%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO140^5 : 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 : n022.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 09:53:28 AM UTC 2026
% Result : Theorem 1.55s 1.32s
% Output : Refutation 1.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 2
% Syntax : Number of formulae : 15 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 100 ( 28 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 80 ( 15 ~; 5 |; 8 &; 39 @)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 3 usr; 3 con; 0-2 aty)
% Number of variables : 27 ( 0 ^; 15 !; 12 ?; 27 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cQ: $i > $o ).
thf(func_def_1,type,
cP: $i > $o ).
thf(f16,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f15]) ).
thf(f15,plain,
$true != $true,
inference(superposition,[status(thm)],[f14,f13]) ).
thf(f13,plain,
( $true
= ( cP @ sK0 ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ( $true
= ( cP @ sK0 ) )
& ! [X1: $i] :
( ( cQ @ X1 )
!= $true )
& ! [X2: $i] :
( ( $true
!= ( cP @ X2 ) )
| ( $true
= ( cQ @ X2 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f8,f9]) ).
thf(f9,plain,
( ? [X0: $i] :
( ( cP @ X0 )
= $true )
=> ( $true
= ( cP @ sK0 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
( ? [X0: $i] :
( ( cP @ X0 )
= $true )
& ! [X1: $i] :
( ( cQ @ X1 )
!= $true )
& ! [X2: $i] :
( ( $true
!= ( cP @ X2 ) )
| ( $true
= ( cQ @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
( ? [X0: $i] :
( ( cP @ X0 )
= $true )
& ! [X2: $i] :
( $true
!= ( cQ @ X2 ) )
& ! [X1: $i] :
( ( $true
!= ( cP @ X1 ) )
| ( ( cQ @ X1 )
= $true ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
( ! [X2: $i] :
( $true
!= ( cQ @ X2 ) )
& ! [X1: $i] :
( ( $true
!= ( cP @ X1 ) )
| ( ( cQ @ X1 )
= $true ) )
& ? [X0: $i] :
( ( cP @ X0 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ? [X0: $i] :
( ( cP @ X0 )
= $true )
=> ( ! [X1: $i] :
( ( $true
= ( cP @ X1 ) )
=> ( ( cQ @ X1 )
= $true ) )
=> ? [X2: $i] :
( $true
= ( cQ @ X2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ? [X0: $i] : ( cP @ X0 )
=> ( ! [X1: $i] :
( ( cP @ X1 )
=> ( cQ @ X1 ) )
=> ? [X2: $i] : ( cQ @ X2 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ? [X0: $i] : ( cP @ X0 )
=> ( ! [X0: $i] :
( ( cP @ X0 )
=> ( cQ @ X0 ) )
=> ? [X0: $i] : ( cQ @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ? [X0: $i] : ( cP @ X0 )
=> ( ! [X0: $i] :
( ( cP @ X0 )
=> ( cQ @ X0 ) )
=> ? [X0: $i] : ( cQ @ X0 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.co8VD7iCyC/DTF2THF_23275.p',cADDHYP6) ).
thf(f14,plain,
! [X2: $i] :
( $true
!= ( cP @ X2 ) ),
inference(subsumption_resolution,[status(thm)],[f11,f12]) ).
thf(f12,plain,
! [X1: $i] :
( ( cQ @ X1 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f11,plain,
! [X2: $i] :
( ( $true
!= ( cP @ X2 ) )
| ( $true
= ( cQ @ X2 ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SYO140^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.09 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.13/0.29 % Computer : n022.cluster.edu
% 0.13/0.29 % Model : x86_64 x86_64
% 0.13/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.29 % Memory : 8042.1875MB
% 0.13/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.29 % CPULimit : 300
% 0.13/0.29 % WCLimit : 300
% 0.13/0.29 % DateTime : Tue Feb 24 14:25:21 EST 2026
% 0.13/0.29 % CPUTime :
% 0.13/0.29 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.39 ---- Original DTF file ---
% 0.17/0.39 thf(spec,logic,$$dhol).
