%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO171^5 : 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 : n006.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 09:53:34 AM UTC 2026
% Result : Theorem 1.47s 1.27s
% Output : Refutation 1.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 1
% Syntax : Number of formulae : 18 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 213 ( 50 equ; 0 cnn)
% Maximal formula atoms : 13 ( 11 avg)
% Number of connectives : 293 ( 40 ~; 39 |; 24 &; 190 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 3 usr; 3 con; 0-2 aty)
% Number of variables : 59 ( 0 ^; 59 !; 0 ?; 59 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_1,type,
g: $i > $i > $o ).
thf(func_def_2,type,
f: $i > $i ).
thf(f32,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f31,f20]) ).
thf(f20,plain,
! [X0: $i] :
( ( g @ X0 @ ( f @ a ) )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f18]) ).
thf(f18,plain,
! [X0: $i] :
( ( ( g @ X0 @ ( f @ a ) )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f12,f16]) ).
thf(f16,plain,
( $true
= ( g @ ( f @ a ) @ a ) ),
inference(condensation,[status(thm)],[f15]) ).
thf(f15,plain,
! [X0: $i] :
( ( $true
= ( g @ ( f @ a ) @ a ) )
| ( ( g @ ( f @ X0 ) @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: $i] :
( ( $true
= ( g @ ( f @ a ) @ a ) )
| ( ( g @ ( f @ X0 ) @ X0 )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f8,f9]) ).
thf(f9,plain,
! [X5: $i] :
( ( $true
= ( g @ X5 @ a ) )
| ( ( g @ ( f @ X5 ) @ X5 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( ! [X0: $i,X1: $i] :
( ( ( g @ X0 @ X1 )
!= $true )
| ( ( g @ X1 @ a )
!= $true ) )
& ! [X2: $i,X3: $i] :
( ( $true
!= ( g @ X3 @ X2 ) )
| ( ( g @ X2 @ ( f @ X2 ) )
= $true ) )
& ! [X4: $i] :
( ( $true
= ( g @ X4 @ ( f @ X4 ) ) )
| ( ( g @ X4 @ a )
= $true ) )
& ! [X5: $i] :
( ( $true
= ( g @ X5 @ a ) )
| ( ( g @ ( f @ X5 ) @ X5 )
= $true ) )
& ! [X6: $i,X7: $i] :
( ( $true
= ( g @ ( f @ X7 ) @ X7 ) )
| ( ( g @ X6 @ X7 )
!= $true ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,plain,
( ! [X2: $i,X3: $i] :
( ( ( g @ X2 @ X3 )
!= $true )
| ( $true
!= ( g @ X3 @ a ) ) )
& ! [X6: $i,X7: $i] :
( ( ( g @ X7 @ X6 )
!= $true )
| ( ( g @ X6 @ ( f @ X6 ) )
= $true ) )
& ! [X4: $i] :
( ( $true
= ( g @ X4 @ ( f @ X4 ) ) )
| ( ( g @ X4 @ a )
= $true ) )
& ! [X5: $i] :
( ( $true
= ( g @ X5 @ a ) )
| ( ( g @ ( f @ X5 ) @ X5 )
= $true ) )
& ! [X1: $i,X0: $i] :
( ( ( g @ ( f @ X0 ) @ X0 )
= $true )
| ( $true
!= ( g @ X1 @ X0 ) ) ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
~ ~ ( ! [X0: $i,X1: $i] :
( ( ( g @ ( f @ X0 ) @ X0 )
= $true )
| ( $true
!= ( g @ X1 @ X0 ) ) )
& ! [X2: $i,X3: $i] :
