 @ b )
& ! [X1: $i] :
( ( X0 @ X1 )
=> ( cP @ X1 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
? [X0: $i > $o] :
( ( ( cP @ a )
& ( a != b ) )
=> ( ? [X2: $i] : ( X0 @ X2 )
& ~ ( X0 @ b )
& ! [X1: $i] :
( ( X0 @ X1 )
=> ( cP @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.77E4iiCh4m/DTF2THF_6473.p',cBLEDSOE6) ).
thf(f60,plain,
! [X0: $i] :
( ( a = b )
| ( a != X0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f56]) ).
thf(f56,plain,
! [X0: $i] :
( ( $true != $true )
| ( a = b )
| ( a != X0 ) ),
inference(superposition,[status(thm)],[f54,f15]) ).
thf(f15,plain,
( ( cP @ a )
= $true ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f54,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( cP @ X0 ) )
| ( b = X0 )
| ( X0 != X1 ) ),
inference(equality_proxy_clausification,[status(thm)],[f53]) ).
thf(f53,plain,
! [X0: $i,X1: $i] :
( ( b = X0 )
| ( $true
!= ( cP @ X0 ) )
| ( $true
!= ( X0 = X1 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f52]) ).
thf(f52,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( X0 = X1 ) )
| ( b = X0 )
| ( $true
!= ( cP @ X0 ) )
| ( b = X0 ) ),
inference(equality_proxy_clausification,[status(thm)],[f51]) ).
thf(f51,plain,
! [X0: $i,X1: $i] :
( ( b = X0 )
| ( $true
!= ( cP @ X0 ) )
| ( $true
= ( X0 = b ) )
| ( $true
!= ( X0 = X1 ) ) ),
inference(superposition,[status(thm)],[f13,f33]) ).
thf(f33,plain,
! [X0: $i] :
( ( ( sK0 @ ( (=) @ X0 ) )
= X0 )
| ( b = X0 ) ),
inference(equality_proxy_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
! [X0: $i] :
( ( $true
= ( X0 = b ) )
| ( ( sK0 @ ( (=) @ X0 ) )
= X0 ) ),
inference(leibniz_equality_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
! [X2: $i,X0: $i > $o] :
( ( $true
= ( X0 @ ( sK0 @ X0 ) ) )
| ( ( X0 @ X2 )
!= $true )
| ( ( X0 @ b )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f13,plain,
! [X2: $i,X0: $i > $o] :
( ( $true
!= ( cP @ ( sK0 @ X0 ) ) )
| ( ( X0 @ X2 )
!= $true )
| ( ( X0 @ b )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SYO221^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.10 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.30 % Computer : n016.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 300
% 0.11/0.30 % DateTime : Tue Feb 24 14:26:51 EST 2026
% 0.11/0.30 % CPUTime :
% 0.11/0.30 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.40 ---- Original DTF file ---
% 0.17/0.40 thf(spec,logic,$$dhol).
% 0.17/0.40 %------------------------------------------------------------------------------
% 0.17/0.40 % File : SYO221^5 : TPTP v9.2.1. Released v4.0.0.
% 0.17/0.40 % Domain : Syntactic
% 0.17/0.40 % Problem : TPS problem BLEDSOE6
% 0.17/0.40 % Version : Especial.
