%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO261^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n027.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 09:53:47 AM UTC 2026
% Result : Theorem 1.50s 1.27s
% Output : Refutation 1.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 2
% Syntax : Number of formulae : 21 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 221 ( 62 equ; 0 cnn)
% Maximal formula atoms : 8 ( 10 avg)
% Number of connectives : 212 ( 34 ~; 23 |; 26 &; 112 @)
% ( 0 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 25 ( 0 ^; 22 !; 3 ?; 25 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_1,type,
cP: $i > $o ).
thf(func_def_2,type,
c1_plus: $i > $i ).
thf(func_def_7,type,
sK0: ( $i > $o ) > $i ).
thf(func_def_10,type,
ph2:
!>[X0: $tType] : X0 ).
thf(f79,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f78,f13]) ).
thf(f13,plain,
( ( cP @ cO )
= $true ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ! [X0: $i] :
( ( ( cP @ ( c1_plus @ X0 ) )
= $true )
| ( ( cP @ X0 )
!= $true ) )
& ( ( cP @ cO )
= $true )
& ( ( cP @ n )
!= $true )
& ! [X1: $i > $o] :
( ( ( ( X1 @ ( c1_plus @ ( sK0 @ X1 ) ) )
!= $true )
& ( ( X1 @ ( sK0 @ X1 ) )
= $true ) )
| ( ( X1 @ n )
= $true )
| ( ( X1 @ cO )
!= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f7,f8]) ).
thf(f8,plain,
! [X1: $i > $o] :
( ? [X2: $i] :
( ( ( X1 @ ( c1_plus @ X2 ) )
!= $true )
& ( ( X1 @ X2 )
= $true ) )
=> ( ( ( X1 @ ( c1_plus @ ( sK0 @ X1 ) ) )
!= $true )
& ( ( X1 @ ( sK0 @ X1 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f7,plain,
( ! [X0: $i] :
( ( ( cP @ ( c1_plus @ X0 ) )
= $true )
| ( ( cP @ X0 )
!= $true ) )
& ( ( cP @ cO )
= $true )
& ( ( cP @ n )
!= $true )
& ! [X1: $i > $o] :
( ? [X2: $i] :
( ( ( X1 @ ( c1_plus @ X2 ) )
!= $true )
& ( ( X1 @ X2 )
= $true ) )
| ( ( X1 @ n )
= $true )
| ( ( X1 @ cO )
!= $true ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ( cP @ n )
!= $true )
& ! [X0: $i] :
( ( ( cP @ ( c1_plus @ X0 ) )
= $true )
| ( ( cP @ X0 )
!= $true ) )
& ( ( cP @ cO )
= $true )
& ! [X1: $i > $o] :
( ( ( X1 @ n )
= $true )
| ( ( X1 @ cO )
!= $true )
| ? [X2: $i] :
( ( ( X1 @ ( c1_plus @ X2 ) )
!= $true )
& ( ( X1 @ X2 )
= $true ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ! [X0: $i] :
( ( ( cP @ X0 )
= $true )
=> ( ( cP @ ( c1_plus @ X0 ) )
= $true ) )
& ( ( cP @ cO )
= $true )
& ! [X1: $i > $o] :
( ( ( ( X1 @ cO )
= $true )
& ! [X2: $i] :
( ( ( X1 @ X2 )
= $true )
=> ( ( X1 @ ( c1_plus @ X2 ) )
= $true ) ) )
=> ( ( X1 @ n )
= $true ) ) )
=> ( ( cP @ n )
= $true ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ( cP @ cO )
& ! [X0: $i] :
( ( cP @ X0 )
=> ( cP @ ( c1_plus @ X0 ) ) )
& ! [X1: $i > $o] :
( ( ( X1 @ cO )
& ! [X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( c1_plus @ X2 ) ) ) )
=> ( X1 @ n ) ) )
=> ( cP @ n ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ( cP @ cO )
& ! [X1: $i] :
( ( cP @ X1 )
=> ( cP @ ( c1_plus @ X1 ) ) )
& ! [X0: $i > $o] :
( ( ( X0 @ cO )
& ! [X1: $i] :
( ( X0 @ X1 )
=> ( X0 @ ( c1_plus @ X1 ) ) ) )
=> ( X0 @ n ) ) )
=> ( cP @ n ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ( cP @ cO )
& ! [X1: $i] :
( ( cP @ X1 )
=> ( cP @ ( c1_plus @ X1 ) ) )
& ! [X0: $i > $o] :
( ( ( X0 @ cO )
& ! [X1: $i] :
( ( X0 @ X1 )
=> ( X0 @ ( c1_plus @ X1 ) ) ) )
=> ( X0 @ n ) ) )
=> ( cP @ n ) ),
file('/export/starexec/sandbox2/tmp/tmp.tnCTxI7UJE/DTF2THF_28603.p',cBLEDSOE_FENG_SV_I1) ).
