%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO159^5 : 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 : n003.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 09:53:32 AM UTC 2026
% Result : Theorem 1.51s 1.27s
% Output : Refutation 1.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 21 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 201 ( 56 equ; 0 cnn)
% Maximal formula atoms : 6 ( 9 avg)
% Number of connectives : 207 ( 46 ~; 14 |; 23 &; 107 @)
% ( 0 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 38 ( 0 ^; 17 !; 21 ?; 38 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cC: $i > $o ).
thf(func_def_1,type,
cB: $i > $i > $o ).
thf(func_def_2,type,
cA: $i > $o ).
thf(func_def_6,type,
sK0: $i > $i ).
thf(f22,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f21,f17]) ).
thf(f17,plain,
( ( cC @ ( sK0 @ sK1 ) )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f16]) ).
thf(f16,plain,
( ( ( cC @ ( sK0 @ sK1 ) )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f14,f13]) ).
thf(f13,plain,
( ( cA @ sK1 )
= $true ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ! [X0: $i] :
( ( ( ( cB @ X0 @ ( sK0 @ X0 ) )
= $true )
& ( $true
= ( cC @ ( sK0 @ X0 ) ) ) )
| ( ( cA @ X0 )
!= $true ) )
& ( ( cA @ sK1 )
= $true )
& ! [X3: $i] :
( ( ( cC @ X3 )
!= $true )
| ( $true
!= ( cB @ sK1 @ X3 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f8,f10,f9]) ).
thf(f9,plain,
! [X0: $i] :
( ? [X1: $i] :
( ( ( cB @ X0 @ X1 )
= $true )
& ( ( cC @ X1 )
= $true ) )
=> ( ( ( cB @ X0 @ ( sK0 @ X0 ) )
= $true )
& ( $true
= ( cC @ ( sK0 @ X0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
( ? [X2: $i] :
( ( ( cA @ X2 )
= $true )
& ! [X3: $i] :
( ( ( cC @ X3 )
!= $true )
| ( ( cB @ X2 @ X3 )
!= $true ) ) )
=> ( ( ( cA @ sK1 )
= $true )
& ! [X3: $i] :
( ( ( cC @ X3 )
!= $true )
| ( $true
!= ( cB @ sK1 @ X3 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
( ! [X0: $i] :
( ? [X1: $i] :
( ( ( cB @ X0 @ X1 )
= $true )
& ( ( cC @ X1 )
= $true ) )
| ( ( cA @ X0 )
!= $true ) )
& ? [X2: $i] :
( ( ( cA @ X2 )
= $true )
& ! [X3: $i] :
( ( ( cC @ X3 )
!= $true )
| ( ( cB @ X2 @ X3 )
!= $true ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
( ! [X2: $i] :
( ? [X3: $i] :
( ( ( cB @ X2 @ X3 )
= $true )
& ( ( cC @ X3 )
= $true ) )
| ( ( cA @ X2 )
!= $true ) )
& ? [X0: $i] :
( ( ( cA @ X0 )
= $true )
& ! [X1: $i] :
( ( ( cC @ X1 )
!= $true )
| ( ( cB @ X0 @ X1 )
!= $true ) ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( ~ ! [X0: $i] :
( ( ( cA @ X0 )
= $true )
=> ? [X1: $i] :
( ( ( cC @ X1 )
= $true )
& ( ( cB @ X0 @ X1 )
= $true ) ) )
=> ? [X2: $i] :
( ~ ? [X3: $i] :
~ ( ( ( cB @ X2 @ X3 )
= $true )
=> ( ( cC @ X3 )
!= $true ) )
& ( ( cA @ X2 )
= $true ) ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ~ ! [X0: $i] :
( ( ( cA @ X0 )
= $true )
=> ? [X1: $i] :
( ( ( cC @ X1 )
= $true )
& ( ( cB @ X0 @ X1 )
= $true ) ) )
=> ? [X2: $i] :
( ( ( cA @ X2 )
= $true )
& ~ ? [X3: $i] :
~ ( ( ( cB @ X2 @ X3 )
= $true )
=> ( ( cC @ X3 )
!= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ~ ! [X0: $i] :
( ( cA @ X0 )
=> ? [X1: $i] :
( ( cC @ X1 )
& ( cB @ X0 @ X1 ) ) )
=> ? [X2: $i] :
( ( cA @ X2 )
& ~ ? [X3: $i] :
~ ( ( cB @ X2 @ X3 )
=> ~ ( cC @ X3 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ~ ! [X0: $i] :
( ( cA @ X0 )
=> ? [X1: $i] :
( ( cC @ X1 )
& ( cB @ X0 @ X1 ) ) )
=> ? [X2: $i] :
( ( cA @ X2 )
& ~ ? [X3: $i] :
~ ( ( cB @ X2 @ X3 )
=> ~ ( cC @ X3 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ~ ! [X0: $i] :
( ( cA @ X0 )
=> ? [X1: $i] :
( ( cC @ X1 )
& ( cB @ X0 @ X1 ) ) )
=> ? [X2: $i] :
( ( cA @ X2 )
& ~ ? [X3: $i] :
~ ( ( cB @ X2 @ X3 )
=> ~ ( cC @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.KcBnJd9xnd/DTF2THF_30962.p',cNNF_EXAMPLE) ).