% 0.17/0.40 % English :
% 0.17/0.40
% 0.17/0.40 % Refs : [BF93] Bledsoe & Feng (1993), SET-VAR
% 0.17/0.40 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.17/0.40 % Source : [Bro09]
% 0.17/0.40 % Names : tps_0231 [Bro09]
% 0.17/0.40 % : BLEDSOE6 [TPS]
% 0.17/0.40
% 0.17/0.40 % Status : Theorem
% 0.17/0.40 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.20 v8.2.0, 0.38 v8.1.0, 0.36 v7.5.0, 0.14 v7.4.0, 0.11 v7.2.0, 0.12 v7.1.0, 0.00 v6.2.0, 0.57 v6.1.0, 0.43 v6.0.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.40 v5.0.0, 0.60 v4.1.0, 0.67 v4.0.0
% 0.17/0.40 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.17/0.40 % Number of atoms : 3 ( 1 equ; 0 cnn)
% 0.17/0.40 % Maximal formula atoms : 3 ( 3 avg)
% 0.17/0.40 % Number of connectives : 12 ( 2 ~; 0 |; 3 &; 5 @)
% 0.17/0.40 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.17/0.40 % Maximal formula depth : 7 ( 7 avg)
% 0.17/0.40 % Number of types : 2 ( 0 usr)
% 0.17/0.40 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.17/0.40 % Number of symbols : 4 ( 3 usr; 2 con; 0-2 aty)
% 0.17/0.40 % Number of variables : 3 ( 0 ^; 1 !; 2 ?; 3 :)
% 0.17/0.40 % SPC : TH0_THM_EQU_NAR
% 0.17/0.40
% 0.17/0.40 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.17/0.40 % project in the Department of Mathematical Sciences at Carnegie
% 0.17/0.40 % Mellon University. Distributed under the Creative Commons copyleft
% 0.17/0.40 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.17/0.40 %------------------------------------------------------------------------------
% 0.17/0.40 thf(b,type,
% 0.17/0.40 b: $i ).
% 0.17/0.40
% 0.17/0.40 thf(cP,type,
% 0.17/0.40 cP: $i > $o ).
% 0.17/0.40
% 0.17/0.40 thf(a,type,
% 0.17/0.40 a: $i ).
% 0.17/0.40
% 0.17/0.40 thf(cBLEDSOE6,conjecture,
% 0.17/0.40 ? [A: $i > $o] :
% 0.17/0.40 ( ( ( cP @ a )
% 0.17/0.40 & ( a != b ) )
% 0.17/0.40 => ( ! [Xx: $i] :
% 0.17/0.40 ( ( A @ Xx )
% 0.17/0.40 => ( cP @ Xx ) )
% 0.17/0.40 & ? [Xy: $i] : ( A @ Xy )
% 0.17/0.40 & ~ ( A @ b ) ) ) ).
% 0.17/0.40
% 0.17/0.40 %------------------------------------------------------------------------------
% 0.17/0.40 ------------------------
% 1.54/1.33 ---- Embedded in THF ---
% 1.54/1.33 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.54/1.33 %%% Generated on Tue Feb 24 14:26:51 EST 2026
% 1.54/1.33 %%% using '$$dhol' embedding, version 1.3.0.
% 1.54/1.33 %%% Logic specification used:
% 1.54/1.33 %%% thf(spec, logic, $$dhol).
% 1.54/1.33
% 1.54/1.33 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.77E4iiCh4m/DTF2DTF6473.p
% See solution above
% 1.54/1.33 ------------------------
% 1.54/1.34 ---- Cleaned THF ---
% 1.54/1.34 thf(b,type,
% 1.54/1.34 b: $i ).
% 1.54/1.34
% 1.54/1.34 thf(cP,type,
% 1.54/1.34 cP: $i > $o ).
% 1.54/1.34
% 1.54/1.34 thf(a,type,
% 1.54/1.34 a: $i ).
% 1.54/1.34
% 1.54/1.34 thf(cBLEDSOE6,conjecture,
% 1.54/1.34 ? [A: $i > $o] :
% 1.54/1.34 ( ( ( cP @ a )
% 1.54/1.34 & ( a != b ) )
% 1.54/1.34 => ( ! [Xx: $i] :
% 1.54/1.34 ( ( A @ Xx )
% 1.54/1.34 => ( cP @ Xx ) )
% 1.54/1.34 & ? [Xy: $i] : ( A @ Xy )
% 1.54/1.34 & ~ ( A @ b ) ) ) ).
% 1.54/1.34 ------------------------
% 1.54/1.36 % (6572)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_6473 for (2999ds/27Mi)
% 1.54/1.36 % (6574)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_6473 for (2999ds/2Mi)
% 1.54/1.36 % (6576)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_6473 for (2999ds/18Mi)
% 1.54/1.36 % (6570)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_6473 for (2999ds/183Mi)
% 1.54/1.36 % (6575)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_6473 for (2999ds/275Mi)
% 1.54/1.36 % (6573)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_6473 for (2999ds/2Mi)
% 1.54/1.36 % (6574)Instruction limit reached!
