%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO227^5 : 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 : n023.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 09:53:43 AM UTC 2026
% Result : Theorem 1.58s 1.32s
% Output : Refutation 1.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 27 ( 6 unt; 0 typ; 2 def)
% Number of atoms : 225 ( 57 equ; 0 cnn)
% Maximal formula atoms : 11 ( 8 avg)
% Number of connectives : 189 ( 40 ~; 21 |; 24 &; 87 @)
% ( 2 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 7 con; 0-2 aty)
% Number of variables : 28 ( 0 ^; 23 !; 5 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_3,type,
c_less_: $i > $i > $o ).
thf(func_def_9,type,
ph1:
!>[X0: $tType] : X0 ).
thf(f58,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f48,f52,f57]) ).
thf(f57,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[status(thm)],[f56]) ).
thf(f56,plain,
( $false
| ~ spl0_1 ),
inference(subsumption_resolution,[status(thm)],[f55,f14]) ).
thf(f14,plain,
! [X2: $i] :
( ( c_less_ @ X2 @ X2 )
!= $true ),
inference(equality_resolution,[status(thm)],[f12]) ).
thf(f12,plain,
! [X2: $i,X1: $i] :
( ( X1 != X2 )
| ( ( c_less_ @ X1 @ X2 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ! [X0: $i > $o] :
( ( ( X0 @ c )
= $true )
| ( ( X0 @ b )
!= $true )
| ( $true
= ( X0 @ a ) ) )
& ! [X1: $i,X2: $i] :
( ( X1 != X2 )
| ( ( c_less_ @ X1 @ X2 )
!= $true ) )
& ( ( c_less_ @ a @ b )
= $true )
& ( ( c_less_ @ b @ c )
= $true ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,plain,
( ! [X2: $i > $o] :
( ( ( X2 @ c )
= $true )
| ( ( X2 @ b )
!= $true )
| ( ( X2 @ a )
= $true ) )
& ! [X0: $i,X1: $i] :
( ( X0 != X1 )
| ( ( c_less_ @ X0 @ X1 )
!= $true ) )
& ( ( c_less_ @ a @ b )
= $true )
& ( ( c_less_ @ b @ c )
= $true ) ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
( ! [X2: $i > $o] :
( ( ( X2 @ c )
= $true )
| ( ( X2 @ b )
!= $true )
| ( ( X2 @ a )
= $true ) )
& ( ( c_less_ @ b @ c )
= $true )
& ( ( c_less_ @ a @ b )
= $true )
& ! [X0: $i,X1: $i] :
( ( X0 != X1 )
| ( ( c_less_ @ X0 @ X1 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( ! [X1: $i,X0: $i] :
( ( ( c_less_ @ X0 @ X1 )
= $true )
=> ( X0 != X1 ) )
=> ( ( ( ( c_less_ @ b @ c )
= $true )
& ( ( c_less_ @ a @ b )
= $true ) )
=> ? [X2: $i > $o] :
( ( ( X2 @ c )
!= $true )
& ( ( X2 @ b )
= $true )
& ( ( X2 @ a )
!= $true ) ) ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ! [X1: $i,X0: $i] :
( ( ( c_less_ @ X0 @ X1 )
= $true )
=> ( X0 != X1 ) )
=> ( ( ( ( c_less_ @ b @ c )
= $true )
& ( ( c_less_ @ a @ b )
= $true ) )
=> ? [X2: $i > $o] :
( ( ( X2 @ b )
= $true )
& ( ( X2 @ a )
!= $true )
& ( ( X2 @ c )
!= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ! [X0: $i,X1: $i] :
( ( c_less_ @ X0 @ X1 )
=> ( X0 != X1 ) )
=> ( ( ( c_less_ @ a @ b )
& ( c_less_ @ b @ c ) )
=> ? [X2: $i > $o] :
( ( X2 @ b )
& ~ ( X2 @ a )
& ~ ( X2 @ c ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ! [X0: $i,X1: $i] :
( ( c_less_ @ X0 @ X1 )
=> ( X0 != X1 ) )
=> ( ( ( c_less_ @ a @ b )
& ( c_less_ @ b @ c ) )
=> ? [X2: $i > $o] :
( ( X2 @ b )
& ~ ( X2 @ a )
& ~ ( X2 @ c ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ! [X0: $i,X1: $i] :
( ( c_less_ @ X0 @ X1 )
=> ( X0 != X1 ) )
=> ( ( ( c_less_ @ a @ b )
& ( c_less_ @ b @ c ) )
=> ? [X2: $i > $o] :
( ( X2 @ b )
& ~ ( X2 @ a )
& ~ ( X2 @ c ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.OcIUdoBIma/DTF2THF_6287.p',cBLEDSOE4_W_AX) ).
