%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYN732^5 : 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 : n017.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 09:51:23 AM UTC 2026
% Result : Theorem 1.66s 1.46s
% Output : Refutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 12 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 94 ( 26 equ; 0 cnn)
% Maximal formula atoms : 5 ( 7 avg)
% Number of connectives : 132 ( 15 ~; 7 |; 9 &; 87 @)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 47 ( 0 ^; 29 !; 18 ?; 47 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cQ: $i > $i > $o ).
thf(func_def_1,type,
cP: $i > $i > $o ).
thf(func_def_5,type,
sK0: $i > $i ).
thf(func_def_6,type,
sK1: $i > $i ).
thf(f15,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f13,f11]) ).
thf(f11,plain,
! [X3: $i,X5: $i] :
( ( cP @ X3 @ X5 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ! [X0: $i] :
( ! [X1: $i] :
( ( cQ @ X1 @ X0 )
= $true )
| ( ( cP @ ( sK0 @ X0 ) @ X0 )
!= $true ) )
& ! [X3: $i] :
( ( ( cP @ ( sK1 @ X3 ) @ X3 )
= $true )
& ! [X5: $i] :
( ( ( cQ @ X5 @ X3 )
!= $true )
& ( ( cP @ X3 @ X5 )
!= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f7,f9,f8]) ).
thf(f8,plain,
! [X0: $i] :
( ? [X2: $i] :
( ( cP @ X2 @ X0 )
!= $true )
=> ( ( cP @ ( sK0 @ X0 ) @ X0 )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
! [X3: $i] :
( ? [X4: $i] :
( ( cP @ X4 @ X3 )
= $true )
=> ( ( cP @ ( sK1 @ X3 ) @ X3 )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f7,plain,
( ! [X0: $i] :
( ! [X1: $i] :
( ( cQ @ X1 @ X0 )
= $true )
| ? [X2: $i] :
( ( cP @ X2 @ X0 )
!= $true ) )
& ! [X3: $i] :
( ? [X4: $i] :
( ( cP @ X4 @ X3 )
= $true )
& ! [X5: $i] :
( ( ( cQ @ X5 @ X3 )
!= $true )
& ( ( cP @ X3 @ X5 )
!= $true ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,plain,
( ! [X0: $i] :
( ! [X2: $i] :
( ( cQ @ X2 @ X0 )
= $true )
| ? [X1: $i] :
( ( cP @ X1 @ X0 )
!= $true ) )
& ! [X3: $i] :
( ? [X4: $i] :
( ( cP @ X4 @ X3 )
= $true )
& ! [X5: $i] :
( ( ( cQ @ X5 @ X3 )
!= $true )
& ( ( cP @ X3 @ X5 )
!= $true ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ! [X0: $i] :
( ! [X1: $i] :
( ( cP @ X1 @ X0 )
= $true )
=> ! [X2: $i] :
( ( cQ @ X2 @ X0 )
= $true ) )
=> ? [X3: $i] :
( ? [X4: $i] :
( ( cP @ X4 @ X3 )
= $true )
=> ? [X5: $i] :
( ( ( cQ @ X5 @ X3 )
= $true )
| ( ( cP @ X3 @ X5 )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ! [X0: $i] :
( ! [X1: $i] : ( cP @ X1 @ X0 )
=> ! [X2: $i] : ( cQ @ X2 @ X0 ) )
=> ? [X3: $i] :
( ? [X4: $i] : ( cP @ X4 @ X3 )
=> ? [X5: $i] :
( ( cP @ X3 @ X5 )
| ( cQ @ X5 @ X3 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ! [X0: $i] :
( ! [X1: $i] : ( cP @ X1 @ X0 )
=> ! [X2: $i] : ( cQ @ X2 @ X0 ) )
=> ? [X3: $i] :
( ? [X4: $i] : ( cP @ X4 @ X3 )
=> ? [X5: $i] :
( ( cP @ X3 @ X5 )
| ( cQ @ X5 @ X3 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ! [X0: $i] :
( ! [X1: $i] : ( cP @ X1 @ X0 )
=> ! [X2: $i] : ( cQ @ X2 @ X0 ) )
=> ? [X3: $i] :
( ? [X4: $i] : ( cP @ X4 @ X3 )
=> ? [X5: $i] :
( ( cP @ X3 @ X5 )
| ( cQ @ X5 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.GQ6ghZ9ovB/DTF2THF_16787.p',cX3411) ).
thf(f13,plain,
! [X3: $i] :
( ( cP @ ( sK1 @ X3 ) @ X3 )
= $true ),
inference(cnf_transformation,[status(thm)],[f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN732^5 : 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 : n017.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 14:14:11 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
% 0.20/0.48 ---- Original DTF file ---
% 0.20/0.48 thf(spec,logic,$$dhol).