% 1.54/1.36 % (6574)------------------------------
% 1.54/1.36 % (6574)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.36 % (6574)Termination reason: Unknown
% 1.54/1.36 % (6574)Termination phase: Saturation
% 1.54/1.36
% 1.54/1.36 % (6574)Memory used [KB]: 895
% 1.54/1.36 % (6574)Time elapsed: 0.003 s
% 1.54/1.36 % (6574)Instructions burned: 2 (million)
% 1.54/1.36 % (6574)------------------------------
% 1.54/1.36 % (6574)------------------------------
% 1.54/1.36 % (6573)Instruction limit reached!
% 1.54/1.36 % (6573)------------------------------
% 1.54/1.36 % (6573)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.36 % (6573)Termination reason: Unknown
% 1.54/1.36 % (6573)Termination phase: Saturation
% 1.54/1.36
% 1.54/1.36 % (6573)Memory used [KB]: 5500
% 1.54/1.36 % (6573)Time elapsed: 0.003 s
% 1.54/1.36 % (6573)Instructions burned: 2 (million)
% 1.54/1.36 % (6571)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_6473 for (2999ds/4Mi)
% 1.54/1.36 % (6573)------------------------------
% 1.54/1.36 % (6573)------------------------------
% 1.54/1.36 % (6572)Refutation not found, incomplete strategy
% 1.54/1.36 % (6572)------------------------------
% 1.54/1.36 % (6572)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.36 % (6572)Termination reason: Refutation not found, incomplete strategy
% 1.54/1.36
% 1.54/1.36
% 1.54/1.37 % (6572)Memory used [KB]: 5500
% 1.54/1.37 % (6572)Time elapsed: 0.004 s
% 1.54/1.37 % (6572)Instructions burned: 2 (million)
% 1.54/1.37 % (6572)------------------------------
% 1.54/1.37 % (6572)------------------------------
% 1.54/1.37 % (6575)First to succeed.
% 1.54/1.37 % (6570)Also succeeded, but the first one will report.
% 1.54/1.37 % (6571)Instruction limit reached!
% 1.54/1.37 % (6571)------------------------------
% 1.54/1.37 % (6571)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.37 % (6571)Termination reason: Unknown
% 1.54/1.37 % (6571)Termination phase: Saturation
% 1.54/1.37
% 1.54/1.37 % (6571)Memory used [KB]: 5500
% 1.54/1.37 % (6571)Time elapsed: 0.005 s
% 1.54/1.37 % (6571)Instructions burned: 4 (million)
% 1.54/1.37 % (6571)------------------------------
% 1.54/1.37 % (6571)------------------------------
% 1.54/1.37 % (6575)Refutation found. Thanks to Tanya!
% 1.54/1.37 % SZS status Theorem for DTF2THF_6473
% 1.54/1.37 % SZS output start Proof for DTF2THF_6473
% 1.54/1.37 thf(func_def_1, type, cP: $i > $o).
% 1.54/1.37 thf(func_def_6, type, sK0: ($i > $o) > $i).
% 1.54/1.37 thf(func_def_12, type, ph2: !>[X0: $tType]:(X0)).
% 1.54/1.37 thf(f64,plain,(
% 1.54/1.37 $false),
% 1.54/1.37 inference(equality_resolution,[status(thm)],[f61])).
% 1.54/1.37 thf(f61,plain,(
% 1.54/1.37 ( ! [X0 : $i] : ((a != X0)) )),
% 1.54/1.37 inference(subsumption_resolution,[status(thm)],[f60,f12])).
% 1.54/1.37 thf(f12,plain,(
% 1.54/1.37 (a != b)),
% 1.54/1.37 inference(cnf_transformation,[status(thm)],[f11])).
