%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU843^5 : 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 : n021.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 09:37:34 AM UTC 2026
% Result : Theorem 1.29s 1.19s
% Output : Refutation 1.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 3
% Syntax : Number of formulae : 20 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 99 ( 38 equ; 0 cnn)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 108 ( 12 ~; 16 |; 10 &; 58 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 38 ( 11 ^; 19 !; 8 ?; 38 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_7,type,
sK0: a > $o ).
thf(func_def_8,type,
sK1: a > $o ).
thf(func_def_9,type,
sK2: a ).
thf(func_def_11,type,
ph4:
!>[X0: $tType] : X0 ).
thf(f24,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f23]) ).
thf(f23,plain,
$false = $true,
inference(backward_demodulation,[status(thm)],[f13,f22]) ).
thf(f22,plain,
( $false
= ( sK0 @ sK2 ) ),
inference(trivial_inequality_removal,[status(thm)],[f21]) ).
thf(f21,plain,
( ( $false
= ( sK0 @ sK2 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f12,f19]) ).
thf(f19,plain,
! [X1: a] :
( ( ( sK1 @ X1 )
= $true )
| ( ( sK0 @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f16]) ).
thf(f16,plain,
! [X1: a] :
( ( ( sK1 @ X1 )
= $true )
| ( $false
= ( ( sK1 @ X1 )
| ( sK0 @ X1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
! [X1: a] :
( ( sK1 @ X1 )
= ( ( sK1 @ X1 )
| ( sK0 @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f14]) ).
thf(f14,plain,
! [X1: a] :
( ( sK1 @ X1 )
= ( ^ [Y0: a] :
( ( sK1 @ Y0 )
| ( sK0 @ Y0 ) )
@ X1 ) ),
inference(argument_congruence,[status(thm)],[f11]) ).
thf(f11,plain,
( sK1
= ( ^ [Y0: a] :
( ( sK1 @ Y0 )
| ( sK0 @ Y0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ( $true
= ( sK0 @ sK2 ) )
& ( $true
!= ( sK1 @ sK2 ) )
& ( sK1
= ( ^ [Y0: a] :
( ( sK1 @ Y0 )
| ( sK0 @ Y0 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f7,f9,f8]) ).
thf(f8,plain,
( ? [X0: a > $o,X1: a > $o] :
( ? [X2: a] :
( ( ( X0 @ X2 )
= $true )
& ( ( X1 @ X2 )
!= $true ) )
& ( ( ^ [Y0: a] :
( ( X1 @ Y0 )
| ( X0 @ Y0 ) ) )
= X1 ) )
=> ( ? [X2: a] :
( ( $true
= ( sK0 @ X2 ) )
& ( ( sK1 @ X2 )
!= $true ) )
& ( sK1
= ( ^ [Y0: a] :
( ( sK1 @ Y0 )
| ( sK0 @ Y0 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
( ? [X2: a] :
( ( $true
= ( sK0 @ X2 ) )
& ( ( sK1 @ X2 )
!= $true ) )
=> ( ( $true
= ( sK0 @ sK2 ) )
& ( $true
!= ( sK1 @ sK2 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f7,plain,
? [X0: a > $o,X1: a > $o] :
( ? [X2: a] :
( ( ( X0 @ X2 )
= $true )
& ( ( X1 @ X2 )
!= $true ) )
& ( ( ^ [Y0: a] :
( ( X1 @ Y0 )
| ( X0 @ Y0 ) ) )
= X1 ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ( ( ^ [Y0: a] :
( ( X1 @ Y0 )
| ( X0 @ Y0 ) ) )
= X1 )
=> ! [X2: a] :
( ( ( X0 @ X2 )
= $true )
=> ( ( X1 @ X2 )
= $true ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ( ( ^ [Y0: a] :
( ( X1 @ Y0 )
| ( X0 @ Y0 ) ) )
= X1 )
=> ! [X3: a] :
( ( ( X0 @ X3 )
= $true )
=> ( ( X1 @ X3 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ( ( ^ [X2: a] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= X1 )
=> ! [X3: a] :
( ( X0 @ X3 )
=> ( X1 @ X3 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X1: a > $o,X0: a > $o] :
( ( ( ^ [X2: a] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= X0 )
=> ! [X3: a] :
( ( X1 @ X3 )
=> ( X0 @ X3 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X1: a > $o,X0: a > $o] :
( ( ( ^ [X2: a] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= X0 )
=> ! [X3: a] :
( ( X1 @ X3 )
=> ( X0 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.7gt4ogeqld/DTF2THF_9462.p',cGAZING_THM23_pme) ).
thf(f12,plain,
( $true
!= ( sK1 @ sK2 ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f13,plain,
( $true
= ( sK0 @ sK2 ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SEU843^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.15 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.36 % Computer : n021.cluster.edu
% 0.17/0.36 % Model : x86_64 x86_64
% 0.17/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.36 % Memory : 8042.1875MB
% 0.17/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.36 % CPULimit : 300
% 0.17/0.36 % WCLimit : 300
% 0.17/0.36 % DateTime : Tue Feb 24 12:35:24 EST 2026
% 0.17/0.36 % CPUTime :
% 0.17/0.36 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.26/0.49 ---- Original DTF file ---
% 0.26/0.49 thf(spec,logic,$$dhol).
