%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV393^5 : 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 09:41:09 AM UTC 2026
% Result : Theorem 1.62s 1.31s
% Output : Refutation 1.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 2
% Syntax : Number of formulae : 23 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 157 ( 39 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 133 ( 10 ~; 18 |; 17 &; 77 @)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 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 : 31 ( 18 ^; 11 !; 2 ?; 31 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cS: $i > $o ).
thf(func_def_1,type,
cR: $i > $o ).
thf(func_def_3,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_12,type,
ph2:
!>[X0: $tType] : X0 ).
thf(f37,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f36]) ).
thf(f36,plain,
$false = $true,
inference(forward_demodulation,[status(thm)],[f30,f27]) ).
thf(f27,plain,
( ( cS @ sK0 )
= $false ),
inference(trivial_inequality_removal,[status(thm)],[f25]) ).
thf(f25,plain,
( ( ( cS @ sK0 )
= $false )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f11,f21]) ).
thf(f21,plain,
! [X1: $i] :
( ( ( cS @ X1 )
= $true )
| ( ( cS @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f20]) ).
thf(f20,plain,
! [X1: $i] :
( ( ( cS @ X1 )
= $true )
| ( $false
= ( ( cR @ X1 )
| ( cS @ X1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
! [X1: $i] :
( ( ( ( cS @ X1 )
& ( cR @ X1 ) )
= $true )
| ( $false
= ( ( cR @ X1 )
| ( cS @ X1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f14]) ).
thf(f14,plain,
! [X1: $i] :
( ( ( cS @ X1 )
& ( cR @ X1 ) )
= ( ( cR @ X1 )
| ( cS @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f13]) ).
thf(f13,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( cR @ Y0 )
| ( cS @ Y0 ) )
@ X1 )
= ( ^ [Y0: $i] :
( ( cS @ Y0 )
& ( cR @ Y0 ) )
@ X1 ) ),
inference(argument_congruence,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ^ [Y0: $i] :
( ( cS @ Y0 )
& ( cR @ Y0 ) ) )
= ( ^ [Y0: $i] :
( ( cR @ Y0 )
| ( cS @ Y0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ( ( ^ [Y0: $i] :
( ( cS @ Y0 )
& ( cR @ Y0 ) ) )
= ( ^ [Y0: $i] :
( ( cR @ Y0 )
| ( cS @ Y0 ) ) ) )
& ( ( cS @ sK0 )
!= $true )
& ( ( cR @ sK0 )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f7,f8]) ).
thf(f8,plain,
( ? [X0: $i] :
( ( ( cS @ X0 )
!= $true )
& ( ( cR @ X0 )
= $true ) )
=> ( ( ( cS @ sK0 )
!= $true )
& ( ( cR @ sK0 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f7,plain,
( ( ( ^ [Y0: $i] :
( ( cS @ Y0 )
& ( cR @ Y0 ) ) )
= ( ^ [Y0: $i] :
( ( cR @ Y0 )
| ( cS @ Y0 ) ) ) )
& ? [X0: $i] :
( ( ( cS @ X0 )
!= $true )
& ( ( cR @ X0 )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( ( ( ^ [Y0: $i] :
( ( cS @ Y0 )
& ( cR @ Y0 ) ) )
= ( ^ [Y0: $i] :
( ( cR @ Y0 )
| ( cS @ Y0 ) ) ) )
=> ! [X0: $i] :
( ( ( cR @ X0 )
= $true )
=> ( ( cS @ X0 )
= $true ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ( ^ [Y0: $i] :
( ( cS @ Y0 )
& ( cR @ Y0 ) ) )
= ( ^ [Y0: $i] :
( ( cR @ Y0 )
| ( cS @ Y0 ) ) ) )
=> ! [X2: $i] :
( ( $true
= ( cR @ X2 ) )
=> ( ( cS @ X2 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ( ^ [X0: $i] :
( ( cR @ X0 )
& ( cS @ X0 ) ) )
= ( ^ [X1: $i] :
( ( cS @ X1 )
| ( cR @ X1 ) ) ) )
=> ! [X2: $i] :
( ( cR @ X2 )
=> ( cS @ X2 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ( ^ [X1: $i] :
( ( cR @ X1 )
& ( cS @ X1 ) ) )
= ( ^ [X0: $i] :
( ( cS @ X0 )
| ( cR @ X0 ) ) ) )
=> ! [X1: $i] :
( ( cR @ X1 )
=> ( cS @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ( ^ [X1: $i] :
( ( cR @ X1 )
& ( cS @ X1 ) ) )
= ( ^ [X0: $i] :
( ( cS @ X0 )
| ( cR @ X0 ) ) ) )
=> ! [X1: $i] :
( ( cR @ X1 )
=> ( cS @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.tPitQIyzYE/DTF2THF_27329.p',cTHM39_pme) ).