( ( ( g @ X2 @ X3 )
!= $true )
| ( $true
!= ( g @ X3 @ a ) ) )
& ! [X4: $i] :
( ( $true
= ( g @ X4 @ ( f @ X4 ) ) )
| ( ( g @ X4 @ a )
= $true ) )
& ! [X5: $i] :
( ( $true
= ( g @ X5 @ a ) )
| ( ( g @ ( f @ X5 ) @ X5 )
= $true ) )
& ! [X6: $i,X7: $i] :
( ( ( g @ X6 @ ( f @ X6 ) )
= $true )
| ( ( g @ X7 @ X6 )
!= $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ~ ( ! [X0: $i,X1: $i] :
( ( g @ ( f @ X0 ) @ X0 )
| ~ ( g @ X1 @ X0 ) )
& ! [X2: $i,X3: $i] :
( ~ ( g @ X2 @ X3 )
| ~ ( g @ X3 @ a ) )
& ! [X4: $i] :
( ( g @ X4 @ a )
| ( g @ X4 @ ( f @ X4 ) ) )
& ! [X5: $i] :
( ( g @ X5 @ a )
| ( g @ ( f @ X5 ) @ X5 ) )
& ! [X6: $i,X7: $i] :
( ( g @ X6 @ ( f @ X6 ) )
| ~ ( g @ X7 @ X6 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ~ ( ! [X1: $i,X0: $i] :
( ( g @ ( f @ X1 ) @ X1 )
| ~ ( g @ X0 @ X1 ) )
& ! [X0: $i,X1: $i] :
( ~ ( g @ X0 @ X1 )
| ~ ( g @ X1 @ a ) )
& ! [X0: $i] :
( ( g @ X0 @ a )
| ( g @ X0 @ ( f @ X0 ) ) )
& ! [X0: $i] :
( ( g @ X0 @ a )
| ( g @ ( f @ X0 ) @ X0 ) )
& ! [X1: $i,X0: $i] :
( ( g @ X1 @ ( f @ X1 ) )
| ~ ( g @ X0 @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
~ ( ! [X1: $i,X0: $i] :
( ( g @ ( f @ X1 ) @ X1 )
| ~ ( g @ X0 @ X1 ) )
& ! [X0: $i,X1: $i] :
( ~ ( g @ X0 @ X1 )
| ~ ( g @ X1 @ a ) )
& ! [X0: $i] :
( ( g @ X0 @ a )
| ( g @ X0 @ ( f @ X0 ) ) )
& ! [X0: $i] :
( ( g @ X0 @ a )
| ( g @ ( f @ X0 ) @ X0 ) )
& ! [X1: $i,X0: $i] :
( ( g @ X1 @ ( f @ X1 ) )
| ~ ( g @ X0 @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Q5MctDGz91/DTF2THF_15529.p',cSYN031_1) ).
thf(f8,plain,
! [X6: $i,X7: $i] :
( ( ( g @ X6 @ X7 )
!= $true )
| ( $true
= ( g @ ( f @ X7 ) @ X7 ) ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f12,plain,
! [X0: $i,X1: $i] :
( ( ( g @ X1 @ a )
!= $true )
| ( ( g @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f31,plain,
( $true
= ( g @ a @ ( f @ a ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f27]) ).
thf(f27,plain,
( ( $true != $true )
| ( $true
= ( g @ a @ ( f @ a ) ) ) ),
inference(superposition,[status(thm)],[f11,f16]) ).
thf(f11,plain,
! [X2: $i,X3: $i] :
( ( $true
!= ( g @ X3 @ X2 ) )
| ( ( g @ X2 @ ( f @ X2 ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO171^5 : TPTP v9.2.1. Released v4.0.0.
% 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n006.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 14:25:15 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.45 ---- Original DTF file ---
% 0.30/0.45 thf(spec,logic,$$dhol).
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 % File : SYO171^5 : TPTP v9.2.1. Released v4.0.0.
% 0.30/0.45 % Domain : Syntactic
% 0.30/0.45 % Problem : TPS problem from BASIC-FO-THMS
% 0.30/0.45 % Version : Especial.