thf(f78,plain,
( ( cP @ cO )
!= $true ),
inference(subsumption_resolution,[status(thm)],[f77,f12]) ).
thf(f12,plain,
( ( cP @ n )
!= $true ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f77,plain,
( ( ( cP @ n )
= $true )
| ( ( cP @ cO )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f76]) ).
thf(f76,plain,
( ( ( cP @ n )
= $true )
| ( ( cP @ cO )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f66,f10]) ).
thf(f10,plain,
! [X1: $i > $o] :
( ( ( X1 @ ( sK0 @ X1 ) )
= $true )
| ( ( X1 @ cO )
!= $true )
| ( ( X1 @ n )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f66,plain,
( ( cP @ ( sK0 @ cP ) )
!= $true ),
inference(subsumption_resolution,[status(thm)],[f65,f13]) ).
thf(f65,plain,
( ( ( cP @ ( sK0 @ cP ) )
!= $true )
| ( ( cP @ cO )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f55,f12]) ).
thf(f55,plain,
( ( ( cP @ n )
= $true )
| ( ( cP @ cO )
!= $true )
| ( ( cP @ ( sK0 @ cP ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f43]) ).
thf(f43,plain,
( ( ( cP @ ( sK0 @ cP ) )
!= $true )
| ( $true != $true )
| ( ( cP @ n )
= $true )
| ( ( cP @ cO )
!= $true ) ),
inference(superposition,[status(thm)],[f11,f14]) ).
thf(f14,plain,
! [X0: $i] :
( ( ( cP @ ( c1_plus @ X0 ) )
= $true )
| ( ( cP @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f11,plain,
! [X1: $i > $o] :
( ( ( X1 @ ( c1_plus @ ( sK0 @ X1 ) ) )
!= $true )
| ( ( X1 @ cO )
!= $true )
| ( ( X1 @ n )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO261^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n027.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 14:27:22 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.29/0.45 ---- Original DTF file ---
% 0.29/0.46 thf(spec,logic,$$dhol).
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 % File : SYO261^5 : TPTP v9.2.1. Released v4.0.0.
% 0.29/0.46 % Domain : Syntactic
% 0.29/0.46 % Problem : TPS problem BLEDSOE-FENG-SV-I1
% 0.29/0.46 % Version : Especial.
% 0.29/0.46 % English :
% 0.29/0.46
% 0.29/0.46 % Refs : [BF93] Bledsoe & Feng (1993), SET-VAR
% 0.29/0.46 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.29/0.46 % Source : [Bro09]
% 0.29/0.46 % Names : tps_0149 [Bro09]
% 0.29/0.46 % : BLEDSOE-FENG-SV-I1 [TPS]
% 0.29/0.46 % : Example I1 [BF93]
% 0.29/0.46
% 0.29/0.46 % Status : Theorem
% 0.29/0.46 % Rating : 0.00 v8.1.0, 0.08 v7.4.0, 0.00 v7.3.0, 0.10 v7.2.0, 0.12 v7.1.0, 0.00 v6.2.0, 0.33 v6.1.0, 0.00 v5.1.0, 0.25 v5.0.0, 0.00 v4.0.0
% 0.29/0.46 % Syntax : Number of formulae : 5 ( 0 unt; 4 typ; 0 def)
% 0.29/0.46 % Number of atoms : 4 ( 0 equ; 0 cnn)
% 0.29/0.46 % Maximal formula atoms : 4 ( 4 avg)
% 0.29/0.46 % Number of connectives : 17 ( 0 ~; 0 |; 3 &; 10 @)
% 0.29/0.46 % ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% 0.29/0.46 % Maximal formula depth : 10 ( 10 avg)
% 0.29/0.46 % Number of types : 2 ( 0 usr)
% 0.29/0.46 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.29/0.46 % Number of symbols : 4 ( 4 usr; 2 con; 0-1 aty)
% 0.29/0.46 % Number of variables : 3 ( 0 ^; 3 !; 0 ?; 3 :)
% 0.29/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.29/0.46
% 0.29/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.29/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.29/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.29/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 thf(n,type,
% 0.29/0.46 n: $i ).
