%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYN361^5 : 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 09:50:51 AM UTC 2026
% Result : Theorem 1.48s 1.25s
% Output : Refutation 1.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 20 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 177 ( 51 equ; 0 cnn)
% Maximal formula atoms : 6 ( 8 avg)
% Number of connectives : 201 ( 33 ~; 11 |; 22 &; 118 @)
% ( 0 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 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 : 74 ( 0 ^; 51 !; 23 ?; 74 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cS: $i > $o ).
thf(func_def_1,type,
cQ: $i > $i > $o ).
thf(func_def_2,type,
cP: $i > $i > $o ).
thf(func_def_6,type,
sK0: $i > $i ).
thf(f28,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f26]) ).
thf(f26,plain,
$true != $true,
inference(superposition,[status(thm)],[f23,f17]) ).
thf(f17,plain,
! [X3: $i] :
( ( cQ @ ( sK0 @ X3 ) @ X3 )
= $true ),
inference(subsumption_resolution,[status(thm)],[f14,f15]) ).
thf(f15,plain,
! [X2: $i] :
( $true
= ( cS @ X2 ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ! [X0: $i,X1: $i] :
( ( ( cQ @ X1 @ X0 )
!= $true )
| ( ( cP @ X1 @ X0 )
!= $true ) )
& ! [X2: $i] :
( $true
= ( cS @ X2 ) )
& ! [X3: $i] :
( ( ( cS @ X3 )
!= $true )
| ( ( cQ @ ( sK0 @ X3 ) @ X3 )
= $true ) )
& ! [X6: $i] :
( ( cP @ X6 @ sK1 )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f9,f11,f10]) ).
thf(f10,plain,
! [X3: $i] :
( ? [X4: $i] :
( ( cQ @ X4 @ X3 )
= $true )
=> ( ( cQ @ ( sK0 @ X3 ) @ X3 )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
( ? [X5: $i] :
! [X6: $i] :
( ( cP @ X6 @ X5 )
= $true )
=> ! [X6: $i] :
( ( cP @ X6 @ sK1 )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
( ! [X0: $i,X1: $i] :
( ( ( cQ @ X1 @ X0 )
!= $true )
| ( ( cP @ X1 @ X0 )
!= $true ) )
& ! [X2: $i] :
( $true
= ( cS @ X2 ) )
& ! [X3: $i] :
( ( ( cS @ X3 )
!= $true )
| ? [X4: $i] :
( ( cQ @ X4 @ X3 )
= $true ) )
& ? [X5: $i] :
! [X6: $i] :
( ( cP @ X6 @ X5 )
= $true ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,plain,
( ! [X5: $i,X4: $i] :
( ( ( cQ @ X4 @ X5 )
!= $true )
| ( ( cP @ X4 @ X5 )
!= $true ) )
& ! [X6: $i] :
( ( cS @ X6 )
= $true )
& ! [X2: $i] :
( ( $true
!= ( cS @ X2 ) )
| ? [X3: $i] :
( ( cQ @ X3 @ X2 )
= $true ) )
& ? [X0: $i] :
! [X1: $i] :
( ( cP @ X1 @ X0 )
= $true ) ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
( ! [X6: $i] :
( ( cS @ X6 )
= $true )
& ! [X5: $i,X4: $i] :
( ( ( cQ @ X4 @ X5 )
!= $true )
| ( ( cP @ X4 @ X5 )
!= $true ) )
& ! [X2: $i] :
( ( $true
!= ( cS @ X2 ) )
| ? [X3: $i] :
( ( cQ @ X3 @ X2 )
= $true ) )
& ? [X0: $i] :
! [X1: $i] :
( ( cP @ X1 @ X0 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( ( ! [X4: $i,X5: $i] :
( ( ( cP @ X4 @ X5 )
= $true )
=> ( ( cQ @ X4 @ X5 )
!= $true ) )
& ! [X2: $i] :
( ( $true
= ( cS @ X2 ) )
=> ? [X3: $i] :
( ( cQ @ X3 @ X2 )
= $true ) )
& ? [X0: $i] :
! [X1: $i] :
( ( cP @ X1 @ X0 )
= $true ) )
=> ? [X6: $i] :
( ( cS @ X6 )
!= $true ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ? [X0: $i] :
