%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO092^5 : 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 : n031.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 09:53:21 AM UTC 2026
% Result : Theorem 1.51s 1.39s
% Output : Refutation 1.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 2
% Syntax : Number of formulae : 16 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 127 ( 37 equ; 0 cnn)
% Maximal formula atoms : 6 ( 7 avg)
% Number of connectives : 105 ( 15 ~; 16 |; 16 &; 53 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 29 ( 0 ^; 18 !; 11 ?; 29 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cQ: $i > $o ).
thf(func_def_1,type,
cP: $i > $o ).
thf(func_def_5,type,
sK0: $i > $i ).
thf(f17,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f16,f14]) ).
thf(f14,plain,
! [X0: $i] :
( ( cQ @ X0 )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: $i] :
( ( ( cQ @ X0 )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f12,f11]) ).
thf(f11,plain,
! [X1: $i] :
( ( cP @ X1 )
= $true ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ! [X0: $i] :
( ( ( cP @ X0 )
!= $true )
| ( ( cQ @ X0 )
!= $true ) )
& ! [X1: $i] :
( ( ( cP @ X1 )
= $true )
& ( ( $true
= ( cQ @ ( sK0 @ X1 ) ) )
| ( ( cQ @ X1 )
= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f7,f8]) ).
thf(f8,plain,
! [X1: $i] :
( ? [X2: $i] :
( ( ( cP @ X1 )
= $true )
& ( ( ( cQ @ X2 )
= $true )
| ( ( cQ @ X1 )
= $true ) ) )
=> ( ( ( cP @ X1 )
= $true )
& ( ( $true
= ( cQ @ ( sK0 @ X1 ) ) )
| ( ( cQ @ X1 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f7,plain,
( ! [X0: $i] :
( ( ( cP @ X0 )
!= $true )
| ( ( cQ @ X0 )
!= $true ) )
& ! [X1: $i] :
? [X2: $i] :
( ( ( cP @ X1 )
= $true )
& ( ( ( cQ @ X2 )
= $true )
| ( ( cQ @ X1 )
= $true ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,plain,
( ! [X2: $i] :
( ( ( cP @ X2 )
!= $true )
| ( ( cQ @ X2 )
!= $true ) )
& ! [X0: $i] :
? [X1: $i] :
( ( ( cP @ X0 )
= $true )
& ( ( ( cQ @ X1 )
= $true )
| ( ( cQ @ X0 )
= $true ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ! [X0: $i] :
? [X1: $i] :
( ( ( cP @ X0 )
= $true )
& ( ( ( cQ @ X1 )
= $true )
| ( ( cQ @ X0 )
= $true ) ) )
=> ? [X2: $i] :
( ( ( cQ @ X2 )
= $true )
& ( ( cP @ X2 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ! [X0: $i] :
? [X1: $i] :
( ( ( cQ @ X1 )
| ( cQ @ X0 ) )
& ( cP @ X0 ) )
=> ? [X2: $i] :
( ( cQ @ X2 )
& ( cP @ X2 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ! [X0: $i] :
? [X1: $i] :
( ( ( cQ @ X1 )
| ( cQ @ X0 ) )
& ( cP @ X0 ) )
=> ? [X2: $i] :
( ( cQ @ X2 )
& ( cP @ X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ! [X0: $i] :
? [X1: $i] :
( ( ( cQ @ X1 )
| ( cQ @ X0 ) )
& ( cP @ X0 ) )
=> ? [X2: $i] :
( ( cQ @ X2 )
& ( cP @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.RugnlebYnB/DTF2THF_10080.p',cY2141) ).
thf(f12,plain,
! [X0: $i] :
( ( ( cP @ X0 )
!= $true )
| ( ( cQ @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f16,plain,
! [X0: $i] :
( ( cQ @ X0 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f15]) ).
thf(f15,plain,
! [X0: $i] :
( ( $true != $true )
| ( ( cQ @ X0 )
= $true ) ),
inference(superposition,[status(thm)],[f14,f10]) ).
thf(f10,plain,
! [X1: $i] :
( ( $true
= ( cQ @ ( sK0 @ X1 ) ) )
| ( ( cQ @ X1 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO092^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.33 % Computer : n031.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue Feb 24 14:25:03 EST 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.43 ---- Original DTF file ---
% 0.20/0.43 thf(spec,logic,$$dhol).