% 0.29/0.46
% 0.29/0.46 thf(cP,type,
% 0.29/0.46 cP: $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(c1_plus,type,
% 0.29/0.46 c1_plus: $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(cO,type,
% 0.29/0.46 cO: $i ).
% 0.29/0.46
% 0.29/0.46 thf(cBLEDSOE_FENG_SV_I1,conjecture,
% 0.29/0.46 ( ( ! [A: $i > $o] :
% 0.29/0.46 ( ( ( A @ cO )
% 0.29/0.46 & ! [Xx: $i] :
% 0.29/0.46 ( ( A @ Xx )
% 0.29/0.46 => ( A @ ( c1_plus @ Xx ) ) ) )
% 0.29/0.46 => ( A @ n ) )
% 0.29/0.46 & ( cP @ cO )
% 0.29/0.46 & ! [Xx: $i] :
% 0.29/0.46 ( ( cP @ Xx )
% 0.29/0.46 => ( cP @ ( c1_plus @ Xx ) ) ) )
% 0.29/0.46 => ( cP @ n ) ) ).
% 0.29/0.46
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 ------------------------
% 1.50/1.24 ---- Embedded in THF ---
% 1.50/1.25 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.50/1.25 %%% Generated on Tue Feb 24 14:27:23 EST 2026
% 1.50/1.25 %%% using '$$dhol' embedding, version 1.3.0.
% 1.50/1.25 %%% Logic specification used:
% 1.50/1.25 %%% thf(spec, logic, $$dhol).
% 1.50/1.25
% 1.50/1.25 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.tnCTxI7UJE/DTF2DTF28603.p
% See solution above
% 1.50/1.25 ------------------------
% 1.50/1.26 ---- Cleaned THF ---
% 1.50/1.26 thf(n,type,
% 1.50/1.26 n: $i ).
% 1.50/1.26
% 1.50/1.26 thf(cP,type,
% 1.50/1.26 cP: $i > $o ).
% 1.50/1.26
% 1.50/1.26 thf(c1_plus,type,
% 1.50/1.26 c1_plus: $i > $i ).
% 1.50/1.26
% 1.50/1.26 thf(cO,type,
% 1.50/1.26 cO: $i ).
% 1.50/1.26
% 1.50/1.26 thf(cBLEDSOE_FENG_SV_I1,conjecture,
% 1.50/1.26 ( ( ! [A: $i > $o] :
% 1.50/1.26 ( ( ( A @ cO )
% 1.50/1.26 & ! [Xx: $i] :
% 1.50/1.26 ( ( A @ Xx )
% 1.50/1.26 => ( A @ ( c1_plus @ Xx ) ) ) )
% 1.50/1.26 => ( A @ n ) )
% 1.50/1.26 & ( cP @ cO )
% 1.50/1.26 & ! [Xx: $i] :
% 1.50/1.26 ( ( cP @ Xx )
% 1.50/1.26 => ( cP @ ( c1_plus @ Xx ) ) ) )
% 1.50/1.26 => ( cP @ n ) ) ).
% 1.50/1.26 ------------------------
% 1.50/1.27 % (28878)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_28603 for (2999ds/275Mi)
% 1.50/1.27 % (28876)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_28603 for (2999ds/2Mi)
% 1.50/1.27 % (28876)Instruction limit reached!
% 1.50/1.27 % (28876)------------------------------
% 1.50/1.27 % (28876)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.27 % (28876)Termination reason: Unknown
% 1.50/1.27 % (28876)Termination phase: Saturation
% 1.50/1.27
% 1.50/1.27 % (28876)Memory used [KB]: 5500
% 1.50/1.27 % (28876)Time elapsed: 0.002 s
% 1.50/1.27 % (28876)Instructions burned: 2 (million)
% 1.50/1.27 % (28876)------------------------------
% 1.50/1.27 % (28876)------------------------------
% 1.50/1.27 % (28878)First to succeed.
% 1.50/1.27 % (28878)Refutation found. Thanks to Tanya!
% 1.50/1.27 % SZS status Theorem for DTF2THF_28603
% 1.50/1.27 % SZS output start Proof for DTF2THF_28603
% 1.50/1.27 thf(func_def_1, type, cP: $i > $o).
