%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO096^5 : 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 09:53:22 AM UTC 2026
% Result : Theorem 1.67s 1.46s
% Output : Refutation 1.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 1
% Syntax : Number of formulae : 18 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 196 ( 44 equ; 0 cnn)
% Maximal formula atoms : 11 ( 10 avg)
% Number of connectives : 196 ( 24 ~; 15 |; 21 &; 124 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 4 con; 0-2 aty)
% Number of variables : 50 ( 0 ^; 42 !; 8 ?; 50 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_1,type,
cQ: $i > $i > $o ).
thf(func_def_3,type,
cR: $i > $i > $o ).
thf(f30,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f29,f21]) ).
thf(f21,plain,
( $true
= ( cQ @ cA @ cA ) ),
inference(trivial_inequality_removal,[status(thm)],[f19]) ).
thf(f19,plain,
( ( $true
= ( cQ @ cA @ cA ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f11,f12]) ).
thf(f12,plain,
( ( cR @ cA @ cB )
= $true ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ( cR @ cA @ cB )
= $true )
& ! [X0: $i] :
( ( ( cQ @ X0 @ X0 )
= $true )
| ! [X1: $i] :
( ( cR @ X0 @ X1 )
!= $true ) )
& ! [X2: $i,X3: $i] :
( ( $true
!= ( cQ @ X3 @ X2 ) )
| ! [X4: $i] :
( ( cR @ X4 @ X2 )
= $true ) )
& ! [X5: $i] :
( ( ( cR @ cB @ X5 )
!= $true )
| ( ( cQ @ X5 @ cA )
!= $true ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ( cR @ cA @ cB )
= $true )
& ! [X3: $i] :
( ( $true
= ( cQ @ X3 @ X3 ) )
| ! [X4: $i] :
( $true
!= ( cR @ X3 @ X4 ) ) )
& ! [X1: $i,X0: $i] :
( ( $true
!= ( cQ @ X0 @ X1 ) )
| ! [X2: $i] :
( $true
= ( cR @ X2 @ X1 ) ) )
& ! [X5: $i] :
( ( ( cR @ cB @ X5 )
!= $true )
| ( ( cQ @ X5 @ cA )
!= $true ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
( ! [X5: $i] :
( ( ( cR @ cB @ X5 )
!= $true )
| ( ( cQ @ X5 @ cA )
!= $true ) )
& ( ( cR @ cA @ cB )
= $true )
& ! [X3: $i] :
( ( $true
= ( cQ @ X3 @ X3 ) )
| ! [X4: $i] :
( $true
!= ( cR @ X3 @ X4 ) ) )
& ! [X1: $i,X0: $i] :
( ( $true
!= ( cQ @ X0 @ X1 ) )
| ! [X2: $i] :
( $true
= ( cR @ X2 @ X1 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ( ( cR @ cA @ cB )
= $true )
& ! [X3: $i] :
( ? [X4: $i] :
( $true
= ( cR @ X3 @ X4 ) )
=> ( $true
= ( cQ @ X3 @ X3 ) ) )
& ! [X1: $i,X0: $i] :
( ( $true
= ( cQ @ X0 @ X1 ) )
=> ! [X2: $i] :
( $true
= ( cR @ X2 @ X1 ) ) ) )
=> ? [X5: $i] :
( ( ( cR @ cB @ X5 )
= $true )
& ( ( cQ @ X5 @ cA )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ! [X0: $i,X1: $i] :
( ( cQ @ X0 @ X1 )
=> ! [X2: $i] : ( cR @ X2 @ X1 ) )
& ! [X3: $i] :
( ? [X4: $i] : ( cR @ X3 @ X4 )
=> ( cQ @ X3 @ X3 ) )
& ( cR @ cA @ cB ) )
=> ? [X5: $i] :
( ( cR @ cB @ X5 )
& ( cQ @ X5 @ cA ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X2: $i,X3: $i] :
( ( cQ @ X2 @ X3 )
=> ! [X4: $i] : ( cR @ X4 @ X3 ) )
& ! [X0: $i] :
( ? [X1: $i] : ( cR @ X0 @ X1 )
=> ( cQ @ X0 @ X0 ) )
& ( cR @ cA @ cB ) )
=> ? [X5: $i] :
( ( cR @ cB @ X5 )
& ( cQ @ X5 @ cA ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ! [X2: $i,X3: $i] :
( ( cQ @ X2 @ X3 )
=> ! [X4: $i] : ( cR @ X4 @ X3 ) )
& ! [X0: $i] :
( ? [X1: $i] : ( cR @ X0 @ X1 )
=> ( cQ @ X0 @ X0 ) )
& ( cR @ cA @ cB ) )
=> ? [X5: $i] :
( ( cR @ cB @ X5 )
& ( cQ @ X5 @ cA ) ) ),
file('/export/starexec/sandbox/tmp/tmp.T10FoXbwTj/DTF2THF_30256.p',cLX1) ).