% 0.20/0.43 %------------------------------------------------------------------------------
% 0.20/0.43 % File : SYO092^5 : TPTP v9.2.1. Released v4.0.0.
% 0.20/0.43 % Domain : Syntactic
% 0.20/0.43 % Problem : TPS problem Y2141
% 0.20/0.43 % Version : Especial.
% 0.20/0.43 % English :
% 0.20/0.43
% 0.20/0.43 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.20/0.43 % Source : [Bro09]
% 0.20/0.43 % Names : tps_0200 [Bro09]
% 0.20/0.43 % : Y2141 [TPS]
% 0.20/0.43
% 0.20/0.43 % Status : Theorem
% 0.20/0.43 % 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 v4.0.0
% 0.20/0.43 % Syntax : Number of formulae : 3 ( 0 unt; 2 typ; 0 def)
% 0.20/0.43 % Number of atoms : 5 ( 0 equ; 0 cnn)
% 0.20/0.43 % Maximal formula atoms : 5 ( 5 avg)
% 0.20/0.43 % Number of connectives : 9 ( 0 ~; 1 |; 2 &; 5 @)
% 0.20/0.43 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.20/0.43 % Maximal formula depth : 7 ( 7 avg)
% 0.20/0.43 % Number of types : 2 ( 0 usr)
% 0.20/0.43 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.20/0.43 % Number of symbols : 2 ( 2 usr; 0 con; 1-1 aty)
% 0.20/0.43 % Number of variables : 3 ( 0 ^; 1 !; 2 ?; 3 :)
% 0.20/0.43 % SPC : TH0_THM_NEQ_NAR
% 0.20/0.43
% 0.20/0.43 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.20/0.43 % project in the Department of Mathematical Sciences at Carnegie
% 0.20/0.43 % Mellon University. Distributed under the Creative Commons copyleft
% 0.20/0.43 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.20/0.43 %------------------------------------------------------------------------------
% 0.20/0.43 % Proposed additional exercise
% 0.20/0.43 thf(cQ,type,
% 0.20/0.43 cQ: $i > $o ).
% 0.20/0.43
% 0.20/0.43 thf(cP,type,
% 0.20/0.43 cP: $i > $o ).
% 0.20/0.43
% 0.20/0.43 thf(cY2141,conjecture,
% 0.20/0.43 ( ! [Xx: $i] :
% 0.20/0.43 ? [Xy: $i] :
% 0.20/0.43 ( ( cP @ Xx )
% 0.20/0.43 & ( ( cQ @ Xy )
% 0.20/0.43 | ( cQ @ Xx ) ) )
% 0.20/0.43 => ? [Xz: $i] :
% 0.20/0.43 ( ( cP @ Xz )
% 0.20/0.43 & ( cQ @ Xz ) ) ) ).
% 0.20/0.43
% 0.20/0.43 %------------------------------------------------------------------------------
% 0.20/0.43 ------------------------
% 1.51/1.36 ---- Embedded in THF ---
% 1.51/1.36 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.51/1.36 %%% Generated on Tue Feb 24 14:25:04 EST 2026
% 1.51/1.36 %%% using '$$dhol' embedding, version 1.3.0.
% 1.51/1.36 %%% Logic specification used:
% 1.51/1.36 %%% thf(spec, logic, $$dhol).
% 1.51/1.36
% 1.51/1.36 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.RugnlebYnB/DTF2DTF10080.p
% See solution above
% 1.51/1.36 ------------------------
% 1.51/1.37 ---- Cleaned THF ---
% 1.51/1.37 thf(cQ,type,
% 1.51/1.37 cQ: $i > $o ).
% 1.51/1.37
% 1.51/1.37 thf(cP,type,
% 1.51/1.37 cP: $i > $o ).