thf(f11,plain,
( ( cS @ sK0 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f30,plain,
( ( cS @ sK0 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f29]) ).
thf(f29,plain,
( ( ( cS @ sK0 )
= $true )
| ( $false = $true ) ),
inference(superposition,[status(thm)],[f10,f22]) ).
thf(f22,plain,
! [X1: $i] :
( ( ( cR @ X1 )
= $false )
| ( ( cS @ X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f20]) ).
thf(f10,plain,
( ( cR @ sK0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV393^5 : 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
% 0.16/0.34 % Computer : n006.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:46:00 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
% 0.31/0.46 ---- Original DTF file ---
% 0.31/0.46 thf(spec,logic,$$dhol).
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 % File : SEV393^5 : TPTP v9.2.1. Released v4.0.0.
% 0.31/0.46 % Domain : Set Theory
% 0.31/0.46 % Problem : TPS problem THM39
% 0.31/0.46 % Version : Especial.
% 0.31/0.46 % English :
% 0.31/0.46
% 0.31/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.31/0.46 % Source : [Bro09]
% 0.31/0.46 % Names : tps_0285 [Bro09]
% 0.31/0.46 % : THM39 [TPS]
% 0.31/0.46
% 0.31/0.46 % Status : Theorem
% 0.31/0.46 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.31/0.46 % Syntax : Number of formulae : 3 ( 0 unt; 2 typ; 0 def)
% 0.31/0.46 % Number of atoms : 7 ( 1 equ; 0 cnn)
% 0.31/0.46 % Maximal formula atoms : 3 ( 7 avg)
% 0.31/0.46 % Number of connectives : 10 ( 0 ~; 1 |; 1 &; 6 @)
% 0.31/0.46 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.31/0.46 % Maximal formula depth : 5 ( 5 avg)
% 0.31/0.46 % Number of types : 2 ( 0 usr)
% 0.31/0.46 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.31/0.46 % Number of symbols : 3 ( 2 usr; 0 con; 1-2 aty)
% 0.31/0.46 % Number of variables : 3 ( 2 ^; 1 !; 0 ?; 3 :)
% 0.31/0.46 % SPC : TH0_THM_EQU_NAR
% 0.31/0.46
% 0.31/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.31/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.31/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.31/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.31/0.46 % : Polymorphic definitions expanded.
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 thf(cS,type,
% 0.31/0.46 cS: $i > $o ).
% 0.31/0.46
% 0.31/0.46 thf(cR,type,
% 0.31/0.46 cR: $i > $o ).
% 0.31/0.46
% 0.31/0.46 thf(cTHM39_pme,conjecture,
% 0.31/0.46 ( ( ( ^ [Xz: $i] :
% 0.31/0.46 ( ( cR @ Xz )
% 0.31/0.46 | ( cS @ Xz ) ) )
% 0.31/0.46 = ( ^ [Xx: $i] :
% 0.31/0.46 ( ( cR @ Xx )
% 0.31/0.46 & ( cS @ Xx ) ) ) )
% 0.31/0.46 => ! [Xx: $i] :
% 0.31/0.46 ( ( cR @ Xx )
% 0.31/0.46 => ( cS @ Xx ) ) ) ).