% 0.30/0.45 % English :
% 0.30/0.45
% 0.30/0.45 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.30/0.45 % Source : [Bro09]
% 0.30/0.45 % Names : tps_1002 [Bro09]
% 0.30/0.45
% 0.30/0.45 % Status : Theorem
% 0.30/0.45 % Rating : 0.08 v9.1.0, 0.12 v9.0.0, 0.08 v8.2.0, 0.09 v8.1.0, 0.08 v7.4.0, 0.11 v7.3.0, 0.10 v7.2.0, 0.12 v7.1.0, 0.14 v7.0.0, 0.12 v6.4.0, 0.14 v6.3.0, 0.17 v6.0.0, 0.00 v4.0.0
% 0.30/0.45 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.30/0.45 % Number of atoms : 10 ( 0 equ; 0 cnn)
% 0.30/0.45 % Maximal formula atoms : 10 ( 10 avg)
% 0.30/0.45 % Number of connectives : 38 ( 5 ~; 5 |; 4 &; 24 @)
% 0.30/0.45 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.30/0.45 % Maximal formula depth : 12 ( 12 avg)
% 0.30/0.45 % Number of types : 2 ( 0 usr)
% 0.30/0.45 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.30/0.45 % Number of symbols : 3 ( 3 usr; 1 con; 0-2 aty)
% 0.30/0.45 % Number of variables : 8 ( 0 ^; 8 !; 0 ?; 8 :)
% 0.30/0.45 % SPC : TH0_THM_NEQ_NAR
% 0.30/0.45
% 0.30/0.45 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.30/0.45 % project in the Department of Mathematical Sciences at Carnegie
% 0.30/0.45 % Mellon University. Distributed under the Creative Commons copyleft
% 0.30/0.45 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 thf(a,type,
% 0.30/0.45 a: $i ).
% 0.30/0.45
% 0.30/0.45 thf(g,type,
% 0.30/0.45 g: $i > $i > $o ).
% 0.30/0.45
% 0.30/0.45 thf(f,type,
% 0.30/0.45 f: $i > $i ).
% 0.30/0.45
% 0.30/0.45 thf(cSYN031_1,conjecture,
% 0.30/0.45 ~ ( ! [A: $i] :
% 0.30/0.45 ( ( g @ A @ a )
% 0.30/0.45 | ( g @ ( f @ A ) @ A ) )
% 0.30/0.45 & ! [A: $i] :
% 0.30/0.45 ( ( g @ A @ a )
% 0.30/0.45 | ( g @ A @ ( f @ A ) ) )
% 0.30/0.45 & ! [A: $i,B: $i] :
% 0.30/0.45 ( ~ ( g @ A @ B )
% 0.30/0.45 | ( g @ ( f @ B ) @ B ) )
% 0.30/0.45 & ! [A: $i,B: $i] :
% 0.30/0.45 ( ~ ( g @ A @ B )
% 0.30/0.45 | ( g @ B @ ( f @ B ) ) )
% 0.30/0.45 & ! [A: $i,B: $i] :
% 0.30/0.45 ( ~ ( g @ A @ B )
% 0.30/0.45 | ~ ( g @ B @ a ) ) ) ).
% 0.30/0.45
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 ------------------------
% 1.47/1.25 ---- Embedded in THF ---
% 1.47/1.25 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.47/1.25 %%% Generated on Tue Feb 24 14:25:16 EST 2026
% 1.47/1.25 %%% using '$$dhol' embedding, version 1.3.0.
% 1.47/1.25 %%% Logic specification used:
% 1.47/1.25 %%% thf(spec, logic, $$dhol).
% 1.47/1.25
% 1.47/1.25 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.Q5MctDGz91/DTF2DTF15529.p
% See solution above
% 1.47/1.25 ------------------------
% 1.47/1.26 ---- Cleaned THF ---
% 1.47/1.26 thf(a,type,
% 1.47/1.26 a: $i ).
% 1.47/1.26
% 1.47/1.26 thf(g,type,
% 1.47/1.26 g: $i > $i > $o ).