% 0.20/0.48 %------------------------------------------------------------------------------
% 0.20/0.48 % File : SYN732^5 : TPTP v9.2.1. Released v4.0.0.
% 0.20/0.48 % Domain : Syntactic
% 0.20/0.48 % Problem : TPS problem X3411
% 0.20/0.48 % Version : Especial.
% 0.20/0.48 % English :
% 0.20/0.48
% 0.20/0.48 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.20/0.48 % Source : [Bro09]
% 0.20/0.48 % Names : tps_0148 [Bro09]
% 0.20/0.48 % : X3411 [TPS]
% 0.20/0.48
% 0.20/0.48 % Status : Theorem
% 0.20/0.48 % 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
% 0.20/0.48 % Syntax : Number of formulae : 3 ( 0 unt; 2 typ; 0 def)
% 0.20/0.48 % Number of atoms : 5 ( 0 equ; 0 cnn)
% 0.20/0.48 % Maximal formula atoms : 5 ( 5 avg)
% 0.20/0.48 % Number of connectives : 14 ( 0 ~; 1 |; 0 &; 10 @)
% 0.20/0.48 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.20/0.48 % Maximal formula depth : 8 ( 8 avg)
% 0.20/0.48 % Number of types : 2 ( 0 usr)
% 0.20/0.48 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.20/0.48 % Number of symbols : 2 ( 2 usr; 0 con; 2-2 aty)
% 0.20/0.48 % Number of variables : 6 ( 0 ^; 3 !; 3 ?; 6 :)
% 0.20/0.48 % SPC : TH0_THM_NEQ_NAR
% 0.20/0.48
% 0.20/0.48 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.20/0.48 % project in the Department of Mathematical Sciences at Carnegie
% 0.20/0.48 % Mellon University. Distributed under the Creative Commons copyleft
% 0.20/0.48 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.20/0.48 % :
% 0.20/0.48 %------------------------------------------------------------------------------
% 0.20/0.48 thf(cQ,type,
% 0.20/0.48 cQ: $i > $i > $o ).
% 0.20/0.48
% 0.20/0.48 thf(cP,type,
% 0.20/0.48 cP: $i > $i > $o ).
% 0.20/0.48
% 0.20/0.48 thf(cX3411,conjecture,
% 0.20/0.48 ( ! [Xy: $i] :
% 0.20/0.48 ( ! [Xx: $i] : ( cP @ Xx @ Xy )
% 0.20/0.48 => ! [Xu: $i] : ( cQ @ Xu @ Xy ) )
% 0.20/0.48 => ? [Xz: $i] :
% 0.20/0.48 ( ? [Xv: $i] : ( cP @ Xv @ Xz )
% 0.20/0.48 => ? [Xw: $i] :
% 0.20/0.48 ( ( cP @ Xz @ Xw )
% 0.20/0.48 | ( cQ @ Xw @ Xz ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 %------------------------------------------------------------------------------
% 0.20/0.48 ------------------------
% 1.66/1.43 ---- Embedded in THF ---
% 1.66/1.43 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.66/1.43 %%% Generated on Tue Feb 24 14:14:12 EST 2026
% 1.66/1.43 %%% using '$$dhol' embedding, version 1.3.0.
% 1.66/1.43 %%% Logic specification used:
% 1.66/1.43 %%% thf(spec, logic, $$dhol).
% 1.66/1.43
% 1.66/1.43 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.GQ6ghZ9ovB/DTF2DTF16787.p
% See solution above
% 1.66/1.43 ------------------------
% 1.66/1.44 ---- Cleaned THF ---
% 1.66/1.44 thf(cQ,type,
% 1.66/1.44 cQ: $i > $i > $o ).
% 1.66/1.44
% 1.66/1.44 thf(cP,type,
% 1.66/1.44 cP: $i > $i > $o ).