thf(f11,plain,
! [X0: $i,X1: $i] :
( ( ( cR @ X0 @ X1 )
!= $true )
| ( ( cQ @ X0 @ X0 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f29,plain,
( $true
!= ( cQ @ cA @ cA ) ),
inference(trivial_inequality_removal,[status(thm)],[f26]) ).
thf(f26,plain,
( ( $true != $true )
| ( $true
!= ( cQ @ cA @ cA ) ) ),
inference(superposition,[status(thm)],[f9,f24]) ).
thf(f24,plain,
! [X0: $i] :
( $true
= ( cR @ X0 @ cA ) ),
inference(trivial_inequality_removal,[status(thm)],[f23]) ).
thf(f23,plain,
! [X0: $i] :
( ( $true
= ( cR @ X0 @ cA ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f10,f21]) ).
thf(f10,plain,
! [X2: $i,X3: $i,X4: $i] :
( ( $true
!= ( cQ @ X3 @ X2 ) )
| ( ( cR @ X4 @ X2 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f9,plain,
! [X5: $i] :
( ( ( cR @ cB @ X5 )
!= $true )
| ( ( cQ @ X5 @ cA )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO096^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n016.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 14:24:51 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.48 ---- Original DTF file ---
% 0.19/0.48 thf(spec,logic,$$dhol).
% 0.19/0.48 %------------------------------------------------------------------------------
% 0.19/0.48 % File : SYO096^5 : TPTP v9.2.1. Released v4.0.0.
% 0.19/0.48 % Domain : Syntactic
% 0.19/0.48 % Problem : TPS problem LX1
% 0.19/0.48 % Version : Especial.
% 0.19/0.48 % English :
% 0.19/0.48
% 0.19/0.48 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.19/0.48 % Source : [Bro09]
% 0.19/0.48 % Names : tps_0262 [Bro09]
% 0.19/0.48 % : LX1 [TPS]
% 0.19/0.48
% 0.19/0.48 % Status : Theorem
% 0.19/0.48 % Rating : 0.00 v6.2.0, 0.17 v6.0.0, 0.00 v4.0.0
% 0.19/0.48 % Syntax : Number of formulae : 5 ( 0 unt; 4 typ; 0 def)
% 0.19/0.48 % Number of atoms : 7 ( 0 equ; 0 cnn)
% 0.19/0.48 % Maximal formula atoms : 7 ( 7 avg)
% 0.19/0.48 % Number of connectives : 20 ( 0 ~; 0 |; 3 &; 14 @)
% 0.19/0.48 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.19/0.48 % Maximal formula depth : 10 ( 10 avg)
% 0.19/0.48 % Number of types : 2 ( 0 usr)
% 0.19/0.48 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.19/0.48 % Number of symbols : 4 ( 4 usr; 2 con; 0-2 aty)
% 0.19/0.48 % Number of variables : 6 ( 0 ^; 4 !; 2 ?; 6 :)
% 0.19/0.48 % SPC : TH0_THM_NEQ_NAR
% 0.19/0.48
% 0.19/0.48 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.19/0.48 % project in the Department of Mathematical Sciences at Carnegie
% 0.19/0.48 % Mellon University. Distributed under the Creative Commons copyleft
% 0.19/0.48 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.19/0.48 %------------------------------------------------------------------------------
% 0.19/0.48 thf(cA,type,
% 0.19/0.48 cA: $i ).
% 0.19/0.48
% 0.19/0.48 thf(cQ,type,
% 0.19/0.48 cQ: $i > $i > $o ).
% 0.19/0.48
% 0.19/0.48 thf(cB,type,
% 0.19/0.48 cB: $i ).
% 0.19/0.48
% 0.19/0.48 thf(cR,type,
% 0.19/0.48 cR: $i > $i > $o ).