thf(f14,plain,
! [X0: $i] :
( ( ( cA @ X0 )
!= $true )
| ( $true
= ( cC @ ( sK0 @ X0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f21,plain,
( ( cC @ ( sK0 @ sK1 ) )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f20]) ).
thf(f20,plain,
( ( $true != $true )
| ( ( cC @ ( sK0 @ sK1 ) )
!= $true ) ),
inference(superposition,[status(thm)],[f12,f19]) ).
thf(f19,plain,
( ( cB @ sK1 @ ( sK0 @ sK1 ) )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f18]) ).
thf(f18,plain,
( ( $true != $true )
| ( ( cB @ sK1 @ ( sK0 @ sK1 ) )
= $true ) ),
inference(superposition,[status(thm)],[f15,f13]) ).
thf(f15,plain,
! [X0: $i] :
( ( ( cA @ X0 )
!= $true )
| ( ( cB @ X0 @ ( sK0 @ X0 ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f12,plain,
! [X3: $i] :
( ( $true
!= ( cB @ sK1 @ X3 ) )
| ( ( cC @ X3 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO159^5 : TPTP v9.2.1. Released v4.0.0.
% 0.11/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.14/0.33 % Computer : n003.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue Feb 24 14:24:40 EST 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.27/0.45 ---- Original DTF file ---
% 0.27/0.45 thf(spec,logic,$$dhol).
% 0.27/0.45 %------------------------------------------------------------------------------
% 0.27/0.45 % File : SYO159^5 : TPTP v9.2.1. Released v4.0.0.
% 0.27/0.45 % Domain : Syntactic
% 0.27/0.45 % Problem : TPS problem from BASIC-FO-THMS
% 0.27/0.45 % Version : Especial.
% 0.27/0.45 % English :
% 0.27/0.45
% 0.27/0.45 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.27/0.45 % Source : [Bro09]
% 0.27/0.45 % Names : tps_0855 [Bro09]
% 0.27/0.45
% 0.27/0.45 % Status : Theorem
% 0.27/0.45 % Rating : 0.17 v9.1.0, 0.12 v9.0.0, 0.17 v8.2.0, 0.18 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
% 0.27/0.45 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.27/0.45 % Number of atoms : 6 ( 0 equ; 0 cnn)
% 0.27/0.45 % Maximal formula atoms : 6 ( 6 avg)
% 0.27/0.45 % Number of connectives : 17 ( 4 ~; 0 |; 2 &; 8 @)
% 0.27/0.45 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.27/0.45 % Maximal formula depth : 10 ( 10 avg)
% 0.27/0.45 % Number of types : 2 ( 0 usr)
% 0.27/0.45 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.27/0.45 % Number of symbols : 3 ( 3 usr; 0 con; 1-2 aty)
% 0.27/0.45 % Number of variables : 4 ( 0 ^; 1 !; 3 ?; 4 :)
% 0.27/0.45 % SPC : TH0_THM_NEQ_NAR
% 0.27/0.45
% 0.27/0.45 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.27/0.45 % project in the Department of Mathematical Sciences at Carnegie
% 0.27/0.45 % Mellon University. Distributed under the Creative Commons copyleft
% 0.27/0.45 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.27/0.45 %------------------------------------------------------------------------------
% 0.27/0.45 thf(cC,type,
% 0.27/0.45 cC: $i > $o ).
% 0.27/0.45
% 0.27/0.45 thf(cB,type,
% 0.27/0.45 cB: $i > $i > $o ).
% 0.27/0.45
% 0.27/0.45 thf(cA,type,
% 0.27/0.45 cA: $i > $o ).