% 1.66/1.44
% 1.66/1.44 thf(cX3411,conjecture,
% 1.66/1.44 ( ! [Xy: $i] :
% 1.66/1.44 ( ! [Xx: $i] : ( cP @ Xx @ Xy )
% 1.66/1.44 => ! [Xu: $i] : ( cQ @ Xu @ Xy ) )
% 1.66/1.44 => ? [Xz: $i] :
% 1.66/1.44 ( ? [Xv: $i] : ( cP @ Xv @ Xz )
% 1.66/1.44 => ? [Xw: $i] :
% 1.66/1.44 ( ( cP @ Xz @ Xw )
% 1.66/1.44 | ( cQ @ Xw @ Xz ) ) ) ) ).
% 1.66/1.44 ------------------------
% 1.66/1.46 % (16886)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_16787 for (2999ds/27Mi)
% 1.66/1.46 % (16885)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_16787 for (2999ds/4Mi)
% 1.66/1.46 % (16887)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_16787 for (2999ds/2Mi)
% 1.66/1.46 % (16889)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_16787 for (2999ds/275Mi)
% 1.66/1.46 % (16884)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_16787 for (2999ds/183Mi)
% 1.66/1.46 % (16890)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_16787 for (2999ds/18Mi)
% 1.66/1.46 % (16888)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_16787 for (2999ds/2Mi)
% 1.66/1.46 % (16887)Instruction limit reached!
% 1.66/1.46 % (16887)------------------------------
% 1.66/1.46 % (16887)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.46 % (16887)Termination reason: Unknown
% 1.66/1.46 % (16887)Termination phase: Saturation
% 1.66/1.46 % (16889)First to succeed.
% 1.66/1.46
% 1.66/1.46 % (16888)Instruction limit reached!
% 1.66/1.46 % (16888)------------------------------
% 1.66/1.46 % (16888)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.46 % (16888)Termination reason: Unknown
% 1.66/1.46 % (16888)Termination phase: Saturation
% 1.66/1.46
% 1.66/1.46 % (16888)Memory used [KB]: 5500
% 1.66/1.46 % (16888)Time elapsed: 0.003 s
% 1.66/1.46 % (16888)Instructions burned: 2 (million)
% 1.66/1.46 % (16888)------------------------------
% 1.66/1.46 % (16888)------------------------------
% 1.66/1.46 % (16887)Memory used [KB]: 5500
% 1.66/1.46 % (16887)Time elapsed: 0.003 s
% 1.66/1.46 % (16887)Instructions burned: 2 (million)
% 1.66/1.46 % (16887)------------------------------
% 1.66/1.46 % (16887)------------------------------
% 1.66/1.46 % (16890)Also succeeded, but the first one will report.
% 1.66/1.46 % (16884)Also succeeded, but the first one will report.
% 1.66/1.46 % (16889)Refutation found. Thanks to Tanya!
% 1.66/1.46 % SZS status Theorem for DTF2THF_16787
% 1.66/1.46 % SZS output start Proof for DTF2THF_16787
% 1.66/1.46 thf(func_def_0, type, cQ: $i > $i > $o).
% 1.66/1.46 thf(func_def_1, type, cP: $i > $i > $o).
% 1.66/1.46 thf(func_def_5, type, sK0: $i > $i).
% 1.66/1.46 thf(func_def_6, type, sK1: $i > $i).
% 1.66/1.46 thf(f15,plain,(
% 1.66/1.46 $false),
% 1.66/1.46 inference(subsumption_resolution,[status(thm)],[f13,f11])).
% 1.66/1.46 thf(f11,plain,(
% 1.66/1.46 ( ! [X3 : $i,X5 : $i] : (((cP @ X3 @ X5) != $true)) )),
% 1.66/1.46 inference(cnf_transformation,[status(thm)],[f10])).
% 1.66/1.46 thf(f10,plain,(
% 1.66/1.46 ! [X0 : $i] : (! [X1 : $i] : ((cQ @ X1 @ X0) = $true) | ((cP @ (sK0 @ X0) @ X0) != $true)) & ! [X3 : $i] : (((cP @ (sK1 @ X3) @ X3) = $true) & ! [X5 : $i] : (((cQ @ X5 @ X3) != $true) & ((cP @ X3 @ X5) != $true)))),
% 1.66/1.46 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f7,f9,f8])).
% 1.66/1.46 thf(f8,plain,(
% 1.66/1.46 ! [X0 : $i] : (? [X2 : $i] : ((cP @ X2 @ X0) != $true) => ((cP @ (sK0 @ X0) @ X0) != $true))),
% 1.66/1.46 introduced(definition,[],[choice_axiom])).
% 1.66/1.46 thf(f9,plain,(
% 1.66/1.46 ! [X3 : $i] : (? [X4 : $i] : ((cP @ X4 @ X3) = $true) => ((cP @ (sK1 @ X3) @ X3) = $true))),
% 1.66/1.46 introduced(definition,[],[choice_axiom])).