! [X1: $i] :
( ( cP @ X1 @ X0 )
= $true )
& ! [X2: $i] :
( ( $true
= ( cS @ X2 ) )
=> ? [X3: $i] :
( ( cQ @ X3 @ X2 )
= $true ) )
& ! [X4: $i,X5: $i] :
( ( ( cP @ X4 @ X5 )
= $true )
=> ( ( cQ @ X4 @ X5 )
!= $true ) ) )
=> ? [X6: $i] :
( ( cS @ X6 )
!= $true ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ? [X0: $i] :
! [X1: $i] : ( cP @ X1 @ X0 )
& ! [X2: $i] :
( ( cS @ X2 )
=> ? [X3: $i] : ( cQ @ X3 @ X2 ) )
& ! [X4: $i,X5: $i] :
( ( cP @ X4 @ X5 )
=> ~ ( cQ @ X4 @ X5 ) ) )
=> ? [X6: $i] :
~ ( cS @ X6 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ? [X0: $i] :
! [X1: $i] : ( cP @ X1 @ X0 )
& ! [X1: $i] :
( ( cS @ X1 )
=> ? [X2: $i] : ( cQ @ X2 @ X1 ) )
& ! [X1: $i,X2: $i] :
( ( cP @ X1 @ X2 )
=> ~ ( cQ @ X1 @ X2 ) ) )
=> ? [X3: $i] :
~ ( cS @ X3 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ? [X0: $i] :
! [X1: $i] : ( cP @ X1 @ X0 )
& ! [X1: $i] :
( ( cS @ X1 )
=> ? [X2: $i] : ( cQ @ X2 @ X1 ) )
& ! [X1: $i,X2: $i] :
( ( cP @ X1 @ X2 )
=> ~ ( cQ @ X1 @ X2 ) ) )
=> ? [X3: $i] :
~ ( cS @ X3 ) ),
file('/export/starexec/sandbox/tmp/tmp.n9V4nLkolM/DTF2THF_10721.p',cX2112) ).
thf(f14,plain,
! [X3: $i] :
( ( ( cQ @ ( sK0 @ X3 ) @ X3 )
= $true )
| ( ( cS @ X3 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f23,plain,
! [X0: $i] :
( $true
!= ( cQ @ X0 @ sK1 ) ),
inference(trivial_inequality_removal,[status(thm)],[f22]) ).
thf(f22,plain,
! [X0: $i] :
( ( $true != $true )
| ( $true
!= ( cQ @ X0 @ sK1 ) ) ),
inference(superposition,[status(thm)],[f16,f13]) ).
thf(f13,plain,
! [X6: $i] :
( ( cP @ X6 @ sK1 )
= $true ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f16,plain,
! [X0: $i,X1: $i] :
( ( ( cP @ X1 @ X0 )
!= $true )
| ( ( cQ @ X1 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYN361^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n003.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 13:55:55 EST 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.33 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 : SYN361^5 : TPTP v9.2.1. Released v4.0.0.
% 0.30/0.45 % Domain : Syntactic
% 0.30/0.45 % Problem : TPS problem X2112
% 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_0260 [Bro09]
% 0.30/0.45 % : X2112 [TPS]
% 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 v5.3.0, 0.25 v5.2.0, 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 : 6 ( 0 equ; 0 cnn)
% 0.30/0.45 % Maximal formula atoms : 6 ( 6 avg)
% 0.30/0.45 % Number of connectives : 17 ( 2 ~; 0 |; 2 &; 10 @)
% 0.30/0.45 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.30/0.45 % Maximal formula depth : 10 ( 10 avg)
% 0.30/0.45 % Number of types : 2 ( 0 usr)
% 0.30/0.45 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.30/0.45 % Number of symbols : 3 ( 3 usr; 0 con; 1-2 aty)
% 0.30/0.45 % Number of variables : 7 ( 0 ^; 4 !; 3 ?; 7 :)
% 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 %------------------------------------------------------------------------------
% 0.30/0.45 thf(cS,type,
% 0.30/0.45 cS: $i > $o ).
% 0.30/0.45
% 0.30/0.45 thf(cQ,type,
% 0.30/0.45 cQ: $i > $i > $o ).