% 1.51/1.37
% 1.51/1.37 thf(cY2141,conjecture,
% 1.51/1.37 ( ! [Xx: $i] :
% 1.51/1.37 ? [Xy: $i] :
% 1.51/1.37 ( ( cP @ Xx )
% 1.51/1.37 & ( ( cQ @ Xy )
% 1.51/1.37 | ( cQ @ Xx ) ) )
% 1.51/1.37 => ? [Xz: $i] :
% 1.51/1.37 ( ( cP @ Xz )
% 1.51/1.37 & ( cQ @ Xz ) ) ) ).
% 1.51/1.37 ------------------------
% 1.51/1.39 % (10182)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_10080 for (3000ds/2Mi)
% 1.51/1.39 % (10179)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_10080 for (3000ds/4Mi)
% 1.51/1.39 % (10178)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_10080 for (3000ds/183Mi)
% 1.51/1.39 % (10183)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_10080 for (3000ds/275Mi)
% 1.51/1.39 % (10181)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_10080 for (3000ds/2Mi)
% 1.51/1.39 % (10180)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_10080 for (3000ds/27Mi)
% 1.51/1.39 % (10184)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_10080 for (3000ds/18Mi)
% 1.51/1.39 % (10183)First to succeed.
% 1.51/1.39 % (10182)Instruction limit reached!
% 1.51/1.39 % (10182)------------------------------
% 1.51/1.39 % (10182)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.39 % (10182)Termination reason: Unknown
% 1.51/1.39 % (10182)Termination phase: Saturation
% 1.51/1.39
% 1.51/1.39 % (10182)Memory used [KB]: 5500
% 1.51/1.39 % (10182)Time elapsed: 0.004 s
% 1.51/1.39 % (10182)Instructions burned: 3 (million)
% 1.51/1.39 % (10182)------------------------------
% 1.51/1.39 % (10182)------------------------------
% 1.51/1.39 % (10178)Also succeeded, but the first one will report.
% 1.51/1.39 % (10184)Also succeeded, but the first one will report.
% 1.51/1.39 % (10183)Refutation found. Thanks to Tanya!
% 1.51/1.39 % SZS status Theorem for DTF2THF_10080
% 1.51/1.39 % SZS output start Proof for DTF2THF_10080
% 1.51/1.39 thf(func_def_0, type, cQ: $i > $o).
% 1.51/1.39 thf(func_def_1, type, cP: $i > $o).
% 1.51/1.39 thf(func_def_5, type, sK0: $i > $i).
% 1.51/1.39 thf(f17,plain,(
% 1.51/1.39 $false),
% 1.51/1.39 inference(subsumption_resolution,[status(thm)],[f16,f14])).
% 1.51/1.39 thf(f14,plain,(
% 1.51/1.39 ( ! [X0 : $i] : (((cQ @ X0) != $true)) )),
% 1.51/1.39 inference(trivial_inequality_removal,[status(thm)],[f13])).
% 1.51/1.39 thf(f13,plain,(
% 1.51/1.39 ( ! [X0 : $i] : (((cQ @ X0) != $true) | ($true != $true)) )),
% 1.51/1.39 inference(superposition,[status(thm)],[f12,f11])).
% 1.51/1.39 thf(f11,plain,(
% 1.51/1.39 ( ! [X1 : $i] : (((cP @ X1) = $true)) )),
% 1.51/1.39 inference(cnf_transformation,[status(thm)],[f9])).
% 1.51/1.39 thf(f9,plain,(
% 1.51/1.39 ! [X0 : $i] : (((cP @ X0) != $true) | ((cQ @ X0) != $true)) & ! [X1 : $i] : (((cP @ X1) = $true) & (($true = (cQ @ (sK0 @ X1))) | ((cQ @ X1) = $true)))),
% 1.51/1.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f7,f8])).
% 1.51/1.39 thf(f8,plain,(
% 1.51/1.39 ! [X1 : $i] : (? [X2 : $i] : (((cP @ X1) = $true) & (((cQ @ X2) = $true) | ((cQ @ X1) = $true))) => (((cP @ X1) = $true) & (($true = (cQ @ (sK0 @ X1))) | ((cQ @ X1) = $true))))),
% 1.51/1.39 introduced(definition,[],[choice_axiom])).