% 0.17/0.39 %------------------------------------------------------------------------------
% 0.17/0.39 % File : SYO140^5 : TPTP v9.2.1. Released v4.0.0.
% 0.17/0.39 % Domain : Syntactic
% 0.17/0.39 % Problem : TPS problem from BASIC-FO-THMS
% 0.17/0.39 % Version : Especial.
% 0.17/0.39 % English :
% 0.17/0.39
% 0.17/0.39 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.17/0.39 % Source : [Bro09]
% 0.17/0.39 % Names : tps_0749 [Bro09]
% 0.17/0.39
% 0.17/0.39 % Status : Theorem
% 0.17/0.39 % Rating : 0.00 v6.2.0, 0.17 v6.1.0, 0.00 v4.0.0
% 0.17/0.39 % Syntax : Number of formulae : 3 ( 0 unt; 2 typ; 0 def)
% 0.17/0.39 % Number of atoms : 4 ( 0 equ; 0 cnn)
% 0.17/0.39 % Maximal formula atoms : 4 ( 4 avg)
% 0.17/0.39 % Number of connectives : 7 ( 0 ~; 0 |; 0 &; 4 @)
% 0.17/0.39 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.17/0.39 % Maximal formula depth : 6 ( 6 avg)
% 0.17/0.39 % Number of types : 2 ( 0 usr)
% 0.17/0.39 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.17/0.39 % Number of symbols : 2 ( 2 usr; 0 con; 1-1 aty)
% 0.17/0.39 % Number of variables : 3 ( 0 ^; 1 !; 2 ?; 3 :)
% 0.17/0.39 % SPC : TH0_THM_NEQ_NAR
% 0.17/0.39
% 0.17/0.39 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.17/0.39 % project in the Department of Mathematical Sciences at Carnegie
% 0.17/0.39 % Mellon University. Distributed under the Creative Commons copyleft
% 0.17/0.39 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.17/0.39 %------------------------------------------------------------------------------
% 0.17/0.39 thf(cQ,type,
% 0.17/0.39 cQ: $i > $o ).
% 0.17/0.39
% 0.17/0.39 thf(cP,type,
% 0.17/0.39 cP: $i > $o ).
% 0.17/0.39
% 0.17/0.39 thf(cADDHYP6,conjecture,
% 0.17/0.39 ( ? [Xx: $i] : ( cP @ Xx )
% 0.17/0.39 => ( ! [Xx: $i] :
% 0.17/0.39 ( ( cP @ Xx )
% 0.17/0.39 => ( cQ @ Xx ) )
% 0.17/0.39 => ? [Xx: $i] : ( cQ @ Xx ) ) ) ).
% 0.17/0.39
% 0.17/0.39 %------------------------------------------------------------------------------
% 0.17/0.39 ------------------------
% 1.36/1.29 ---- Embedded in THF ---
% 1.36/1.29 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.36/1.29 %%% Generated on Tue Feb 24 14:25:22 EST 2026
% 1.36/1.29 %%% using '$$dhol' embedding, version 1.3.0.
% 1.36/1.29 %%% Logic specification used:
% 1.36/1.29 %%% thf(spec, logic, $$dhol).
% 1.36/1.29
% 1.36/1.29 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.co8VD7iCyC/DTF2DTF23275.p
% See solution above
% 1.36/1.29 ------------------------
% 1.36/1.29 ---- Cleaned THF ---
% 1.36/1.30 thf(cQ,type,
% 1.36/1.30 cQ: $i > $o ).
% 1.36/1.30
% 1.36/1.30 thf(cP,type,
% 1.36/1.30 cP: $i > $o ).
% 1.36/1.30
% 1.36/1.30 thf(cADDHYP6,conjecture,
% 1.36/1.30 ( ? [Xx: $i] : ( cP @ Xx )
% 1.36/1.30 => ( ! [Xx: $i] :
% 1.36/1.30 ( ( cP @ Xx )
% 1.36/1.30 => ( cQ @ Xx ) )
% 1.36/1.30 => ? [Xx: $i] : ( cQ @ Xx ) ) ) ).