% 0.30/0.45
% 0.30/0.45 thf(cP,type,
% 0.30/0.45 cP: $i > $i > $o ).
% 0.30/0.45
% 0.30/0.45 thf(cX2112,conjecture,
% 0.30/0.45 ( ( ? [Xv: $i] :
% 0.30/0.45 ! [Xx: $i] : ( cP @ Xx @ Xv )
% 0.30/0.45 & ! [Xx: $i] :
% 0.30/0.45 ( ( cS @ Xx )
% 0.30/0.45 => ? [Xy: $i] : ( cQ @ Xy @ Xx ) )
% 0.30/0.45 & ! [Xx: $i,Xy: $i] :
% 0.30/0.45 ( ( cP @ Xx @ Xy )
% 0.30/0.45 => ~ ( cQ @ Xx @ Xy ) ) )
% 0.30/0.45 => ? [Xu: $i] :
% 0.30/0.45 ~ ( cS @ Xu ) ) ).
% 0.30/0.45
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 ------------------------
% 1.48/1.22 ---- Embedded in THF ---
% 1.48/1.22 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.48/1.22 %%% Generated on Tue Feb 24 13:55:56 EST 2026
% 1.48/1.22 %%% using '$$dhol' embedding, version 1.3.0.
% 1.48/1.22 %%% Logic specification used:
% 1.48/1.22 %%% thf(spec, logic, $$dhol).
% 1.48/1.22
% 1.48/1.22 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.n9V4nLkolM/DTF2DTF10721.p
% See solution above
% 1.48/1.22 ------------------------
% 1.48/1.23 ---- Cleaned THF ---
% 1.48/1.23 thf(cS,type,
% 1.48/1.23 cS: $i > $o ).
% 1.48/1.23
% 1.48/1.23 thf(cQ,type,
% 1.48/1.23 cQ: $i > $i > $o ).
% 1.48/1.23
% 1.48/1.23 thf(cP,type,
% 1.48/1.23 cP: $i > $i > $o ).
% 1.48/1.23
% 1.48/1.23 thf(cX2112,conjecture,
% 1.48/1.23 ( ( ? [Xv: $i] :
% 1.48/1.23 ! [Xx: $i] : ( cP @ Xx @ Xv )
% 1.48/1.23 & ! [Xx: $i] :
% 1.48/1.23 ( ( cS @ Xx )
% 1.48/1.23 => ? [Xy: $i] : ( cQ @ Xy @ Xx ) )
% 1.48/1.23 & ! [Xx: $i,Xy: $i] :
% 1.48/1.23 ( ( cP @ Xx @ Xy )
% 1.48/1.23 => ~ ( cQ @ Xx @ Xy ) ) )
% 1.48/1.23 => ? [Xu: $i] :
% 1.48/1.23 ~ ( cS @ Xu ) ) ).
% 1.48/1.23 ------------------------
% 1.48/1.25 % (10836)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_10721 for (2999ds/4Mi)
% 1.48/1.25 % (10835)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_10721 for (2999ds/183Mi)
% 1.48/1.25 % (10836)First to succeed.
% 1.48/1.25 % (10835)Also succeeded, but the first one will report.
% 1.48/1.25 % (10836)Refutation found. Thanks to Tanya!
% 1.48/1.25 % SZS status Theorem for DTF2THF_10721
% 1.48/1.25 % SZS output start Proof for DTF2THF_10721
% 1.48/1.25 thf(func_def_0, type, cS: $i > $o).
% 1.48/1.25 thf(func_def_1, type, cQ: $i > $i > $o).
% 1.48/1.25 thf(func_def_2, type, cP: $i > $i > $o).
% 1.48/1.25 thf(func_def_6, type, sK0: $i > $i).
% 1.48/1.25 thf(f28,plain,(
% 1.48/1.25 $false),
% 1.48/1.25 inference(trivial_inequality_removal,[status(thm)],[f26])).
% 1.48/1.25 thf(f26,plain,(
% 1.48/1.25 ($true != $true)),
% 1.48/1.25 inference(superposition,[status(thm)],[f23,f17])).
% 1.48/1.25 thf(f17,plain,(
% 1.48/1.25 ( ! [X3 : $i] : (((cQ @ (sK0 @ X3) @ X3) = $true)) )),
% 1.48/1.25 inference(subsumption_resolution,[status(thm)],[f14,f15])).