% 1.54/1.37 thf(f11,plain,(
% 1.54/1.37 ! [X0 : $i > $o] : (((cP @ a) = $true) & (((X0 @ b) = $true) | (($true = (X0 @ (sK0 @ X0))) & ($true != (cP @ (sK0 @ X0)))) | ! [X2 : $i] : ((X0 @ X2) != $true)) & (a != b))),
% 1.54/1.37 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f9,f10])).
% 1.54/1.37 thf(f10,plain,(
% 1.54/1.37 ! [X0 : $i > $o] : (? [X1 : $i] : (((X0 @ X1) = $true) & ((cP @ X1) != $true)) => (($true = (X0 @ (sK0 @ X0))) & ($true != (cP @ (sK0 @ X0)))))),
% 1.54/1.37 introduced(definition,[],[choice_axiom])).
% 1.54/1.37 thf(f9,plain,(
% 1.54/1.37 ! [X0 : $i > $o] : (((cP @ a) = $true) & (((X0 @ b) = $true) | ? [X1 : $i] : (((X0 @ X1) = $true) & ((cP @ X1) != $true)) | ! [X2 : $i] : ((X0 @ X2) != $true)) & (a != b))),
% 1.54/1.37 inference(rectify,[status(thm)],[f8])).
% 1.54/1.37 thf(f8,plain,(
% 1.54/1.37 ! [X0 : $i > $o] : (((cP @ a) = $true) & (((X0 @ b) = $true) | ? [X2 : $i] : (((X0 @ X2) = $true) & ($true != (cP @ X2))) | ! [X1 : $i] : ((X0 @ X1) != $true)) & (a != b))),
% 1.54/1.37 inference(flattening,[status(thm)],[f7])).
% 1.54/1.37 thf(f7,plain,(
% 1.54/1.37 ! [X0 : $i > $o] : ((((X0 @ b) = $true) | ? [X2 : $i] : (((X0 @ X2) = $true) & ($true != (cP @ X2))) | ! [X1 : $i] : ((X0 @ X1) != $true)) & ((a != b) & ((cP @ a) = $true)))),
% 1.54/1.37 inference(ennf_transformation,[status(thm)],[f6])).
% 1.54/1.37 thf(f6,plain,(
% 1.54/1.37 ~? [X0 : $i > $o] : (((a != b) & ((cP @ a) = $true)) => (? [X1 : $i] : ((X0 @ X1) = $true) & ! [X2 : $i] : (((X0 @ X2) = $true) => ($true = (cP @ X2))) & ((X0 @ b) != $true)))),
% 1.54/1.37 inference(flattening,[status(thm)],[f5])).
% 1.54/1.37 thf(f5,plain,(
% 1.54/1.37 ~? [X0 : $i > $o] : (((a != b) & ((cP @ a) = $true)) => (? [X1 : $i] : ((X0 @ X1) = $true) & ~((X0 @ b) = $true) & ! [X2 : $i] : (((X0 @ X2) = $true) => ($true = (cP @ X2)))))),
% 1.54/1.37 inference(fool_elimination,[status(thm)],[f4])).
% 1.54/1.37 thf(f4,plain,(
% 1.54/1.37 ~? [X0 : $i > $o] : (((cP @ a) & (a != b)) => (? [X1 : $i] : (X0 @ X1) & ~(X0 @ b) & ! [X2 : $i] : ((X0 @ X2) => (cP @ X2))))),
% 1.54/1.37 inference(rectify,[status(thm)],[f2])).
% 1.54/1.37 thf(f2,negated_conjecture,(
% 1.54/1.37 ~? [X0 : $i > $o] : (((cP @ a) & (a != b)) => (? [X2 : $i] : (X0 @ X2) & ~(X0 @ b) & ! [X1 : $i] : ((X0 @ X1) => (cP @ X1))))),
% 1.54/1.37 inference(negated_conjecture,[status(cth)],[f1])).
% 1.54/1.37 thf(f1,conjecture,(
% 1.54/1.37 ? [X0 : $i > $o] : (((cP @ a) & (a != b)) => (? [X2 : $i] : (X0 @ X2) & ~(X0 @ b) & ! [X1 : $i] : ((X0 @ X1) => (cP @ X1))))),
% 1.54/1.37 file('/export/starexec/sandbox/tmp/tmp.77E4iiCh4m/DTF2THF_6473.p',cBLEDSOE6)).