% 0.31/0.46
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 ------------------------
% 1.45/1.27 ---- Embedded in THF ---
% 1.45/1.27 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.45/1.27 %%% Generated on Tue Feb 24 12:46:01 EST 2026
% 1.45/1.27 %%% using '$$dhol' embedding, version 1.3.0.
% 1.45/1.27 %%% Logic specification used:
% 1.45/1.27 %%% thf(spec, logic, $$dhol).
% 1.45/1.27
% 1.45/1.27 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.tPitQIyzYE/DTF2DTF27329.p
% See solution above
% 1.45/1.27 ------------------------
% 1.45/1.28 ---- Cleaned THF ---
% 1.45/1.28 thf(cS,type,
% 1.45/1.28 cS: $i > $o ).
% 1.45/1.28
% 1.45/1.28 thf(cR,type,
% 1.45/1.28 cR: $i > $o ).
% 1.45/1.28
% 1.45/1.28 thf(cTHM39_pme,conjecture,
% 1.45/1.28 ( ( ( ^ [Xz: $i] :
% 1.45/1.28 ( ( cR @ Xz )
% 1.45/1.28 | ( cS @ Xz ) ) )
% 1.45/1.28 = ( ^ [Xx: $i] :
% 1.45/1.28 ( ( cR @ Xx )
% 1.45/1.28 & ( cS @ Xx ) ) ) )
% 1.45/1.28 => ! [Xx: $i] :
% 1.45/1.28 ( ( cR @ Xx )
% 1.45/1.28 => ( cS @ Xx ) ) ) ).
% 1.45/1.28 ------------------------
% 1.62/1.30 % (27430)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_27329 for (2999ds/2Mi)
% 1.62/1.30 % (27430)Instruction limit reached!
% 1.62/1.30 % (27430)------------------------------
% 1.62/1.30 % (27430)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.30 % (27430)Termination reason: Unknown
% 1.62/1.30 % (27430)Termination phase: Saturation
% 1.62/1.30
% 1.62/1.30 % (27430)Memory used [KB]: 5373
% 1.62/1.30 % (27430)Time elapsed: 0.002 s
% 1.62/1.30 % (27430)Instructions burned: 2 (million)
% 1.62/1.30 % (27430)------------------------------
% 1.62/1.30 % (27430)------------------------------
% 1.62/1.31 % (27428)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_27329 for (2999ds/27Mi)
% 1.62/1.31 % (27431)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_27329 for (2999ds/275Mi)
% 1.62/1.31 % (27426)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_27329 for (2999ds/183Mi)
% 1.62/1.31 % (27427)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_27329 for (2999ds/4Mi)
% 1.62/1.31 % (27428)First to succeed.
% 1.62/1.31 % (27433)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_27329 for (2999ds/3Mi)
% 1.62/1.31 % (27427)Instruction limit reached!
% 1.62/1.31 % (27427)------------------------------
% 1.62/1.31 % (27427)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.31 % (27427)Termination reason: Unknown
% 1.62/1.31 % (27427)Termination phase: Saturation
% 1.62/1.31
% 1.62/1.31 % (27427)Memory used [KB]: 5500
% 1.62/1.31 % (27427)Time elapsed: 0.003 s
% 1.62/1.31 % (27427)Instructions burned: 4 (million)
% 1.62/1.31 % (27427)------------------------------
% 1.62/1.31 % (27427)------------------------------
% 1.62/1.31 % (27428)Refutation found. Thanks to Tanya!
% 1.62/1.31 % SZS status Theorem for DTF2THF_27329
% 1.62/1.31 % SZS output start Proof for DTF2THF_27329
% 1.62/1.31 thf(func_def_0, type, cS: $i > $o).
% 1.62/1.31 thf(func_def_1, type, cR: $i > $o).
% 1.62/1.31 thf(func_def_3, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.62/1.31 thf(func_def_12, type, ph2: !>[X0: $tType]:(X0)).