% 0.19/0.48
% 0.19/0.48 thf(cLX1,conjecture,
% 0.19/0.48 ( ( ( cR @ cA @ cB )
% 0.19/0.48 & ! [X: $i] :
% 0.19/0.48 ( ? [Y: $i] : ( cR @ X @ Y )
% 0.19/0.48 => ( cQ @ X @ X ) )
% 0.19/0.48 & ! [U: $i,V: $i] :
% 0.19/0.48 ( ( cQ @ U @ V )
% 0.19/0.48 => ! [Z: $i] : ( cR @ Z @ V ) ) )
% 0.19/0.48 => ? [W: $i] :
% 0.19/0.48 ( ( cR @ cB @ W )
% 0.19/0.48 & ( cQ @ W @ cA ) ) ) ).
% 0.19/0.48
% 0.19/0.48 %------------------------------------------------------------------------------
% 0.19/0.48 ------------------------
% 1.67/1.42 ---- Embedded in THF ---
% 1.67/1.42 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.67/1.42 %%% Generated on Tue Feb 24 14:24:52 EST 2026
% 1.67/1.42 %%% using '$$dhol' embedding, version 1.3.0.
% 1.67/1.42 %%% Logic specification used:
% 1.67/1.42 %%% thf(spec, logic, $$dhol).
% 1.67/1.42
% 1.67/1.42 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.T10FoXbwTj/DTF2DTF30256.p
% See solution above
% 1.67/1.42 ------------------------
% 1.67/1.43 ---- Cleaned THF ---
% 1.67/1.43 thf(cA,type,
% 1.67/1.43 cA: $i ).
% 1.67/1.43
% 1.67/1.43 thf(cQ,type,
% 1.67/1.43 cQ: $i > $i > $o ).
% 1.67/1.43
% 1.67/1.43 thf(cB,type,
% 1.67/1.43 cB: $i ).
% 1.67/1.43
% 1.67/1.43 thf(cR,type,
% 1.67/1.43 cR: $i > $i > $o ).
% 1.67/1.43
% 1.67/1.43 thf(cLX1,conjecture,
% 1.67/1.43 ( ( ( cR @ cA @ cB )
% 1.67/1.43 & ! [X: $i] :
% 1.67/1.43 ( ? [Y: $i] : ( cR @ X @ Y )
% 1.67/1.43 => ( cQ @ X @ X ) )
% 1.67/1.43 & ! [U: $i,V: $i] :
% 1.67/1.43 ( ( cQ @ U @ V )
% 1.67/1.43 => ! [Z: $i] : ( cR @ Z @ V ) ) )
% 1.67/1.43 => ? [W: $i] :
% 1.67/1.43 ( ( cR @ cB @ W )
% 1.67/1.43 & ( cQ @ W @ cA ) ) ) ).
% 1.67/1.43 ------------------------
% 1.67/1.45 % (30356)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_30256 for (2999ds/2Mi)
% 1.67/1.45 % (30353)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_30256 for (2999ds/183Mi)
% 1.67/1.45 % (30354)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_30256 for (2999ds/4Mi)
% 1.67/1.45 % (30357)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_30256 for (2999ds/2Mi)
% 1.67/1.45 % (30359)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_30256 for (2999ds/18Mi)
% 1.67/1.45 % (30358)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_30256 for (2999ds/275Mi)
% 1.67/1.45 % (30355)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_30256 for (2999ds/27Mi)
% 1.67/1.45 % (30357)Instruction limit reached!
% 1.67/1.45 % (30357)------------------------------
% 1.67/1.45 % (30357)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.45 % (30357)Termination reason: Unknown
% 1.67/1.45 % (30357)Termination phase: Saturation
% 1.67/1.45
% 1.67/1.45 % (30357)Memory used [KB]: 895
% 1.67/1.45 % (30357)Time elapsed: 0.003 s
% 1.67/1.45 % (30357)Instructions burned: 2 (million)
% 1.67/1.45 % (30357)------------------------------
% 1.67/1.45 % (30357)------------------------------
% 1.67/1.46 % (30356)Instruction limit reached!
% 1.67/1.46 % (30356)------------------------------
% 1.67/1.46 % (30356)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.46 % (30356)Termination reason: Unknown
% 1.67/1.46 % (30356)Termination phase: Saturation
% 1.67/1.46
% 1.67/1.46 % (30356)Memory used [KB]: 5500
% 1.67/1.46 % (30356)Time elapsed: 0.004 s
% 1.67/1.46 % (30356)Instructions burned: 2 (million)
% 1.67/1.46 % (30356)------------------------------
% 1.67/1.46 % (30356)------------------------------
% 1.67/1.46 % (30354)First to succeed.