% 1.36/1.30 ------------------------
% 1.55/1.32 % (23377)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_23275 for (3000ds/2Mi)
% 1.55/1.32 % (23373)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_23275 for (3000ds/183Mi)
% 1.55/1.32 % (23376)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_23275 for (3000ds/2Mi)
% 1.55/1.32 % (23375)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_23275 for (3000ds/27Mi)
% 1.55/1.32 % (23374)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_23275 for (3000ds/4Mi)
% 1.55/1.32 % (23378)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_23275 for (3000ds/275Mi)
% 1.55/1.32 % (23379)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_23275 for (3000ds/18Mi)
% 1.55/1.32 % (23376)Instruction limit reached!
% 1.55/1.32 % (23376)------------------------------
% 1.55/1.32 % (23376)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.32 % (23376)Termination reason: Unknown
% 1.55/1.32 % (23376)Termination phase: Saturation
% 1.55/1.32 % (23377)Instruction limit reached!
% 1.55/1.32 % (23377)------------------------------
% 1.55/1.32 % (23377)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.32 % (23377)Termination reason: Unknown
% 1.55/1.32 % (23377)Termination phase: Saturation
% 1.55/1.32
% 1.55/1.32 % (23377)Memory used [KB]: 5500
% 1.55/1.32 % (23377)Time elapsed: 0.003 s
% 1.55/1.32 % (23377)Instructions burned: 2 (million)
% 1.55/1.32 % (23377)------------------------------
% 1.55/1.32 % (23377)------------------------------
% 1.55/1.32
% 1.55/1.32 % (23376)Memory used [KB]: 5500
% 1.55/1.32 % (23378)First to succeed.
% 1.55/1.32 % (23376)Time elapsed: 0.003 s
% 1.55/1.32 % (23376)Instructions burned: 2 (million)
% 1.55/1.32 % (23376)------------------------------
% 1.55/1.32 % (23376)------------------------------
% 1.55/1.32 % (23373)Also succeeded, but the first one will report.
% 1.55/1.32 % (23374)Also succeeded, but the first one will report.
% 1.55/1.32 % (23378)Refutation found. Thanks to Tanya!
% 1.55/1.32 % SZS status Theorem for DTF2THF_23275
% 1.55/1.32 % SZS output start Proof for DTF2THF_23275
% 1.55/1.32 thf(func_def_0, type, cQ: $i > $o).
% 1.55/1.32 thf(func_def_1, type, cP: $i > $o).
% 1.55/1.32 thf(f16,plain,(
% 1.55/1.32 $false),
% 1.55/1.32 inference(trivial_inequality_removal,[status(thm)],[f15])).
% 1.55/1.32 thf(f15,plain,(
% 1.55/1.32 ($true != $true)),
% 1.55/1.32 inference(superposition,[status(thm)],[f14,f13])).
% 1.55/1.32 thf(f13,plain,(
% 1.55/1.32 ($true = (cP @ sK0))),
% 1.55/1.32 inference(cnf_transformation,[status(thm)],[f10])).
% 1.55/1.32 thf(f10,plain,(
% 1.55/1.32 ($true = (cP @ sK0)) & ! [X1 : $i] : ((cQ @ X1) != $true) & ! [X2 : $i] : (($true != (cP @ X2)) | ($true = (cQ @ X2)))),
% 1.55/1.32 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f8,f9])).
% 1.55/1.32 thf(f9,plain,(
% 1.55/1.32 ? [X0 : $i] : ((cP @ X0) = $true) => ($true = (cP @ sK0))),
% 1.55/1.32 introduced(definition,[],[choice_axiom])).
% 1.55/1.32 thf(f8,plain,(
% 1.55/1.32 ? [X0 : $i] : ((cP @ X0) = $true) & ! [X1 : $i] : ((cQ @ X1) != $true) & ! [X2 : $i] : (($true != (cP @ X2)) | ($true = (cQ @ X2)))),
% 1.55/1.32 inference(rectify,[status(thm)],[f7])).