% 1.48/1.25 thf(f15,plain,(
% 1.48/1.25 ( ! [X2 : $i] : (($true = (cS @ X2))) )),
% 1.48/1.25 inference(cnf_transformation,[status(thm)],[f12])).
% 1.48/1.25 thf(f12,plain,(
% 1.48/1.25 ! [X0 : $i,X1 : $i] : (((cQ @ X1 @ X0) != $true) | ((cP @ X1 @ X0) != $true)) & ! [X2 : $i] : ($true = (cS @ X2)) & ! [X3 : $i] : (((cS @ X3) != $true) | ((cQ @ (sK0 @ X3) @ X3) = $true)) & ! [X6 : $i] : ((cP @ X6 @ sK1) = $true)),
% 1.48/1.25 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f9,f11,f10])).
% 1.48/1.25 thf(f10,plain,(
% 1.48/1.25 ! [X3 : $i] : (? [X4 : $i] : ((cQ @ X4 @ X3) = $true) => ((cQ @ (sK0 @ X3) @ X3) = $true))),
% 1.48/1.25 introduced(definition,[],[choice_axiom])).
% 1.48/1.25 thf(f11,plain,(
% 1.48/1.25 ? [X5 : $i] : ! [X6 : $i] : ((cP @ X6 @ X5) = $true) => ! [X6 : $i] : ((cP @ X6 @ sK1) = $true)),
% 1.48/1.25 introduced(definition,[],[choice_axiom])).
% 1.48/1.25 thf(f9,plain,(
% 1.48/1.25 ! [X0 : $i,X1 : $i] : (((cQ @ X1 @ X0) != $true) | ((cP @ X1 @ X0) != $true)) & ! [X2 : $i] : ($true = (cS @ X2)) & ! [X3 : $i] : (((cS @ X3) != $true) | ? [X4 : $i] : ((cQ @ X4 @ X3) = $true)) & ? [X5 : $i] : ! [X6 : $i] : ((cP @ X6 @ X5) = $true)),
% 1.48/1.25 inference(rectify,[status(thm)],[f8])).
% 1.48/1.25 thf(f8,plain,(
% 1.48/1.25 ! [X5 : $i,X4 : $i] : (((cQ @ X4 @ X5) != $true) | ((cP @ X4 @ X5) != $true)) & ! [X6 : $i] : ((cS @ X6) = $true) & ! [X2 : $i] : (($true != (cS @ X2)) | ? [X3 : $i] : ((cQ @ X3 @ X2) = $true)) & ? [X0 : $i] : ! [X1 : $i] : ((cP @ X1 @ X0) = $true)),
% 1.48/1.25 inference(flattening,[status(thm)],[f7])).
% 1.48/1.25 thf(f7,plain,(
% 1.48/1.25 ! [X6 : $i] : ((cS @ X6) = $true) & (! [X5 : $i,X4 : $i] : (((cQ @ X4 @ X5) != $true) | ((cP @ X4 @ X5) != $true)) & ! [X2 : $i] : (($true != (cS @ X2)) | ? [X3 : $i] : ((cQ @ X3 @ X2) = $true)) & ? [X0 : $i] : ! [X1 : $i] : ((cP @ X1 @ X0) = $true))),
% 1.48/1.25 inference(ennf_transformation,[status(thm)],[f6])).
% 1.48/1.25 thf(f6,plain,(
% 1.48/1.25 ~((! [X4 : $i,X5 : $i] : (((cP @ X4 @ X5) = $true) => ((cQ @ X4 @ X5) != $true)) & ! [X2 : $i] : (($true = (cS @ X2)) => ? [X3 : $i] : ((cQ @ X3 @ X2) = $true)) & ? [X0 : $i] : ! [X1 : $i] : ((cP @ X1 @ X0) = $true)) => ? [X6 : $i] : ((cS @ X6) != $true))),
% 1.48/1.25 inference(flattening,[status(thm)],[f5])).