% 0.27/0.45
% 0.27/0.45 thf(cNNF_EXAMPLE,conjecture,
% 0.27/0.45 ( ~ ! [Xx: $i] :
% 0.27/0.45 ( ( cA @ Xx )
% 0.27/0.45 => ? [Xy: $i] :
% 0.27/0.45 ( ( cB @ Xx @ Xy )
% 0.27/0.45 & ( cC @ Xy ) ) )
% 0.27/0.45 => ? [Xu: $i] :
% 0.27/0.45 ( ( cA @ Xu )
% 0.27/0.45 & ~ ? [Xv: $i] :
% 0.27/0.45 ~ ( ( cB @ Xu @ Xv )
% 0.27/0.45 => ~ ( cC @ Xv ) ) ) ) ).
% 0.27/0.45
% 0.27/0.45 %------------------------------------------------------------------------------
% 0.27/0.45 ------------------------
% 1.51/1.24 ---- Embedded in THF ---
% 1.51/1.24 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.51/1.24 %%% Generated on Tue Feb 24 14:24:41 EST 2026
% 1.51/1.24 %%% using '$$dhol' embedding, version 1.3.0.
% 1.51/1.24 %%% Logic specification used:
% 1.51/1.24 %%% thf(spec, logic, $$dhol).
% 1.51/1.24
% 1.51/1.24 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.KcBnJd9xnd/DTF2DTF30962.p
% See solution above
% 1.51/1.24 ------------------------
% 1.51/1.25 ---- Cleaned THF ---
% 1.51/1.25 thf(cC,type,
% 1.51/1.25 cC: $i > $o ).
% 1.51/1.25
% 1.51/1.25 thf(cB,type,
% 1.51/1.25 cB: $i > $i > $o ).
% 1.51/1.25
% 1.51/1.25 thf(cA,type,
% 1.51/1.25 cA: $i > $o ).
% 1.51/1.25
% 1.51/1.25 thf(cNNF_EXAMPLE,conjecture,
% 1.51/1.25 ( ~ ! [Xx: $i] :
% 1.51/1.25 ( ( cA @ Xx )
% 1.51/1.25 => ? [Xy: $i] :
% 1.51/1.25 ( ( cB @ Xx @ Xy )
% 1.51/1.25 & ( cC @ Xy ) ) )
% 1.51/1.25 => ? [Xu: $i] :
% 1.51/1.25 ( ( cA @ Xu )
% 1.51/1.25 & ~ ? [Xv: $i] :
% 1.51/1.25 ~ ( ( cB @ Xu @ Xv )
% 1.51/1.25 => ~ ( cC @ Xv ) ) ) ) ).
% 1.51/1.25 ------------------------
% 1.51/1.26 % (31156)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_30962 for (3000ds/2Mi)
% 1.51/1.26 % (31158)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_30962 for (3000ds/18Mi)
% 1.51/1.26 % (31153)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_30962 for (3000ds/4Mi)
% 1.51/1.26 % (31156)Instruction limit reached!
% 1.51/1.26 % (31156)------------------------------
% 1.51/1.26 % (31156)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.26 % (31156)Termination reason: Unknown
% 1.51/1.26 % (31156)Termination phase: Saturation
% 1.51/1.26
% 1.51/1.26 % (31156)Memory used [KB]: 5500
% 1.51/1.26 % (31156)Time elapsed: 0.002 s
% 1.51/1.26 % (31156)Instructions burned: 2 (million)
% 1.51/1.26 % (31156)------------------------------
% 1.51/1.26 % (31156)------------------------------
% 1.51/1.26 % (31155)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_30962 for (3000ds/2Mi)
% 1.51/1.26 % (31158)First to succeed.
% 1.51/1.27 % (31155)Instruction limit reached!
% 1.51/1.27 % (31155)------------------------------
% 1.51/1.27 % (31155)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.27 % (31155)Termination reason: Unknown
% 1.51/1.27 % (31155)Termination phase: Saturation
% 1.51/1.27
% 1.51/1.27 % (31155)Memory used [KB]: 5500
% 1.51/1.27 % (31155)Time elapsed: 0.002 s
% 1.51/1.27 % (31155)Instructions burned: 2 (million)
% 1.51/1.27 % (31155)------------------------------
% 1.51/1.27 % (31155)------------------------------
% 1.51/1.27 % (31153)Also succeeded, but the first one will report.
% 1.51/1.27 % (31158)Refutation found. Thanks to Tanya!