% 0.26/0.49 %------------------------------------------------------------------------------
% 0.26/0.49 % File : SEU843^5 : TPTP v9.2.1. Released v4.0.0.
% 0.26/0.49 % Domain : Set Theory
% 0.26/0.49 % Problem : TPS problem GAZING-THM23
% 0.26/0.49 % Version : Especial.
% 0.26/0.49 % English :
% 0.26/0.49
% 0.26/0.49 % Refs : [Bar92] Barker-Plummer D (1992), Gazing: An Approach to the Pr
% 0.26/0.49 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.26/0.49 % Source : [Bro09]
% 0.26/0.49 % Names : tps_0203 [Bro09]
% 0.26/0.49 % : 23 [Bar92]
% 0.26/0.49 % : GAZING-THM23 [TPS]
% 0.26/0.49
% 0.26/0.49 % Status : Theorem
% 0.26/0.49 % Rating : 0.00 v8.2.0, 0.15 v8.1.0, 0.09 v7.5.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.26/0.49 % Syntax : Number of formulae : 2 ( 1 unt; 1 typ; 0 def)
% 0.26/0.49 % Number of atoms : 1 ( 1 equ; 0 cnn)
% 0.26/0.49 % Maximal formula atoms : 1 ( 1 avg)
% 0.26/0.49 % Number of connectives : 7 ( 0 ~; 1 |; 0 &; 4 @)
% 0.26/0.49 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.26/0.49 % Maximal formula depth : 7 ( 7 avg)
% 0.26/0.49 % Number of types : 2 ( 1 usr)
% 0.26/0.49 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.26/0.49 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.26/0.49 % Number of variables : 4 ( 1 ^; 3 !; 0 ?; 4 :)
% 0.26/0.49 % SPC : TH0_THM_EQU_NAR
% 0.26/0.49
% 0.26/0.49 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.26/0.49 % project in the Department of Mathematical Sciences at Carnegie
% 0.26/0.49 % Mellon University. Distributed under the Creative Commons copyleft
% 0.26/0.49 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.26/0.49 % : Polymorphic definitions expanded.
% 0.26/0.49 %------------------------------------------------------------------------------
% 0.26/0.49 thf(a_type,type,
% 0.26/0.49 a: $tType ).
% 0.26/0.49
% 0.26/0.49 thf(cGAZING_THM23_pme,conjecture,
% 0.26/0.49 ! [S: a > $o,T: a > $o] :
% 0.26/0.49 ( ( ( ^ [Xz: a] :
% 0.26/0.49 ( ( S @ Xz )
% 0.26/0.49 | ( T @ Xz ) ) )
% 0.26/0.49 = S )
% 0.26/0.49 => ! [Xx: a] :
% 0.26/0.49 ( ( T @ Xx )
% 0.26/0.49 => ( S @ Xx ) ) ) ).
% 0.26/0.49
% 0.26/0.49 %------------------------------------------------------------------------------
% 0.26/0.49 ------------------------
% 1.29/1.16 ---- Embedded in THF ---
% 1.29/1.16 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.29/1.16 %%% Generated on Tue Feb 24 12:35:24 EST 2026
% 1.29/1.16 %%% using '$$dhol' embedding, version 1.3.0.
% 1.29/1.16 %%% Logic specification used:
% 1.29/1.16 %%% thf(spec, logic, $$dhol).
% 1.29/1.16
% 1.29/1.16 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.7gt4ogeqld/DTF2DTF9462.p
% See solution above
% 1.29/1.16 ------------------------
% 1.29/1.17 ---- Cleaned THF ---
% 1.29/1.17 thf(a_type,type,
% 1.29/1.17 a: $tType ).
% 1.29/1.17
% 1.29/1.17 thf(cGAZING_THM23_pme,conjecture,
% 1.29/1.17 ! [S: a > $o,T: a > $o] :
% 1.29/1.17 ( ( ( ^ [Xz: a] :
% 1.29/1.17 ( ( S @ Xz )
% 1.29/1.17 | ( T @ Xz ) ) )
% 1.29/1.17 = S )
% 1.29/1.17 => ! [Xx: a] :
% 1.29/1.17 ( ( T @ Xx )
% 1.29/1.17 => ( S @ Xx ) ) ) ).
% 1.29/1.17 ------------------------
% 1.29/1.18 % (9561)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_9462 for (3000ds/27Mi)
% 1.29/1.19 % (9565)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_9462 for (3000ds/18Mi)
% 1.29/1.19 % (9562)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_9462 for (3000ds/2Mi)
% 1.29/1.19 % (9560)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_9462 for (3000ds/4Mi)
% 1.29/1.19 % (9559)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_9462 for (3000ds/183Mi)
% 1.29/1.19 % (9565)First to succeed.