% 1.54/1.37 thf(f60,plain,(
% 1.54/1.37 ( ! [X0 : $i] : ((a = b) | (a != X0)) )),
% 1.54/1.37 inference(trivial_inequality_removal,[status(thm)],[f56])).
% 1.54/1.37 thf(f56,plain,(
% 1.54/1.37 ( ! [X0 : $i] : (($true != $true) | (a = b) | (a != X0)) )),
% 1.54/1.37 inference(superposition,[status(thm)],[f54,f15])).
% 1.54/1.37 thf(f15,plain,(
% 1.54/1.37 ((cP @ a) = $true)),
% 1.54/1.37 inference(cnf_transformation,[status(thm)],[f11])).
% 1.54/1.37 thf(f54,plain,(
% 1.54/1.37 ( ! [X0 : $i,X1 : $i] : (($true != (cP @ X0)) | (b = X0) | (X0 != X1)) )),
% 1.54/1.37 inference(equality_proxy_clausification,[status(thm)],[f53])).
% 1.54/1.37 thf(f53,plain,(
% 1.54/1.37 ( ! [X0 : $i,X1 : $i] : ((b = X0) | ($true != (cP @ X0)) | ($true != (X0 = X1))) )),
% 1.54/1.37 inference(duplicate_literal_removal,[status(thm)],[f52])).
% 1.54/1.37 thf(f52,plain,(
% 1.54/1.37 ( ! [X0 : $i,X1 : $i] : (($true != (X0 = X1)) | (b = X0) | ($true != (cP @ X0)) | (b = X0)) )),
% 1.54/1.37 inference(equality_proxy_clausification,[status(thm)],[f51])).
% 1.54/1.37 thf(f51,plain,(
% 1.54/1.37 ( ! [X0 : $i,X1 : $i] : ((b = X0) | ($true != (cP @ X0)) | ($true = (X0 = b)) | ($true != (X0 = X1))) )),
% 1.54/1.37 inference(superposition,[status(thm)],[f13,f33])).
% 1.54/1.37 thf(f33,plain,(
% 1.54/1.37 ( ! [X0 : $i] : (((sK0 @ (= @ X0)) = X0) | (b = X0)) )),
% 1.54/1.37 inference(equality_proxy_clausification,[status(thm)],[f26])).
% 1.54/1.37 thf(f26,plain,(
% 1.54/1.37 ( ! [X0 : $i] : (($true = (X0 = b)) | ((sK0 @ (= @ X0)) = X0)) )),
% 1.54/1.37 inference(leibniz_equality_elimination,[status(thm)],[f14])).
% 1.54/1.37 thf(f14,plain,(
% 1.54/1.37 ( ! [X2 : $i,X0 : $i > $o] : (($true = (X0 @ (sK0 @ X0))) | ((X0 @ X2) != $true) | ((X0 @ b) = $true)) )),
% 1.54/1.37 inference(cnf_transformation,[status(thm)],[f11])).
% 1.54/1.37 thf(f13,plain,(
% 1.54/1.37 ( ! [X2 : $i,X0 : $i > $o] : (($true != (cP @ (sK0 @ X0))) | ((X0 @ X2) != $true) | ((X0 @ b) = $true)) )),
% 1.54/1.37 inference(cnf_transformation,[status(thm)],[f11])).
% 1.54/1.37 % SZS output end Proof for DTF2THF_6473
% 1.54/1.37 % (6575)------------------------------
% 1.54/1.37 % (6575)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.37 % (6575)Termination reason: Refutation
% 1.54/1.37
% 1.54/1.37 % (6575)Memory used [KB]: 5500
% 1.54/1.37 % (6575)Time elapsed: 0.005 s
% 1.54/1.37 % (6575)Instructions burned: 4 (million)
% 1.54/1.37 % (6575)------------------------------
% 1.54/1.37 % (6575)------------------------------
% 1.54/1.37 % (6569)Success in time 0.019 s
%------------------------------------------------------------------------------