% 1.47/1.26
% 1.47/1.26 thf(f,type,
% 1.47/1.26 f: $i > $i ).
% 1.47/1.26
% 1.47/1.26 thf(cSYN031_1,conjecture,
% 1.47/1.26 ~ ( ! [A: $i] :
% 1.47/1.26 ( ( g @ A @ a )
% 1.47/1.26 | ( g @ ( f @ A ) @ A ) )
% 1.47/1.26 & ! [A: $i] :
% 1.47/1.26 ( ( g @ A @ a )
% 1.47/1.26 | ( g @ A @ ( f @ A ) ) )
% 1.47/1.26 & ! [A: $i,B: $i] :
% 1.47/1.26 ( ~ ( g @ A @ B )
% 1.47/1.26 | ( g @ ( f @ B ) @ B ) )
% 1.47/1.26 & ! [A: $i,B: $i] :
% 1.47/1.26 ( ~ ( g @ A @ B )
% 1.47/1.26 | ( g @ B @ ( f @ B ) ) )
% 1.47/1.26 & ! [A: $i,B: $i] :
% 1.47/1.26 ( ~ ( g @ A @ B )
% 1.47/1.26 | ~ ( g @ B @ a ) ) ) ).
% 1.47/1.26 ------------------------
% 1.47/1.27 % (15724)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_15529 for (3000ds/18Mi)
% 1.47/1.27 % (15723)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_15529 for (3000ds/275Mi)
% 1.47/1.27 % (15720)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_15529 for (3000ds/27Mi)
% 1.47/1.27 % (15719)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_15529 for (3000ds/4Mi)
% 1.47/1.27 % (15724)First to succeed.
% 1.47/1.27 % (15723)Also succeeded, but the first one will report.
% 1.47/1.27 % (15719)Instruction limit reached!
% 1.47/1.27 % (15719)------------------------------
% 1.47/1.27 % (15719)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.27 % (15719)Termination reason: Unknown
% 1.47/1.27 % (15719)Termination phase: Saturation
% 1.47/1.27
% 1.47/1.27 % (15719)Memory used [KB]: 5500
% 1.47/1.27 % (15719)Time elapsed: 0.003 s
% 1.47/1.27 % (15719)Instructions burned: 4 (million)
% 1.47/1.27 % (15719)------------------------------
% 1.47/1.27 % (15719)------------------------------
% 1.47/1.27 % (15724)Refutation found. Thanks to Tanya!
% 1.47/1.27 % SZS status Theorem for DTF2THF_15529
% 1.47/1.27 % SZS output start Proof for DTF2THF_15529
% 1.47/1.27 thf(func_def_1, type, g: $i > $i > $o).
% 1.47/1.27 thf(func_def_2, type, f: $i > $i).
% 1.47/1.27 thf(f32,plain,(
% 1.47/1.27 $false),
% 1.47/1.27 inference(subsumption_resolution,[status(thm)],[f31,f20])).
% 1.47/1.27 thf(f20,plain,(
% 1.47/1.27 ( ! [X0 : $i] : (((g @ X0 @ (f @ a)) != $true)) )),
% 1.47/1.27 inference(trivial_inequality_removal,[status(thm)],[f18])).
% 1.47/1.27 thf(f18,plain,(
% 1.47/1.27 ( ! [X0 : $i] : (((g @ X0 @ (f @ a)) != $true) | ($true != $true)) )),
% 1.47/1.27 inference(superposition,[status(thm)],[f12,f16])).
% 1.47/1.27 thf(f16,plain,(
% 1.47/1.27 ($true = (g @ (f @ a) @ a))),
% 1.47/1.27 inference(condensation,[status(thm)],[f15])).
% 1.47/1.27 thf(f15,plain,(
% 1.47/1.27 ( ! [X0 : $i] : (($true = (g @ (f @ a) @ a)) | ((g @ (f @ X0) @ X0) = $true)) )),
% 1.47/1.27 inference(trivial_inequality_removal,[status(thm)],[f14])).