% 1.62/1.31 thf(f37,plain,(
% 1.62/1.31 $false),
% 1.62/1.31 inference(trivial_inequality_removal,[status(thm)],[f36])).
% 1.62/1.31 thf(f36,plain,(
% 1.62/1.31 ($false = $true)),
% 1.62/1.31 inference(forward_demodulation,[status(thm)],[f30,f27])).
% 1.62/1.31 thf(f27,plain,(
% 1.62/1.31 ((cS @ sK0) = $false)),
% 1.62/1.31 inference(trivial_inequality_removal,[status(thm)],[f25])).
% 1.62/1.31 thf(f25,plain,(
% 1.62/1.31 ((cS @ sK0) = $false) | ($true != $true)),
% 1.62/1.31 inference(superposition,[status(thm)],[f11,f21])).
% 1.62/1.31 thf(f21,plain,(
% 1.62/1.31 ( ! [X1 : $i] : (((cS @ X1) = $true) | ((cS @ X1) = $false)) )),
% 1.62/1.31 inference(binary_proxy_clausification,[status(thm)],[f20])).
% 1.62/1.31 thf(f20,plain,(
% 1.62/1.31 ( ! [X1 : $i] : (((cS @ X1) = $true) | ($false = ((cR @ X1) | (cS @ X1)))) )),
% 1.62/1.31 inference(binary_proxy_clausification,[status(thm)],[f15])).
% 1.62/1.31 thf(f15,plain,(
% 1.62/1.31 ( ! [X1 : $i] : ((((cS @ X1) & (cR @ X1)) = $true) | ($false = ((cR @ X1) | (cS @ X1)))) )),
% 1.62/1.31 inference(binary_proxy_clausification,[status(thm)],[f14])).
% 1.62/1.31 thf(f14,plain,(
% 1.62/1.31 ( ! [X1 : $i] : ((((cS @ X1) & (cR @ X1)) = ((cR @ X1) | (cS @ X1)))) )),
% 1.62/1.31 inference(beta_eta_normalization,[status(thm)],[f13])).
% 1.62/1.31 thf(f13,plain,(
% 1.62/1.31 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((cR @ Y0) | (cS @ Y0))) @ X1) = ((^[Y0 : $i]: ((cS @ Y0) & (cR @ Y0))) @ X1))) )),
% 1.62/1.31 inference(argument_congruence,[status(thm)],[f12])).
% 1.62/1.31 thf(f12,plain,(
% 1.62/1.31 ((^[Y0 : $i]: ((cS @ Y0) & (cR @ Y0))) = (^[Y0 : $i]: ((cR @ Y0) | (cS @ Y0))))),
% 1.62/1.31 inference(cnf_transformation,[status(thm)],[f9])).
% 1.62/1.31 thf(f9,plain,(
% 1.62/1.31 ((^[Y0 : $i]: ((cS @ Y0) & (cR @ Y0))) = (^[Y0 : $i]: ((cR @ Y0) | (cS @ Y0)))) & (((cS @ sK0) != $true) & ((cR @ sK0) = $true))),
% 1.62/1.31 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f7,f8])).
% 1.62/1.31 thf(f8,plain,(
% 1.62/1.31 ? [X0 : $i] : (((cS @ X0) != $true) & ((cR @ X0) = $true)) => (((cS @ sK0) != $true) & ((cR @ sK0) = $true))),
% 1.62/1.31 introduced(definition,[],[choice_axiom])).
% 1.62/1.31 thf(f7,plain,(
% 1.62/1.31 ((^[Y0 : $i]: ((cS @ Y0) & (cR @ Y0))) = (^[Y0 : $i]: ((cR @ Y0) | (cS @ Y0)))) & ? [X0 : $i] : (((cS @ X0) != $true) & ((cR @ X0) = $true))),
% 1.62/1.31 inference(ennf_transformation,[status(thm)],[f6])).