% 1.51/1.27 % SZS status Theorem for DTF2THF_30962
% 1.51/1.27 % SZS output start Proof for DTF2THF_30962
% 1.51/1.27 thf(func_def_0, type, cC: $i > $o).
% 1.51/1.27 thf(func_def_1, type, cB: $i > $i > $o).
% 1.51/1.27 thf(func_def_2, type, cA: $i > $o).
% 1.51/1.27 thf(func_def_6, type, sK0: $i > $i).
% 1.51/1.27 thf(f22,plain,(
% 1.51/1.27 $false),
% 1.51/1.27 inference(subsumption_resolution,[status(thm)],[f21,f17])).
% 1.51/1.27 thf(f17,plain,(
% 1.51/1.27 ((cC @ (sK0 @ sK1)) = $true)),
% 1.51/1.27 inference(trivial_inequality_removal,[status(thm)],[f16])).
% 1.51/1.27 thf(f16,plain,(
% 1.51/1.27 ((cC @ (sK0 @ sK1)) = $true) | ($true != $true)),
% 1.51/1.27 inference(superposition,[status(thm)],[f14,f13])).
% 1.51/1.27 thf(f13,plain,(
% 1.51/1.27 ((cA @ sK1) = $true)),
% 1.51/1.27 inference(cnf_transformation,[status(thm)],[f11])).
% 1.51/1.27 thf(f11,plain,(
% 1.51/1.27 ! [X0 : $i] : ((((cB @ X0 @ (sK0 @ X0)) = $true) & ($true = (cC @ (sK0 @ X0)))) | ((cA @ X0) != $true)) & (((cA @ sK1) = $true) & ! [X3 : $i] : (((cC @ X3) != $true) | ($true != (cB @ sK1 @ X3))))),
% 1.51/1.27 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f8,f10,f9])).
% 1.51/1.27 thf(f9,plain,(
% 1.51/1.27 ! [X0 : $i] : (? [X1 : $i] : (((cB @ X0 @ X1) = $true) & ((cC @ X1) = $true)) => (((cB @ X0 @ (sK0 @ X0)) = $true) & ($true = (cC @ (sK0 @ X0)))))),
% 1.51/1.27 introduced(definition,[],[choice_axiom])).
% 1.51/1.27 thf(f10,plain,(
% 1.51/1.27 ? [X2 : $i] : (((cA @ X2) = $true) & ! [X3 : $i] : (((cC @ X3) != $true) | ((cB @ X2 @ X3) != $true))) => (((cA @ sK1) = $true) & ! [X3 : $i] : (((cC @ X3) != $true) | ($true != (cB @ sK1 @ X3))))),
% 1.51/1.27 introduced(definition,[],[choice_axiom])).
% 1.51/1.27 thf(f8,plain,(
% 1.51/1.27 ! [X0 : $i] : (? [X1 : $i] : (((cB @ X0 @ X1) = $true) & ((cC @ X1) = $true)) | ((cA @ X0) != $true)) & ? [X2 : $i] : (((cA @ X2) = $true) & ! [X3 : $i] : (((cC @ X3) != $true) | ((cB @ X2 @ X3) != $true)))),
% 1.51/1.27 inference(rectify,[status(thm)],[f7])).
% 1.51/1.27 thf(f7,plain,(
% 1.51/1.27 ! [X2 : $i] : (? [X3 : $i] : (((cB @ X2 @ X3) = $true) & ((cC @ X3) = $true)) | ((cA @ X2) != $true)) & ? [X0 : $i] : (((cA @ X0) = $true) & ! [X1 : $i] : (((cC @ X1) != $true) | ((cB @ X0 @ X1) != $true)))),
% 1.51/1.27 inference(ennf_transformation,[status(thm)],[f6])).
% 1.51/1.27 thf(f6,plain,(
% 1.51/1.27 ~(~! [X0 : $i] : (((cA @ X0) = $true) => ? [X1 : $i] : (((cC @ X1) = $true) & ((cB @ X0 @ X1) = $true))) => ? [X2 : $i] : (~? [X3 : $i] : ~(((cB @ X2 @ X3) = $true) => ((cC @ X3) != $true)) & ((cA @ X2) = $true)))),
% 1.51/1.27 inference(flattening,[status(thm)],[f5])).