% 1.51/1.39 thf(f7,plain,(
% 1.51/1.39 ! [X0 : $i] : (((cP @ X0) != $true) | ((cQ @ X0) != $true)) & ! [X1 : $i] : ? [X2 : $i] : (((cP @ X1) = $true) & (((cQ @ X2) = $true) | ((cQ @ X1) = $true)))),
% 1.51/1.39 inference(rectify,[status(thm)],[f6])).
% 1.51/1.39 thf(f6,plain,(
% 1.51/1.39 ! [X2 : $i] : (((cP @ X2) != $true) | ((cQ @ X2) != $true)) & ! [X0 : $i] : ? [X1 : $i] : (((cP @ X0) = $true) & (((cQ @ X1) = $true) | ((cQ @ X0) = $true)))),
% 1.51/1.39 inference(ennf_transformation,[status(thm)],[f5])).
% 1.51/1.39 thf(f5,plain,(
% 1.51/1.39 ~(! [X0 : $i] : ? [X1 : $i] : (((cP @ X0) = $true) & (((cQ @ X1) = $true) | ((cQ @ X0) = $true))) => ? [X2 : $i] : (((cQ @ X2) = $true) & ((cP @ X2) = $true)))),
% 1.51/1.39 inference(fool_elimination,[status(thm)],[f4])).
% 1.51/1.39 thf(f4,plain,(
% 1.51/1.39 ~(! [X0 : $i] : ? [X1 : $i] : (((cQ @ X1) | (cQ @ X0)) & (cP @ X0)) => ? [X2 : $i] : ((cQ @ X2) & (cP @ X2)))),
% 1.51/1.39 inference(rectify,[status(thm)],[f2])).
% 1.51/1.39 thf(f2,negated_conjecture,(
% 1.51/1.40 ~(! [X0 : $i] : ? [X1 : $i] : (((cQ @ X1) | (cQ @ X0)) & (cP @ X0)) => ? [X2 : $i] : ((cQ @ X2) & (cP @ X2)))),
% 1.51/1.40 inference(negated_conjecture,[status(cth)],[f1])).
% 1.51/1.40 thf(f1,conjecture,(
% 1.51/1.40 ! [X0 : $i] : ? [X1 : $i] : (((cQ @ X1) | (cQ @ X0)) & (cP @ X0)) => ? [X2 : $i] : ((cQ @ X2) & (cP @ X2))),
% 1.51/1.40 file('/export/starexec/sandbox/tmp/tmp.RugnlebYnB/DTF2THF_10080.p',cY2141)).
% 1.51/1.40 thf(f12,plain,(
% 1.51/1.40 ( ! [X0 : $i] : (((cP @ X0) != $true) | ((cQ @ X0) != $true)) )),
% 1.51/1.40 inference(cnf_transformation,[status(thm)],[f9])).
% 1.51/1.40 thf(f16,plain,(
% 1.51/1.40 ( ! [X0 : $i] : (((cQ @ X0) = $true)) )),
% 1.51/1.40 inference(trivial_inequality_removal,[status(thm)],[f15])).
% 1.51/1.40 thf(f15,plain,(
% 1.51/1.40 ( ! [X0 : $i] : (($true != $true) | ((cQ @ X0) = $true)) )),
% 1.51/1.40 inference(superposition,[status(thm)],[f14,f10])).
% 1.51/1.40 thf(f10,plain,(
% 1.51/1.40 ( ! [X1 : $i] : (($true = (cQ @ (sK0 @ X1))) | ((cQ @ X1) = $true)) )),
% 1.51/1.40 inference(cnf_transformation,[status(thm)],[f9])).
% 1.51/1.40 % SZS output end Proof for DTF2THF_10080
% 1.51/1.40 % (10183)------------------------------
% 1.51/1.40 % (10183)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.40 % (10183)Termination reason: Refutation
% 1.51/1.40
% 1.51/1.40 % (10183)Memory used [KB]: 5500
% 1.51/1.40 % (10183)Time elapsed: 0.004 s
% 1.51/1.40 % (10183)Instructions burned: 1 (million)
% 1.51/1.40 % (10183)------------------------------
% 1.51/1.40 % (10183)------------------------------
% 1.51/1.40 % (10177)Success in time 0.018 s
%------------------------------------------------------------------------------