% 1.48/1.25 thf(f5,plain,(
% 1.48/1.25 ~((? [X0 : $i] : ! [X1 : $i] : ((cP @ X1 @ X0) = $true) & ! [X2 : $i] : (($true = (cS @ X2)) => ? [X3 : $i] : ((cQ @ X3 @ X2) = $true)) & ! [X4 : $i,X5 : $i] : (((cP @ X4 @ X5) = $true) => ~((cQ @ X4 @ X5) = $true))) => ? [X6 : $i] : ~((cS @ X6) = $true))),
% 1.48/1.25 inference(fool_elimination,[status(thm)],[f4])).
% 1.48/1.25 thf(f4,plain,(
% 1.48/1.25 ~((? [X0 : $i] : ! [X1 : $i] : (cP @ X1 @ X0) & ! [X2 : $i] : ((cS @ X2) => ? [X3 : $i] : (cQ @ X3 @ X2)) & ! [X4 : $i,X5 : $i] : ((cP @ X4 @ X5) => ~(cQ @ X4 @ X5))) => ? [X6 : $i] : ~(cS @ X6))),
% 1.48/1.25 inference(rectify,[status(thm)],[f2])).
% 1.48/1.25 thf(f2,negated_conjecture,(
% 1.48/1.25 ~((? [X0 : $i] : ! [X1 : $i] : (cP @ X1 @ X0) & ! [X1 : $i] : ((cS @ X1) => ? [X2 : $i] : (cQ @ X2 @ X1)) & ! [X1 : $i,X2 : $i] : ((cP @ X1 @ X2) => ~(cQ @ X1 @ X2))) => ? [X3 : $i] : ~(cS @ X3))),
% 1.48/1.25 inference(negated_conjecture,[status(cth)],[f1])).
% 1.48/1.25 thf(f1,conjecture,(
% 1.48/1.25 (? [X0 : $i] : ! [X1 : $i] : (cP @ X1 @ X0) & ! [X1 : $i] : ((cS @ X1) => ? [X2 : $i] : (cQ @ X2 @ X1)) & ! [X1 : $i,X2 : $i] : ((cP @ X1 @ X2) => ~(cQ @ X1 @ X2))) => ? [X3 : $i] : ~(cS @ X3)),
% 1.48/1.25 file('/export/starexec/sandbox/tmp/tmp.n9V4nLkolM/DTF2THF_10721.p',cX2112)).
% 1.48/1.25 thf(f14,plain,(
% 1.48/1.25 ( ! [X3 : $i] : (((cQ @ (sK0 @ X3) @ X3) = $true) | ((cS @ X3) != $true)) )),
% 1.48/1.25 inference(cnf_transformation,[status(thm)],[f12])).
% 1.48/1.25 thf(f23,plain,(
% 1.48/1.25 ( ! [X0 : $i] : (($true != (cQ @ X0 @ sK1))) )),
% 1.48/1.25 inference(trivial_inequality_removal,[status(thm)],[f22])).
% 1.48/1.25 thf(f22,plain,(
% 1.48/1.25 ( ! [X0 : $i] : (($true != $true) | ($true != (cQ @ X0 @ sK1))) )),
% 1.48/1.25 inference(superposition,[status(thm)],[f16,f13])).
% 1.48/1.25 thf(f13,plain,(
% 1.48/1.25 ( ! [X6 : $i] : (((cP @ X6 @ sK1) = $true)) )),
% 1.48/1.25 inference(cnf_transformation,[status(thm)],[f12])).
% 1.48/1.25 thf(f16,plain,(
% 1.48/1.25 ( ! [X0 : $i,X1 : $i] : (((cP @ X1 @ X0) != $true) | ((cQ @ X1 @ X0) != $true)) )),
% 1.48/1.25 inference(cnf_transformation,[status(thm)],[f12])).
% 1.48/1.25 % SZS output end Proof for DTF2THF_10721
% 1.48/1.25 % (10836)------------------------------
% 1.48/1.25 % (10836)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.25 % (10836)Termination reason: Refutation
% 1.48/1.25
% 1.48/1.25 % (10836)Memory used [KB]: 5500
% 1.48/1.25 % (10836)Time elapsed: 0.003 s
% 1.48/1.25 % (10836)Instructions burned: 2 (million)
% 1.48/1.25 % (10836)------------------------------
% 1.48/1.25 % (10836)------------------------------
% 1.48/1.25 % (10834)Success in time 0.004 s
%------------------------------------------------------------------------------