% 1.66/1.46 thf(f7,plain,(
% 1.66/1.46 ! [X0 : $i] : (! [X1 : $i] : ((cQ @ X1 @ X0) = $true) | ? [X2 : $i] : ((cP @ X2 @ X0) != $true)) & ! [X3 : $i] : (? [X4 : $i] : ((cP @ X4 @ X3) = $true) & ! [X5 : $i] : (((cQ @ X5 @ X3) != $true) & ((cP @ X3 @ X5) != $true)))),
% 1.66/1.46 inference(rectify,[status(thm)],[f6])).
% 1.66/1.46 thf(f6,plain,(
% 1.66/1.46 ! [X0 : $i] : (! [X2 : $i] : ((cQ @ X2 @ X0) = $true) | ? [X1 : $i] : ((cP @ X1 @ X0) != $true)) & ! [X3 : $i] : (? [X4 : $i] : ((cP @ X4 @ X3) = $true) & ! [X5 : $i] : (((cQ @ X5 @ X3) != $true) & ((cP @ X3 @ X5) != $true)))),
% 1.66/1.46 inference(ennf_transformation,[status(thm)],[f5])).
% 1.66/1.46 thf(f5,plain,(
% 1.66/1.46 ~(! [X0 : $i] : (! [X1 : $i] : ((cP @ X1 @ X0) = $true) => ! [X2 : $i] : ((cQ @ X2 @ X0) = $true)) => ? [X3 : $i] : (? [X4 : $i] : ((cP @ X4 @ X3) = $true) => ? [X5 : $i] : (((cQ @ X5 @ X3) = $true) | ((cP @ X3 @ X5) = $true))))),
% 1.66/1.46 inference(fool_elimination,[status(thm)],[f4])).
% 1.66/1.46 thf(f4,plain,(
% 1.66/1.46 ~(! [X0 : $i] : (! [X1 : $i] : (cP @ X1 @ X0) => ! [X2 : $i] : (cQ @ X2 @ X0)) => ? [X3 : $i] : (? [X4 : $i] : (cP @ X4 @ X3) => ? [X5 : $i] : ((cP @ X3 @ X5) | (cQ @ X5 @ X3))))),
% 1.66/1.46 inference(rectify,[status(thm)],[f2])).
% 1.66/1.46 thf(f2,negated_conjecture,(
% 1.66/1.46 ~(! [X0 : $i] : (! [X1 : $i] : (cP @ X1 @ X0) => ! [X2 : $i] : (cQ @ X2 @ X0)) => ? [X3 : $i] : (? [X4 : $i] : (cP @ X4 @ X3) => ? [X5 : $i] : ((cP @ X3 @ X5) | (cQ @ X5 @ X3))))),
% 1.66/1.46 inference(negated_conjecture,[status(cth)],[f1])).
% 1.66/1.46 thf(f1,conjecture,(
% 1.66/1.46 ! [X0 : $i] : (! [X1 : $i] : (cP @ X1 @ X0) => ! [X2 : $i] : (cQ @ X2 @ X0)) => ? [X3 : $i] : (? [X4 : $i] : (cP @ X4 @ X3) => ? [X5 : $i] : ((cP @ X3 @ X5) | (cQ @ X5 @ X3)))),
% 1.66/1.46 file('/export/starexec/sandbox/tmp/tmp.GQ6ghZ9ovB/DTF2THF_16787.p',cX3411)).
% 1.66/1.46 thf(f13,plain,(
% 1.66/1.46 ( ! [X3 : $i] : (((cP @ (sK1 @ X3) @ X3) = $true)) )),
% 1.66/1.46 inference(cnf_transformation,[status(thm)],[f10])).
% 1.66/1.46 % SZS output end Proof for DTF2THF_16787
% 1.66/1.46 % (16889)------------------------------
% 1.66/1.46 % (16889)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.46 % (16889)Termination reason: Refutation
% 1.66/1.46
% 1.66/1.46 % (16889)Memory used [KB]: 5500
% 1.66/1.46 % (16889)Time elapsed: 0.003 s
% 1.66/1.46 % (16889)Instructions burned: 1 (million)
% 1.66/1.46 % (16889)------------------------------
% 1.66/1.46 % (16889)------------------------------
% 1.66/1.46 % (16883)Success in time 0.016 s
%------------------------------------------------------------------------------