thf(f55,plain,
( ( ( c_less_ @ b @ b )
= $true )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f11,f38]) ).
thf(f38,plain,
( ( a = b )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f36]) ).
thf(f36,definition,
( spl0_1
<=> ( a = b ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f11,plain,
( ( c_less_ @ a @ b )
= $true ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f52,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[status(thm)],[f51]) ).
thf(f51,plain,
( $false
| ~ spl0_3 ),
inference(subsumption_resolution,[status(thm)],[f50,f14]) ).
thf(f50,plain,
( ( $true
= ( c_less_ @ c @ c ) )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f10,f47]) ).
thf(f47,plain,
( ( b = c )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f45]) ).
thf(f45,definition,
( spl0_3
<=> ( b = c ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f10,plain,
( ( c_less_ @ b @ c )
= $true ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f48,plain,
( spl0_3
| spl0_1 ),
inference(avatar_split_clause,[status(thm)],[f21,f36,f45]) ).
thf(f21,plain,
( ( a = b )
| ( b = c ) ),
inference(equality_proxy_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
( ( a = b )
| ( ( b = c )
= $true ) ),
inference(leibniz_equality_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: $i > $o] :
( ( $true
= ( X0 @ a ) )
| ( ( X0 @ c )
= $true )
| ( ( X0 @ b )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SYO227^5 : 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
% 0.12/0.29 % Computer : n023.cluster.edu
% 0.12/0.29 % Model : x86_64 x86_64
% 0.12/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.29 % Memory : 8042.1875MB
% 0.12/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.29 % CPULimit : 300
% 0.12/0.29 % WCLimit : 300
% 0.12/0.29 % DateTime : Tue Feb 24 14:27:04 EST 2026
% 0.12/0.29 % CPUTime :
% 0.12/0.29 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.39 ---- Original DTF file ---
% 0.17/0.39 thf(spec,logic,$$dhol).
% 0.17/0.39 %------------------------------------------------------------------------------
% 0.17/0.39 % File : SYO227^5 : TPTP v9.2.1. Released v4.0.0.
% 0.17/0.39 % Domain : Syntactic
% 0.17/0.39 % Problem : TPS problem BLEDSOE4-W-AX
% 0.17/0.39 % Version : Especial.
% 0.17/0.39 % English :
% 0.17/0.39
% 0.17/0.39 % Refs : [BF93] Bledsoe & Feng (1993), SET-VAR
% 0.17/0.39 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.17/0.39 % Source : [Bro09]
% 0.17/0.39 % Names : tps_0514 [Bro09]
% 0.17/0.39 % : BLEDSOE4-W-AX [TPS]
% 0.17/0.39
% 0.17/0.39 % Status : Theorem
% 0.17/0.39 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.10 v8.2.0, 0.31 v8.1.0, 0.36 v7.5.0, 0.14 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.25 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 v6.0.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.40 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0
% 0.17/0.39 % Syntax : Number of formulae : 5 ( 0 unt; 4 typ; 0 def)
% 0.17/0.39 % Number of atoms : 4 ( 1 equ; 0 cnn)
% 0.17/0.39 % Maximal formula atoms : 4 ( 4 avg)
% 0.17/0.39 % Number of connectives : 18 ( 3 ~; 0 |; 3 &; 9 @)
% 0.17/0.39 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.17/0.39 % Maximal formula depth : 8 ( 8 avg)
% 0.17/0.39 % Number of types : 2 ( 0 usr)
% 0.17/0.39 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.17/0.39 % Number of symbols : 5 ( 4 usr; 3 con; 0-2 aty)
% 0.17/0.39 % Number of variables : 3 ( 0 ^; 2 !; 1 ?; 3 :)
% 0.17/0.39 % SPC : TH0_THM_EQU_NAR
% 0.17/0.39
% 0.17/0.39 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.17/0.39 % project in the Department of Mathematical Sciences at Carnegie
% 0.17/0.39 % Mellon University. Distributed under the Creative Commons copyleft
% 0.17/0.39 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.17/0.39 % : Example 4 of [BF93] is countersatisfiable without assuming <
% 0.17/0.39 % implies not =. This puts in that.