% 1.47/1.27 thf(f14,plain,(
% 1.47/1.27 ( ! [X0 : $i] : (($true = (g @ (f @ a) @ a)) | ((g @ (f @ X0) @ X0) = $true) | ($true != $true)) )),
% 1.47/1.27 inference(superposition,[status(thm)],[f8,f9])).
% 1.47/1.27 thf(f9,plain,(
% 1.47/1.27 ( ! [X5 : $i] : (($true = (g @ X5 @ a)) | ((g @ (f @ X5) @ X5) = $true)) )),
% 1.47/1.27 inference(cnf_transformation,[status(thm)],[f7])).
% 1.47/1.27 thf(f7,plain,(
% 1.47/1.27 ! [X0 : $i,X1 : $i] : (((g @ X0 @ X1) != $true) | ((g @ X1 @ a) != $true)) & ! [X2 : $i,X3 : $i] : (($true != (g @ X3 @ X2)) | ((g @ X2 @ (f @ X2)) = $true)) & ! [X4 : $i] : (($true = (g @ X4 @ (f @ X4))) | ((g @ X4 @ a) = $true)) & ! [X5 : $i] : (($true = (g @ X5 @ a)) | ((g @ (f @ X5) @ X5) = $true)) & ! [X6 : $i,X7 : $i] : (($true = (g @ (f @ X7) @ X7)) | ((g @ X6 @ X7) != $true))),
% 1.47/1.27 inference(rectify,[status(thm)],[f6])).
% 1.47/1.27 thf(f6,plain,(
% 1.47/1.27 ! [X2 : $i,X3 : $i] : (((g @ X2 @ X3) != $true) | ($true != (g @ X3 @ a))) & ! [X6 : $i,X7 : $i] : (((g @ X7 @ X6) != $true) | ((g @ X6 @ (f @ X6)) = $true)) & ! [X4 : $i] : (($true = (g @ X4 @ (f @ X4))) | ((g @ X4 @ a) = $true)) & ! [X5 : $i] : (($true = (g @ X5 @ a)) | ((g @ (f @ X5) @ X5) = $true)) & ! [X1 : $i,X0 : $i] : (((g @ (f @ X0) @ X0) = $true) | ($true != (g @ X1 @ X0)))),
% 1.47/1.27 inference(flattening,[status(thm)],[f5])).
% 1.47/1.27 thf(f5,plain,(
% 1.47/1.27 ~~(! [X0 : $i,X1 : $i] : (((g @ (f @ X0) @ X0) = $true) | ~($true = (g @ X1 @ X0))) & ! [X2 : $i,X3 : $i] : (~((g @ X2 @ X3) = $true) | ~($true = (g @ X3 @ a))) & ! [X4 : $i] : (($true = (g @ X4 @ (f @ X4))) | ((g @ X4 @ a) = $true)) & ! [X5 : $i] : (($true = (g @ X5 @ a)) | ((g @ (f @ X5) @ X5) = $true)) & ! [X6 : $i,X7 : $i] : (((g @ X6 @ (f @ X6)) = $true) | ~((g @ X7 @ X6) = $true)))),
% 1.47/1.27 inference(fool_elimination,[status(thm)],[f4])).
% 1.47/1.27 thf(f4,plain,(
% 1.47/1.27 ~~(! [X0 : $i,X1 : $i] : ((g @ (f @ X0) @ X0) | ~(g @ X1 @ X0)) & ! [X2 : $i,X3 : $i] : (~(g @ X2 @ X3) | ~(g @ X3 @ a)) & ! [X4 : $i] : ((g @ X4 @ a) | (g @ X4 @ (f @ X4))) & ! [X5 : $i] : ((g @ X5 @ a) | (g @ (f @ X5) @ X5)) & ! [X6 : $i,X7 : $i] : ((g @ X6 @ (f @ X6)) | ~(g @ X7 @ X6)))),
% 1.47/1.27 inference(rectify,[status(thm)],[f2])).