% 1.67/1.46 % (30355)Also succeeded, but the first one will report.
% 1.67/1.46 % (30353)Also succeeded, but the first one will report.
% 1.67/1.46 % (30354)Refutation found. Thanks to Tanya!
% 1.67/1.46 % SZS status Theorem for DTF2THF_30256
% 1.67/1.46 % SZS output start Proof for DTF2THF_30256
% 1.67/1.46 thf(func_def_1, type, cQ: $i > $i > $o).
% 1.67/1.46 thf(func_def_3, type, cR: $i > $i > $o).
% 1.67/1.46 thf(f30,plain,(
% 1.67/1.46 $false),
% 1.67/1.46 inference(subsumption_resolution,[status(thm)],[f29,f21])).
% 1.67/1.46 thf(f21,plain,(
% 1.67/1.46 ($true = (cQ @ cA @ cA))),
% 1.67/1.46 inference(trivial_inequality_removal,[status(thm)],[f19])).
% 1.67/1.46 thf(f19,plain,(
% 1.67/1.46 ($true = (cQ @ cA @ cA)) | ($true != $true)),
% 1.67/1.46 inference(superposition,[status(thm)],[f11,f12])).
% 1.67/1.46 thf(f12,plain,(
% 1.67/1.46 ((cR @ cA @ cB) = $true)),
% 1.67/1.46 inference(cnf_transformation,[status(thm)],[f8])).
% 1.67/1.46 thf(f8,plain,(
% 1.67/1.46 ((cR @ cA @ cB) = $true) & ! [X0 : $i] : (((cQ @ X0 @ X0) = $true) | ! [X1 : $i] : ((cR @ X0 @ X1) != $true)) & ! [X2 : $i,X3 : $i] : (($true != (cQ @ X3 @ X2)) | ! [X4 : $i] : ((cR @ X4 @ X2) = $true)) & ! [X5 : $i] : (((cR @ cB @ X5) != $true) | ((cQ @ X5 @ cA) != $true))),
% 1.67/1.46 inference(rectify,[status(thm)],[f7])).
% 1.67/1.46 thf(f7,plain,(
% 1.67/1.46 ((cR @ cA @ cB) = $true) & ! [X3 : $i] : (($true = (cQ @ X3 @ X3)) | ! [X4 : $i] : ($true != (cR @ X3 @ X4))) & ! [X1 : $i,X0 : $i] : (($true != (cQ @ X0 @ X1)) | ! [X2 : $i] : ($true = (cR @ X2 @ X1))) & ! [X5 : $i] : (((cR @ cB @ X5) != $true) | ((cQ @ X5 @ cA) != $true))),
% 1.67/1.46 inference(flattening,[status(thm)],[f6])).
% 1.67/1.46 thf(f6,plain,(
% 1.67/1.46 ! [X5 : $i] : (((cR @ cB @ X5) != $true) | ((cQ @ X5 @ cA) != $true)) & (((cR @ cA @ cB) = $true) & ! [X3 : $i] : (($true = (cQ @ X3 @ X3)) | ! [X4 : $i] : ($true != (cR @ X3 @ X4))) & ! [X1 : $i,X0 : $i] : (($true != (cQ @ X0 @ X1)) | ! [X2 : $i] : ($true = (cR @ X2 @ X1))))),
% 1.67/1.46 inference(ennf_transformation,[status(thm)],[f5])).
% 1.67/1.46 thf(f5,plain,(
% 1.67/1.46 ~((((cR @ cA @ cB) = $true) & ! [X3 : $i] : (? [X4 : $i] : ($true = (cR @ X3 @ X4)) => ($true = (cQ @ X3 @ X3))) & ! [X1 : $i,X0 : $i] : (($true = (cQ @ X0 @ X1)) => ! [X2 : $i] : ($true = (cR @ X2 @ X1)))) => ? [X5 : $i] : (((cR @ cB @ X5) = $true) & ((cQ @ X5 @ cA) = $true)))),
% 1.67/1.46 inference(fool_elimination,[status(thm)],[f4])).