% 1.51/1.27 thf(f5,plain,(
% 1.51/1.27 ~(~! [X0 : $i] : (((cA @ X0) = $true) => ? [X1 : $i] : (((cC @ X1) = $true) & ((cB @ X0 @ X1) = $true))) => ? [X2 : $i] : (((cA @ X2) = $true) & ~? [X3 : $i] : ~(((cB @ X2 @ X3) = $true) => ~((cC @ X3) = $true))))),
% 1.51/1.27 inference(fool_elimination,[status(thm)],[f4])).
% 1.51/1.27 thf(f4,plain,(
% 1.51/1.27 ~(~! [X0 : $i] : ((cA @ X0) => ? [X1 : $i] : ((cC @ X1) & (cB @ X0 @ X1))) => ? [X2 : $i] : ((cA @ X2) & ~? [X3 : $i] : ~((cB @ X2 @ X3) => ~(cC @ X3))))),
% 1.51/1.27 inference(rectify,[status(thm)],[f2])).
% 1.51/1.27 thf(f2,negated_conjecture,(
% 1.51/1.27 ~(~! [X0 : $i] : ((cA @ X0) => ? [X1 : $i] : ((cC @ X1) & (cB @ X0 @ X1))) => ? [X2 : $i] : ((cA @ X2) & ~? [X3 : $i] : ~((cB @ X2 @ X3) => ~(cC @ X3))))),
% 1.51/1.27 inference(negated_conjecture,[status(cth)],[f1])).
% 1.51/1.27 thf(f1,conjecture,(
% 1.51/1.27 ~! [X0 : $i] : ((cA @ X0) => ? [X1 : $i] : ((cC @ X1) & (cB @ X0 @ X1))) => ? [X2 : $i] : ((cA @ X2) & ~? [X3 : $i] : ~((cB @ X2 @ X3) => ~(cC @ X3)))),
% 1.51/1.27 file('/export/starexec/sandbox/tmp/tmp.KcBnJd9xnd/DTF2THF_30962.p',cNNF_EXAMPLE)).
% 1.51/1.27 thf(f14,plain,(
% 1.51/1.27 ( ! [X0 : $i] : (((cA @ X0) != $true) | ($true = (cC @ (sK0 @ X0)))) )),
% 1.51/1.27 inference(cnf_transformation,[status(thm)],[f11])).
% 1.51/1.27 thf(f21,plain,(
% 1.51/1.27 ((cC @ (sK0 @ sK1)) != $true)),
% 1.51/1.27 inference(trivial_inequality_removal,[status(thm)],[f20])).
% 1.51/1.27 thf(f20,plain,(
% 1.51/1.27 ($true != $true) | ((cC @ (sK0 @ sK1)) != $true)),
% 1.51/1.27 inference(superposition,[status(thm)],[f12,f19])).
% 1.51/1.27 thf(f19,plain,(
% 1.51/1.27 ((cB @ sK1 @ (sK0 @ sK1)) = $true)),
% 1.51/1.27 inference(trivial_inequality_removal,[status(thm)],[f18])).
% 1.51/1.27 thf(f18,plain,(
% 1.51/1.27 ($true != $true) | ((cB @ sK1 @ (sK0 @ sK1)) = $true)),
% 1.51/1.27 inference(superposition,[status(thm)],[f15,f13])).
% 1.51/1.27 thf(f15,plain,(
% 1.51/1.27 ( ! [X0 : $i] : (((cA @ X0) != $true) | ((cB @ X0 @ (sK0 @ X0)) = $true)) )),
% 1.51/1.27 inference(cnf_transformation,[status(thm)],[f11])).
% 1.51/1.27 thf(f12,plain,(
% 1.51/1.27 ( ! [X3 : $i] : (($true != (cB @ sK1 @ X3)) | ((cC @ X3) != $true)) )),
% 1.51/1.27 inference(cnf_transformation,[status(thm)],[f11])).
% 1.51/1.27 % SZS output end Proof for DTF2THF_30962
% 1.51/1.27 % (31158)------------------------------
% 1.51/1.27 % (31158)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.27 % (31158)Termination reason: Refutation
% 1.51/1.27
% 1.51/1.27 % (31158)Memory used [KB]: 5500
% 1.51/1.27 % (31158)Time elapsed: 0.002 s
% 1.51/1.27 % (31158)Instructions burned: 2 (million)
% 1.51/1.27 % (31158)------------------------------
% 1.51/1.27 % (31158)------------------------------
% 1.51/1.27 % (31151)Success in time 0.003 s
%------------------------------------------------------------------------------