% 1.55/1.32 thf(f7,plain,(
% 1.55/1.32 ? [X0 : $i] : ((cP @ X0) = $true) & ! [X2 : $i] : ($true != (cQ @ X2)) & ! [X1 : $i] : (($true != (cP @ X1)) | ((cQ @ X1) = $true))),
% 1.55/1.32 inference(flattening,[status(thm)],[f6])).
% 1.55/1.32 thf(f6,plain,(
% 1.55/1.32 (! [X2 : $i] : ($true != (cQ @ X2)) & ! [X1 : $i] : (($true != (cP @ X1)) | ((cQ @ X1) = $true))) & ? [X0 : $i] : ((cP @ X0) = $true)),
% 1.55/1.32 inference(ennf_transformation,[status(thm)],[f5])).
% 1.55/1.32 thf(f5,plain,(
% 1.55/1.32 ~(? [X0 : $i] : ((cP @ X0) = $true) => (! [X1 : $i] : (($true = (cP @ X1)) => ((cQ @ X1) = $true)) => ? [X2 : $i] : ($true = (cQ @ X2))))),
% 1.55/1.32 inference(fool_elimination,[status(thm)],[f4])).
% 1.55/1.32 thf(f4,plain,(
% 1.55/1.32 ~(? [X0 : $i] : (cP @ X0) => (! [X1 : $i] : ((cP @ X1) => (cQ @ X1)) => ? [X2 : $i] : (cQ @ X2)))),
% 1.55/1.32 inference(rectify,[status(thm)],[f2])).
% 1.55/1.32 thf(f2,negated_conjecture,(
% 1.55/1.32 ~(? [X0 : $i] : (cP @ X0) => (! [X0 : $i] : ((cP @ X0) => (cQ @ X0)) => ? [X0 : $i] : (cQ @ X0)))),
% 1.55/1.32 inference(negated_conjecture,[status(cth)],[f1])).
% 1.55/1.32 thf(f1,conjecture,(
% 1.55/1.32 ? [X0 : $i] : (cP @ X0) => (! [X0 : $i] : ((cP @ X0) => (cQ @ X0)) => ? [X0 : $i] : (cQ @ X0))),
% 1.55/1.32 file('/export/starexec/sandbox/tmp/tmp.co8VD7iCyC/DTF2THF_23275.p',cADDHYP6)).
% 1.55/1.32 thf(f14,plain,(
% 1.55/1.32 ( ! [X2 : $i] : (($true != (cP @ X2))) )),
% 1.55/1.32 inference(subsumption_resolution,[status(thm)],[f11,f12])).
% 1.55/1.32 thf(f12,plain,(
% 1.55/1.32 ( ! [X1 : $i] : (((cQ @ X1) != $true)) )),
% 1.55/1.32 inference(cnf_transformation,[status(thm)],[f10])).
% 1.55/1.32 thf(f11,plain,(
% 1.55/1.32 ( ! [X2 : $i] : (($true != (cP @ X2)) | ($true = (cQ @ X2))) )),
% 1.55/1.32 inference(cnf_transformation,[status(thm)],[f10])).
% 1.55/1.32 % SZS output end Proof for DTF2THF_23275
% 1.55/1.32 % (23378)------------------------------
% 1.55/1.32 % (23378)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.55/1.32 % (23378)Termination reason: Refutation
% 1.55/1.32
% 1.55/1.32 % (23378)Memory used [KB]: 5500
% 1.55/1.32 % (23378)Time elapsed: 0.003 s
% 1.55/1.32 % (23378)Instructions burned: 1 (million)
% 1.55/1.32 % (23378)------------------------------
% 1.55/1.32 % (23378)------------------------------
% 1.55/1.32 % (23372)Success in time 0.017 s
%------------------------------------------------------------------------------