% 1.47/1.27 thf(f2,negated_conjecture,(
% 1.47/1.27 ~~(! [X1 : $i,X0 : $i] : ((g @ (f @ X1) @ X1) | ~(g @ X0 @ X1)) & ! [X0 : $i,X1 : $i] : (~(g @ X0 @ X1) | ~(g @ X1 @ a)) & ! [X0 : $i] : ((g @ X0 @ a) | (g @ X0 @ (f @ X0))) & ! [X0 : $i] : ((g @ X0 @ a) | (g @ (f @ X0) @ X0)) & ! [X1 : $i,X0 : $i] : ((g @ X1 @ (f @ X1)) | ~(g @ X0 @ X1)))),
% 1.47/1.28 inference(negated_conjecture,[status(cth)],[f1])).
% 1.47/1.28 thf(f1,conjecture,(
% 1.47/1.28 ~(! [X1 : $i,X0 : $i] : ((g @ (f @ X1) @ X1) | ~(g @ X0 @ X1)) & ! [X0 : $i,X1 : $i] : (~(g @ X0 @ X1) | ~(g @ X1 @ a)) & ! [X0 : $i] : ((g @ X0 @ a) | (g @ X0 @ (f @ X0))) & ! [X0 : $i] : ((g @ X0 @ a) | (g @ (f @ X0) @ X0)) & ! [X1 : $i,X0 : $i] : ((g @ X1 @ (f @ X1)) | ~(g @ X0 @ X1)))),
% 1.47/1.28 file('/export/starexec/sandbox/tmp/tmp.Q5MctDGz91/DTF2THF_15529.p',cSYN031_1)).
% 1.47/1.28 thf(f8,plain,(
% 1.47/1.28 ( ! [X6 : $i,X7 : $i] : (((g @ X6 @ X7) != $true) | ($true = (g @ (f @ X7) @ X7))) )),
% 1.47/1.28 inference(cnf_transformation,[status(thm)],[f7])).
% 1.47/1.28 thf(f12,plain,(
% 1.47/1.28 ( ! [X0 : $i,X1 : $i] : (((g @ X1 @ a) != $true) | ((g @ X0 @ X1) != $true)) )),
% 1.47/1.28 inference(cnf_transformation,[status(thm)],[f7])).
% 1.47/1.28 thf(f31,plain,(
% 1.47/1.28 ($true = (g @ a @ (f @ a)))),
% 1.47/1.28 inference(trivial_inequality_removal,[status(thm)],[f27])).
% 1.47/1.28 thf(f27,plain,(
% 1.47/1.28 ($true != $true) | ($true = (g @ a @ (f @ a)))),
% 1.47/1.28 inference(superposition,[status(thm)],[f11,f16])).
% 1.47/1.28 thf(f11,plain,(
% 1.47/1.28 ( ! [X2 : $i,X3 : $i] : (($true != (g @ X3 @ X2)) | ((g @ X2 @ (f @ X2)) = $true)) )),
% 1.47/1.28 inference(cnf_transformation,[status(thm)],[f7])).
% 1.47/1.28 % SZS output end Proof for DTF2THF_15529
% 1.47/1.28 % (15724)------------------------------
% 1.47/1.28 % (15724)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.28 % (15724)Termination reason: Refutation
% 1.47/1.28
% 1.47/1.28 % (15724)Memory used [KB]: 5500
% 1.47/1.28 % (15724)Time elapsed: 0.003 s
% 1.47/1.28 % (15724)Instructions burned: 2 (million)
% 1.47/1.28 % (15724)------------------------------
% 1.47/1.28 % (15724)------------------------------
% 1.47/1.28 % (15717)Success in time 0.002 s
%------------------------------------------------------------------------------