% 1.50/1.27 thf(func_def_2, type, c1_plus: $i > $i).
% 1.50/1.27 thf(func_def_7, type, sK0: ($i > $o) > $i).
% 1.50/1.27 thf(func_def_10, type, ph2: !>[X0: $tType]:(X0)).
% 1.50/1.27 thf(f79,plain,(
% 1.50/1.27 $false),
% 1.50/1.27 inference(subsumption_resolution,[status(thm)],[f78,f13])).
% 1.50/1.27 thf(f13,plain,(
% 1.50/1.27 ((cP @ cO) = $true)),
% 1.50/1.27 inference(cnf_transformation,[status(thm)],[f9])).
% 1.50/1.27 thf(f9,plain,(
% 1.50/1.27 ! [X0 : $i] : (((cP @ (c1_plus @ X0)) = $true) | ((cP @ X0) != $true)) & ((cP @ cO) = $true) & ((cP @ n) != $true) & ! [X1 : $i > $o] : ((((X1 @ (c1_plus @ (sK0 @ X1))) != $true) & ((X1 @ (sK0 @ X1)) = $true)) | ((X1 @ n) = $true) | ((X1 @ cO) != $true))),
% 1.50/1.27 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f7,f8])).
% 1.50/1.27 thf(f8,plain,(
% 1.50/1.27 ! [X1 : $i > $o] : (? [X2 : $i] : (((X1 @ (c1_plus @ X2)) != $true) & ((X1 @ X2) = $true)) => (((X1 @ (c1_plus @ (sK0 @ X1))) != $true) & ((X1 @ (sK0 @ X1)) = $true)))),
% 1.50/1.27 introduced(definition,[],[choice_axiom])).
% 1.50/1.27 thf(f7,plain,(
% 1.50/1.27 ! [X0 : $i] : (((cP @ (c1_plus @ X0)) = $true) | ((cP @ X0) != $true)) & ((cP @ cO) = $true) & ((cP @ n) != $true) & ! [X1 : $i > $o] : (? [X2 : $i] : (((X1 @ (c1_plus @ X2)) != $true) & ((X1 @ X2) = $true)) | ((X1 @ n) = $true) | ((X1 @ cO) != $true))),
% 1.50/1.27 inference(flattening,[status(thm)],[f6])).
% 1.50/1.27 thf(f6,plain,(
% 1.50/1.27 ((cP @ n) != $true) & (! [X0 : $i] : (((cP @ (c1_plus @ X0)) = $true) | ((cP @ X0) != $true)) & ((cP @ cO) = $true) & ! [X1 : $i > $o] : (((X1 @ n) = $true) | (((X1 @ cO) != $true) | ? [X2 : $i] : (((X1 @ (c1_plus @ X2)) != $true) & ((X1 @ X2) = $true)))))),
% 1.50/1.27 inference(ennf_transformation,[status(thm)],[f5])).
% 1.50/1.27 thf(f5,plain,(
% 1.50/1.27 ~((! [X0 : $i] : (((cP @ X0) = $true) => ((cP @ (c1_plus @ X0)) = $true)) & ((cP @ cO) = $true) & ! [X1 : $i > $o] : ((((X1 @ cO) = $true) & ! [X2 : $i] : (((X1 @ X2) = $true) => ((X1 @ (c1_plus @ X2)) = $true))) => ((X1 @ n) = $true))) => ((cP @ n) = $true))),
% 1.50/1.27 inference(fool_elimination,[status(thm)],[f4])).
% 1.50/1.27 thf(f4,plain,(
% 1.50/1.27 ~(((cP @ cO) & ! [X0 : $i] : ((cP @ X0) => (cP @ (c1_plus @ X0))) & ! [X1 : $i > $o] : (((X1 @ cO) & ! [X2 : $i] : ((X1 @ X2) => (X1 @ (c1_plus @ X2)))) => (X1 @ n))) => (cP @ n))),
% 1.50/1.27 inference(rectify,[status(thm)],[f2])).
% 1.50/1.27 thf(f2,negated_conjecture,(
% 1.50/1.27 ~(((cP @ cO) & ! [X1 : $i] : ((cP @ X1) => (cP @ (c1_plus @ X1))) & ! [X0 : $i > $o] : (((X0 @ cO) & ! [X1 : $i] : ((X0 @ X1) => (X0 @ (c1_plus @ X1)))) => (X0 @ n))) => (cP @ n))),
% 1.50/1.27 inference(negated_conjecture,[status(cth)],[f1])).