% 0.17/0.39 %------------------------------------------------------------------------------
% 0.17/0.39 thf(c,type,
% 0.17/0.39 c: $i ).
% 0.17/0.39
% 0.17/0.39 thf(b,type,
% 0.17/0.39 b: $i ).
% 0.17/0.39
% 0.17/0.39 thf(a,type,
% 0.17/0.39 a: $i ).
% 0.17/0.39
% 0.17/0.39 thf(c_less_,type,
% 0.17/0.39 c_less_: $i > $i > $o ).
% 0.17/0.39
% 0.17/0.39 thf(cBLEDSOE4_W_AX,conjecture,
% 0.17/0.39 ( ! [Xx: $i,Xy: $i] :
% 0.17/0.39 ( ( c_less_ @ Xx @ Xy )
% 0.17/0.39 => ( Xx != Xy ) )
% 0.17/0.39 => ( ( ( c_less_ @ a @ b )
% 0.17/0.39 & ( c_less_ @ b @ c ) )
% 0.17/0.39 => ? [A: $i > $o] :
% 0.17/0.39 ( ~ ( A @ a )
% 0.17/0.39 & ( A @ b )
% 0.17/0.39 & ~ ( A @ c ) ) ) ) ).
% 0.17/0.39
% 0.17/0.39 %------------------------------------------------------------------------------
% 0.17/0.39 ------------------------
% 1.38/1.28 ---- Embedded in THF ---
% 1.38/1.28 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.38/1.28 %%% Generated on Tue Feb 24 14:27:05 EST 2026
% 1.38/1.28 %%% using '$$dhol' embedding, version 1.3.0.
% 1.38/1.28 %%% Logic specification used:
% 1.38/1.28 %%% thf(spec, logic, $$dhol).
% 1.38/1.28
% 1.38/1.28 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.OcIUdoBIma/DTF2DTF6287.p
% See solution above
% 1.38/1.28 ------------------------
% 1.38/1.29 ---- Cleaned THF ---
% 1.38/1.29 thf(c,type,
% 1.38/1.29 c: $i ).
% 1.38/1.29
% 1.38/1.29 thf(b,type,
% 1.38/1.29 b: $i ).
% 1.38/1.29
% 1.38/1.29 thf(a,type,
% 1.38/1.29 a: $i ).
% 1.38/1.29
% 1.38/1.29 thf(c_less_,type,
% 1.38/1.29 c_less_: $i > $i > $o ).
% 1.38/1.29
% 1.38/1.29 thf(cBLEDSOE4_W_AX,conjecture,
% 1.38/1.29 ( ! [Xx: $i,Xy: $i] :
% 1.38/1.29 ( ( c_less_ @ Xx @ Xy )
% 1.38/1.29 => ( Xx != Xy ) )
% 1.38/1.29 => ( ( ( c_less_ @ a @ b )
% 1.38/1.29 & ( c_less_ @ b @ c ) )
% 1.38/1.29 => ? [A: $i > $o] :
% 1.38/1.29 ( ~ ( A @ a )
% 1.38/1.29 & ( A @ b )
% 1.38/1.29 & ~ ( A @ c ) ) ) ) ).