% 1.62/1.31 thf(f6,plain,(
% 1.62/1.31 ~(((^[Y0 : $i]: ((cS @ Y0) & (cR @ Y0))) = (^[Y0 : $i]: ((cR @ Y0) | (cS @ Y0)))) => ! [X0 : $i] : (((cR @ X0) = $true) => ((cS @ X0) = $true)))),
% 1.62/1.31 inference(rectify,[status(thm)],[f5])).
% 1.62/1.31 thf(f5,plain,(
% 1.62/1.31 ~(((^[Y0 : $i]: ((cS @ Y0) & (cR @ Y0))) = (^[Y0 : $i]: ((cR @ Y0) | (cS @ Y0)))) => ! [X2 : $i] : (($true = (cR @ X2)) => ((cS @ X2) = $true)))),
% 1.62/1.31 inference(fool_elimination,[status(thm)],[f4])).
% 1.62/1.31 thf(f4,plain,(
% 1.62/1.31 ~(((^[X0 : $i] : ((cR @ X0) & (cS @ X0))) = (^[X1 : $i] : ((cS @ X1) | (cR @ X1)))) => ! [X2 : $i] : ((cR @ X2) => (cS @ X2)))),
% 1.62/1.31 inference(rectify,[status(thm)],[f2])).
% 1.62/1.31 thf(f2,negated_conjecture,(
% 1.62/1.31 ~(((^[X1 : $i] : ((cR @ X1) & (cS @ X1))) = (^[X0 : $i] : ((cS @ X0) | (cR @ X0)))) => ! [X1 : $i] : ((cR @ X1) => (cS @ X1)))),
% 1.62/1.31 inference(negated_conjecture,[status(cth)],[f1])).
% 1.62/1.31 thf(f1,conjecture,(
% 1.62/1.31 ((^[X1 : $i] : ((cR @ X1) & (cS @ X1))) = (^[X0 : $i] : ((cS @ X0) | (cR @ X0)))) => ! [X1 : $i] : ((cR @ X1) => (cS @ X1))),
% 1.62/1.31 file('/export/starexec/sandbox/tmp/tmp.tPitQIyzYE/DTF2THF_27329.p',cTHM39_pme)).
% 1.62/1.31 thf(f11,plain,(
% 1.62/1.31 ((cS @ sK0) != $true)),
% 1.62/1.31 inference(cnf_transformation,[status(thm)],[f9])).
% 1.62/1.31 thf(f30,plain,(
% 1.62/1.31 ((cS @ sK0) = $true)),
% 1.62/1.31 inference(trivial_inequality_removal,[status(thm)],[f29])).
% 1.62/1.31 thf(f29,plain,(
% 1.62/1.31 ((cS @ sK0) = $true) | ($false = $true)),
% 1.62/1.31 inference(superposition,[status(thm)],[f10,f22])).
% 1.62/1.31 thf(f22,plain,(
% 1.62/1.31 ( ! [X1 : $i] : (((cR @ X1) = $false) | ((cS @ X1) = $true)) )),
% 1.62/1.31 inference(binary_proxy_clausification,[status(thm)],[f20])).
% 1.62/1.31 thf(f10,plain,(
% 1.62/1.31 ((cR @ sK0) = $true)),
% 1.62/1.31 inference(cnf_transformation,[status(thm)],[f9])).
% 1.62/1.31 % SZS output end Proof for DTF2THF_27329
% 1.62/1.31 % (27428)------------------------------
% 1.62/1.31 % (27428)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.31 % (27428)Termination reason: Refutation
% 1.62/1.31
% 1.62/1.31 % (27428)Memory used [KB]: 5500
% 1.62/1.31 % (27428)Time elapsed: 0.005 s
% 1.62/1.31 % (27428)Instructions burned: 3 (million)
% 1.62/1.31 % (27428)------------------------------
% 1.62/1.31 % (27428)------------------------------
% 1.62/1.31 % (27425)Success in time 0.022 s
%------------------------------------------------------------------------------