% 1.50/1.27 thf(f1,conjecture,(
% 1.50/1.27 ((cP @ cO) & ! [X1 : $i] : ((cP @ X1) => (cP @ (c1_plus @ X1))) & ! [X0 : $i > $o] : (((X0 @ cO) & ! [X1 : $i] : ((X0 @ X1) => (X0 @ (c1_plus @ X1)))) => (X0 @ n))) => (cP @ n)),
% 1.50/1.27 file('/export/starexec/sandbox2/tmp/tmp.tnCTxI7UJE/DTF2THF_28603.p',cBLEDSOE_FENG_SV_I1)).
% 1.50/1.27 thf(f78,plain,(
% 1.50/1.27 ((cP @ cO) != $true)),
% 1.50/1.27 inference(subsumption_resolution,[status(thm)],[f77,f12])).
% 1.50/1.27 thf(f12,plain,(
% 1.50/1.27 ((cP @ n) != $true)),
% 1.50/1.27 inference(cnf_transformation,[status(thm)],[f9])).
% 1.50/1.27 thf(f77,plain,(
% 1.50/1.27 ((cP @ n) = $true) | ((cP @ cO) != $true)),
% 1.50/1.27 inference(trivial_inequality_removal,[status(thm)],[f76])).
% 1.50/1.27 thf(f76,plain,(
% 1.50/1.27 ((cP @ n) = $true) | ((cP @ cO) != $true) | ($true != $true)),
% 1.50/1.27 inference(superposition,[status(thm)],[f66,f10])).
% 1.50/1.27 thf(f10,plain,(
% 1.50/1.27 ( ! [X1 : $i > $o] : (((X1 @ (sK0 @ X1)) = $true) | ((X1 @ cO) != $true) | ((X1 @ n) = $true)) )),
% 1.50/1.27 inference(cnf_transformation,[status(thm)],[f9])).
% 1.50/1.27 thf(f66,plain,(
% 1.50/1.27 ((cP @ (sK0 @ cP)) != $true)),
% 1.50/1.27 inference(subsumption_resolution,[status(thm)],[f65,f13])).
% 1.50/1.27 thf(f65,plain,(
% 1.50/1.27 ((cP @ (sK0 @ cP)) != $true) | ((cP @ cO) != $true)),
% 1.50/1.27 inference(subsumption_resolution,[status(thm)],[f55,f12])).
% 1.50/1.27 thf(f55,plain,(
% 1.50/1.27 ((cP @ n) = $true) | ((cP @ cO) != $true) | ((cP @ (sK0 @ cP)) != $true)),
% 1.50/1.27 inference(trivial_inequality_removal,[status(thm)],[f43])).
% 1.50/1.27 thf(f43,plain,(
% 1.50/1.27 ((cP @ (sK0 @ cP)) != $true) | ($true != $true) | ((cP @ n) = $true) | ((cP @ cO) != $true)),
% 1.50/1.27 inference(superposition,[status(thm)],[f11,f14])).
% 1.50/1.27 thf(f14,plain,(
% 1.50/1.27 ( ! [X0 : $i] : (((cP @ (c1_plus @ X0)) = $true) | ((cP @ X0) != $true)) )),
% 1.50/1.27 inference(cnf_transformation,[status(thm)],[f9])).
% 1.50/1.27 thf(f11,plain,(
% 1.50/1.27 ( ! [X1 : $i > $o] : (((X1 @ (c1_plus @ (sK0 @ X1))) != $true) | ((X1 @ cO) != $true) | ((X1 @ n) = $true)) )),
% 1.50/1.27 inference(cnf_transformation,[status(thm)],[f9])).
% 1.50/1.27 % SZS output end Proof for DTF2THF_28603
% 1.50/1.27 % (28878)------------------------------
% 1.50/1.27 % (28878)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.27 % (28878)Termination reason: Refutation
% 1.50/1.27
% 1.50/1.27 % (28878)Memory used [KB]: 5500
% 1.50/1.27 % (28878)Time elapsed: 0.004 s
% 1.50/1.27 % (28878)Instructions burned: 3 (million)
% 1.50/1.27 % (28878)------------------------------
% 1.50/1.27 % (28878)------------------------------
% 1.50/1.27 % (28872)Success in time 0.013 s
%------------------------------------------------------------------------------