% 1.38/1.29 ------------------------
% 1.58/1.31 % (6385)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_6287 for (2999ds/183Mi)
% 1.58/1.31 % (6391)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_6287 for (2999ds/18Mi)
% 1.58/1.31 % (6390)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_6287 for (2999ds/275Mi)
% 1.58/1.31 % (6387)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_6287 for (2999ds/27Mi)
% 1.58/1.31 % (6389)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_6287 for (2999ds/2Mi)
% 1.58/1.31 % (6388)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_6287 for (2999ds/2Mi)
% 1.58/1.31 % (6386)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_6287 for (2999ds/4Mi)
% 1.58/1.31 % (6388)Instruction limit reached!
% 1.58/1.31 % (6388)------------------------------
% 1.58/1.31 % (6388)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.31 % (6388)Termination reason: Unknown
% 1.58/1.31 % (6388)Termination phase: Saturation
% 1.58/1.31
% 1.58/1.31 % (6388)Memory used [KB]: 5373
% 1.58/1.31 % (6388)Time elapsed: 0.003 s
% 1.58/1.31 % (6388)Instructions burned: 2 (million)
% 1.58/1.31 % (6388)------------------------------
% 1.58/1.31 % (6388)------------------------------
% 1.58/1.31 % (6389)Instruction limit reached!
% 1.58/1.31 % (6389)------------------------------
% 1.58/1.31 % (6389)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.31 % (6389)Termination reason: Unknown
% 1.58/1.31 % (6389)Termination phase: Saturation
% 1.58/1.31
% 1.58/1.31 % (6389)Memory used [KB]: 5500
% 1.58/1.31 % (6389)Time elapsed: 0.003 s
% 1.58/1.31 % (6389)Instructions burned: 2 (million)
% 1.58/1.31 % (6389)------------------------------
% 1.58/1.31 % (6389)------------------------------
% 1.58/1.31 % (6387)Refutation not found, incomplete strategy
% 1.58/1.31 % (6387)------------------------------
% 1.58/1.31 % (6387)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.32 % (6387)Termination reason: Refutation not found, incomplete strategy
% 1.58/1.32
% 1.58/1.32
% 1.58/1.32 % (6387)Memory used [KB]: 5500
% 1.58/1.32 % (6387)Time elapsed: 0.004 s
% 1.58/1.32 % (6387)Instructions burned: 3 (million)
% 1.58/1.32 % (6387)------------------------------
% 1.58/1.32 % (6387)------------------------------
% 1.58/1.32 % (6390)First to succeed.
% 1.58/1.32 % (6386)Instruction limit reached!
% 1.58/1.32 % (6386)------------------------------
% 1.58/1.32 % (6386)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.32 % (6386)Termination reason: Unknown
% 1.58/1.32 % (6386)Termination phase: Saturation
% 1.58/1.32
% 1.58/1.32 % (6386)Memory used [KB]: 5500
% 1.58/1.32 % (6386)Time elapsed: 0.005 s
% 1.58/1.32 % (6386)Instructions burned: 5 (million)
% 1.58/1.32 % (6386)------------------------------
% 1.58/1.32 % (6386)------------------------------
% 1.58/1.32 % (6385)Also succeeded, but the first one will report.
% 1.58/1.32 % (6390)Refutation found. Thanks to Tanya!
% 1.58/1.32 % SZS status Theorem for DTF2THF_6287
% 1.58/1.32 % SZS output start Proof for DTF2THF_6287
% 1.58/1.32 thf(func_def_3, type, c_less_: $i > $i > $o).
% 1.58/1.32 thf(func_def_9, type, ph1: !>[X0: $tType]:(X0)).
% 1.58/1.32 thf(f58,plain,(
% 1.58/1.32 $false),
% 1.58/1.32 inference(avatar_sat_refutation,[status(thm)],[f48,f52,f57])).
% 1.58/1.32 thf(f57,plain,(
% 1.58/1.32 ~spl0_1),
% 1.58/1.32 inference(avatar_contradiction_clause,[status(thm)],[f56])).
% 1.58/1.32 thf(f56,plain,(
% 1.58/1.32 $false | ~spl0_1),
% 1.58/1.32 inference(subsumption_resolution,[status(thm)],[f55,f14])).
% 1.58/1.32 thf(f14,plain,(
% 1.58/1.32 ( ! [X2 : $i] : (((c_less_ @ X2 @ X2) != $true)) )),
% 1.58/1.32 inference(equality_resolution,[status(thm)],[f12])).