% 1.67/1.46 thf(f4,plain,(
% 1.67/1.46 ~((! [X0 : $i,X1 : $i] : ((cQ @ X0 @ X1) => ! [X2 : $i] : (cR @ X2 @ X1)) & ! [X3 : $i] : (? [X4 : $i] : (cR @ X3 @ X4) => (cQ @ X3 @ X3)) & (cR @ cA @ cB)) => ? [X5 : $i] : ((cR @ cB @ X5) & (cQ @ X5 @ cA)))),
% 1.67/1.46 inference(rectify,[status(thm)],[f2])).
% 1.67/1.46 thf(f2,negated_conjecture,(
% 1.67/1.46 ~((! [X2 : $i,X3 : $i] : ((cQ @ X2 @ X3) => ! [X4 : $i] : (cR @ X4 @ X3)) & ! [X0 : $i] : (? [X1 : $i] : (cR @ X0 @ X1) => (cQ @ X0 @ X0)) & (cR @ cA @ cB)) => ? [X5 : $i] : ((cR @ cB @ X5) & (cQ @ X5 @ cA)))),
% 1.67/1.46 inference(negated_conjecture,[status(cth)],[f1])).
% 1.67/1.46 thf(f1,conjecture,(
% 1.67/1.46 (! [X2 : $i,X3 : $i] : ((cQ @ X2 @ X3) => ! [X4 : $i] : (cR @ X4 @ X3)) & ! [X0 : $i] : (? [X1 : $i] : (cR @ X0 @ X1) => (cQ @ X0 @ X0)) & (cR @ cA @ cB)) => ? [X5 : $i] : ((cR @ cB @ X5) & (cQ @ X5 @ cA))),
% 1.67/1.46 file('/export/starexec/sandbox/tmp/tmp.T10FoXbwTj/DTF2THF_30256.p',cLX1)).
% 1.67/1.46 thf(f11,plain,(
% 1.67/1.46 ( ! [X0 : $i,X1 : $i] : (((cR @ X0 @ X1) != $true) | ((cQ @ X0 @ X0) = $true)) )),
% 1.67/1.46 inference(cnf_transformation,[status(thm)],[f8])).
% 1.67/1.46 thf(f29,plain,(
% 1.67/1.46 ($true != (cQ @ cA @ cA))),
% 1.67/1.46 inference(trivial_inequality_removal,[status(thm)],[f26])).
% 1.67/1.46 thf(f26,plain,(
% 1.67/1.46 ($true != $true) | ($true != (cQ @ cA @ cA))),
% 1.67/1.46 inference(superposition,[status(thm)],[f9,f24])).
% 1.67/1.46 thf(f24,plain,(
% 1.67/1.46 ( ! [X0 : $i] : (($true = (cR @ X0 @ cA))) )),
% 1.67/1.46 inference(trivial_inequality_removal,[status(thm)],[f23])).
% 1.67/1.46 thf(f23,plain,(
% 1.67/1.46 ( ! [X0 : $i] : (($true = (cR @ X0 @ cA)) | ($true != $true)) )),
% 1.67/1.46 inference(superposition,[status(thm)],[f10,f21])).
% 1.67/1.46 thf(f10,plain,(
% 1.67/1.46 ( ! [X2 : $i,X3 : $i,X4 : $i] : (($true != (cQ @ X3 @ X2)) | ((cR @ X4 @ X2) = $true)) )),
% 1.67/1.46 inference(cnf_transformation,[status(thm)],[f8])).
% 1.67/1.46 thf(f9,plain,(
% 1.67/1.46 ( ! [X5 : $i] : (((cR @ cB @ X5) != $true) | ((cQ @ X5 @ cA) != $true)) )),
% 1.67/1.46 inference(cnf_transformation,[status(thm)],[f8])).
% 1.67/1.46 % SZS output end Proof for DTF2THF_30256
% 1.67/1.46 % (30354)------------------------------
% 1.67/1.46 % (30354)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.46 % (30354)Termination reason: Refutation
% 1.67/1.46
% 1.67/1.46 % (30354)Memory used [KB]: 5500
% 1.67/1.46 % (30354)Time elapsed: 0.006 s
% 1.67/1.46 % (30354)Instructions burned: 2 (million)
% 1.67/1.46 % (30354)------------------------------
% 1.67/1.46 % (30354)------------------------------
% 1.67/1.46 % (30352)Success in time 0.02 s
%------------------------------------------------------------------------------