% 1.58/1.32 thf(f12,plain,(
% 1.58/1.32 ( ! [X2 : $i,X1 : $i] : ((X1 != X2) | ((c_less_ @ X1 @ X2) != $true)) )),
% 1.58/1.32 inference(cnf_transformation,[status(thm)],[f9])).
% 1.58/1.32 thf(f9,plain,(
% 1.58/1.32 ! [X0 : $i > $o] : (((X0 @ c) = $true) | ((X0 @ b) != $true) | ($true = (X0 @ a))) & ! [X1 : $i,X2 : $i] : ((X1 != X2) | ((c_less_ @ X1 @ X2) != $true)) & ((c_less_ @ a @ b) = $true) & ((c_less_ @ b @ c) = $true)),
% 1.58/1.32 inference(rectify,[status(thm)],[f8])).
% 1.58/1.32 thf(f8,plain,(
% 1.58/1.32 ! [X2 : $i > $o] : (((X2 @ c) = $true) | ((X2 @ b) != $true) | ((X2 @ a) = $true)) & ! [X0 : $i,X1 : $i] : ((X0 != X1) | ((c_less_ @ X0 @ X1) != $true)) & ((c_less_ @ a @ b) = $true) & ((c_less_ @ b @ c) = $true)),
% 1.58/1.32 inference(flattening,[status(thm)],[f7])).
% 1.58/1.32 thf(f7,plain,(
% 1.58/1.32 (! [X2 : $i > $o] : (((X2 @ c) = $true) | ((X2 @ b) != $true) | ((X2 @ a) = $true)) & (((c_less_ @ b @ c) = $true) & ((c_less_ @ a @ b) = $true))) & ! [X0 : $i,X1 : $i] : ((X0 != X1) | ((c_less_ @ X0 @ X1) != $true))),
% 1.58/1.32 inference(ennf_transformation,[status(thm)],[f6])).
% 1.58/1.32 thf(f6,plain,(
% 1.58/1.32 ~(! [X1 : $i,X0 : $i] : (((c_less_ @ X0 @ X1) = $true) => (X0 != X1)) => ((((c_less_ @ b @ c) = $true) & ((c_less_ @ a @ b) = $true)) => ? [X2 : $i > $o] : (((X2 @ c) != $true) & ((X2 @ b) = $true) & ((X2 @ a) != $true))))),
% 1.58/1.32 inference(flattening,[status(thm)],[f5])).
% 1.58/1.32 thf(f5,plain,(
% 1.58/1.32 ~(! [X1 : $i,X0 : $i] : (((c_less_ @ X0 @ X1) = $true) => (X0 != X1)) => ((((c_less_ @ b @ c) = $true) & ((c_less_ @ a @ b) = $true)) => ? [X2 : $i > $o] : (((X2 @ b) = $true) & ~((X2 @ a) = $true) & ~((X2 @ c) = $true))))),
% 1.58/1.32 inference(fool_elimination,[status(thm)],[f4])).
% 1.58/1.32 thf(f4,plain,(
% 1.58/1.32 ~(! [X0 : $i,X1 : $i] : ((c_less_ @ X0 @ X1) => (X0 != X1)) => (((c_less_ @ a @ b) & (c_less_ @ b @ c)) => ? [X2 : $i > $o] : ((X2 @ b) & ~(X2 @ a) & ~(X2 @ c))))),
% 1.58/1.32 inference(rectify,[status(thm)],[f2])).
% 1.58/1.32 thf(f2,negated_conjecture,(
% 1.58/1.32 ~(! [X0 : $i,X1 : $i] : ((c_less_ @ X0 @ X1) => (X0 != X1)) => (((c_less_ @ a @ b) & (c_less_ @ b @ c)) => ? [X2 : $i > $o] : ((X2 @ b) & ~(X2 @ a) & ~(X2 @ c))))),
% 1.58/1.32 inference(negated_conjecture,[status(cth)],[f1])).
% 1.58/1.32 thf(f1,conjecture,(
% 1.58/1.32 ! [X0 : $i,X1 : $i] : ((c_less_ @ X0 @ X1) => (X0 != X1)) => (((c_less_ @ a @ b) & (c_less_ @ b @ c)) => ? [X2 : $i > $o] : ((X2 @ b) & ~(X2 @ a) & ~(X2 @ c)))),
% 1.58/1.32 file('/export/starexec/sandbox/tmp/tmp.OcIUdoBIma/DTF2THF_6287.p',cBLEDSOE4_W_AX)).
% 1.58/1.32 thf(f55,plain,(
% 1.58/1.32 ((c_less_ @ b @ b) = $true) | ~spl0_1),
% 1.58/1.32 inference(superposition,[status(thm)],[f11,f38])).
% 1.58/1.32 thf(f38,plain,(
% 1.58/1.32 (a = b) | ~spl0_1),
% 1.58/1.32 inference(avatar_component_clause,[status(thm)],[f36])).
% 1.58/1.32 thf(f36,definition,(
% 1.58/1.32 spl0_1 <=> (a = b)),
% 1.58/1.32 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.58/1.32 thf(f11,plain,(
% 1.58/1.32 ((c_less_ @ a @ b) = $true)),
% 1.58/1.32 inference(cnf_transformation,[status(thm)],[f9])).
% 1.58/1.32 thf(f52,plain,(
% 1.58/1.32 ~spl0_3),
% 1.58/1.32 inference(avatar_contradiction_clause,[status(thm)],[f51])).
% 1.58/1.32 thf(f51,plain,(
% 1.58/1.32 $false | ~spl0_3),
% 1.58/1.32 inference(subsumption_resolution,[status(thm)],[f50,f14])).
% 1.58/1.32 thf(f50,plain,(
% 1.58/1.32 ($true = (c_less_ @ c @ c)) | ~spl0_3),
% 1.58/1.32 inference(superposition,[status(thm)],[f10,f47])).
% 1.58/1.32 thf(f47,plain,(
% 1.58/1.32 (b = c) | ~spl0_3),
% 1.58/1.32 inference(avatar_component_clause,[status(thm)],[f45])).
% 1.58/1.32 thf(f45,definition,(
% 1.58/1.32 spl0_3 <=> (b = c)),
% 1.58/1.32 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.58/1.32 thf(f10,plain,(
% 1.58/1.32 ((c_less_ @ b @ c) = $true)),
% 1.58/1.32 inference(cnf_transformation,[status(thm)],[f9])).
% 1.58/1.32 thf(f48,plain,(
% 1.58/1.32 spl0_3 | spl0_1),
% 1.58/1.32 inference(avatar_split_clause,[status(thm)],[f21,f36,f45])).
% 1.58/1.32 thf(f21,plain,(
% 1.58/1.32 (a = b) | (b = c)),
% 1.58/1.32 inference(equality_proxy_clausification,[status(thm)],[f15])).
% 1.58/1.32 thf(f15,plain,(
% 1.58/1.32 (a = b) | ((b = c) = $true)),
% 1.58/1.32 inference(leibniz_equality_elimination,[status(thm)],[f13])).
% 1.58/1.32 thf(f13,plain,(
% 1.58/1.32 ( ! [X0 : $i > $o] : (($true = (X0 @ a)) | ((X0 @ c) = $true) | ((X0 @ b) != $true)) )),
% 1.58/1.32 inference(cnf_transformation,[status(thm)],[f9])).
% 1.58/1.32 % SZS output end Proof for DTF2THF_6287
% 1.58/1.32 % (6390)------------------------------
% 1.58/1.32 % (6390)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.58/1.32 % (6390)Termination reason: Refutation
% 1.58/1.32
% 1.58/1.32 % (6390)Memory used [KB]: 5500
% 1.58/1.32 % (6390)Time elapsed: 0.005 s
% 1.58/1.32 % (6390)Instructions burned: 3 (million)
% 1.58/1.32 % (6390)------------------------------
% 1.58/1.32 % (6390)------------------------------
% 1.58/1.32 % (6384)Success in time 0.018 s
%------------------------------------------------------------------------------