% 1.29/1.19 % (9561)Also succeeded, but the first one will report.
% 1.29/1.19 % (9562)Also succeeded, but the first one will report.
% 1.29/1.19 % (9565)Refutation found. Thanks to Tanya!
% 1.29/1.19 % SZS status Theorem for DTF2THF_9462
% 1.29/1.19 % SZS output start Proof for DTF2THF_9462
% 1.29/1.19 thf(type_def_5, type, a: $tType).
% 1.29/1.19 thf(func_def_0, type, a: $tType).
% 1.29/1.19 thf(func_def_7, type, sK0: a > $o).
% 1.29/1.19 thf(func_def_8, type, sK1: a > $o).
% 1.29/1.19 thf(func_def_9, type, sK2: a).
% 1.29/1.19 thf(func_def_11, type, ph4: !>[X0: $tType]:(X0)).
% 1.29/1.19 thf(f24,plain,(
% 1.29/1.19 $false),
% 1.29/1.19 inference(trivial_inequality_removal,[status(thm)],[f23])).
% 1.29/1.19 thf(f23,plain,(
% 1.29/1.19 ($false = $true)),
% 1.29/1.19 inference(backward_demodulation,[status(thm)],[f13,f22])).
% 1.29/1.19 thf(f22,plain,(
% 1.29/1.19 ($false = (sK0 @ sK2))),
% 1.29/1.19 inference(trivial_inequality_removal,[status(thm)],[f21])).
% 1.29/1.19 thf(f21,plain,(
% 1.29/1.19 ($false = (sK0 @ sK2)) | ($true != $true)),
% 1.29/1.19 inference(superposition,[status(thm)],[f12,f19])).
% 1.29/1.19 thf(f19,plain,(
% 1.29/1.19 ( ! [X1 : a] : (((sK1 @ X1) = $true) | ((sK0 @ X1) = $false)) )),
% 1.29/1.19 inference(binary_proxy_clausification,[status(thm)],[f16])).
% 1.29/1.19 thf(f16,plain,(
% 1.29/1.19 ( ! [X1 : a] : (((sK1 @ X1) = $true) | ($false = ((sK1 @ X1) | (sK0 @ X1)))) )),
% 1.29/1.19 inference(binary_proxy_clausification,[status(thm)],[f15])).
% 1.29/1.20 thf(f15,plain,(
% 1.29/1.20 ( ! [X1 : a] : (((sK1 @ X1) = ((sK1 @ X1) | (sK0 @ X1)))) )),
% 1.29/1.20 inference(beta_eta_normalization,[status(thm)],[f14])).
% 1.29/1.20 thf(f14,plain,(
% 1.29/1.20 ( ! [X1 : a] : (((sK1 @ X1) = ((^[Y0 : a]: ((sK1 @ Y0) | (sK0 @ Y0))) @ X1))) )),
% 1.29/1.20 inference(argument_congruence,[status(thm)],[f11])).
% 1.29/1.20 thf(f11,plain,(
% 1.29/1.20 (sK1 = (^[Y0 : a]: ((sK1 @ Y0) | (sK0 @ Y0))))),
% 1.29/1.20 inference(cnf_transformation,[status(thm)],[f10])).
% 1.29/1.20 thf(f10,plain,(
% 1.29/1.20 (($true = (sK0 @ sK2)) & ($true != (sK1 @ sK2))) & (sK1 = (^[Y0 : a]: ((sK1 @ Y0) | (sK0 @ Y0))))),
% 1.29/1.20 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f7,f9,f8])).
% 1.29/1.20 thf(f8,plain,(
% 1.29/1.20 ? [X0 : a > $o,X1 : a > $o] : (? [X2 : a] : (((X0 @ X2) = $true) & ((X1 @ X2) != $true)) & ((^[Y0 : a]: ((X1 @ Y0) | (X0 @ Y0))) = X1)) => (? [X2 : a] : (($true = (sK0 @ X2)) & ((sK1 @ X2) != $true)) & (sK1 = (^[Y0 : a]: ((sK1 @ Y0) | (sK0 @ Y0)))))),
% 1.29/1.20 introduced(definition,[],[choice_axiom])).
% 1.29/1.20 thf(f9,plain,(
% 1.29/1.20 ? [X2 : a] : (($true = (sK0 @ X2)) & ((sK1 @ X2) != $true)) => (($true = (sK0 @ sK2)) & ($true != (sK1 @ sK2)))),
% 1.29/1.20 introduced(definition,[],[choice_axiom])).
% 1.29/1.20 thf(f7,plain,(
% 1.29/1.20 ? [X0 : a > $o,X1 : a > $o] : (? [X2 : a] : (((X0 @ X2) = $true) & ((X1 @ X2) != $true)) & ((^[Y0 : a]: ((X1 @ Y0) | (X0 @ Y0))) = X1))),
% 1.29/1.20 inference(ennf_transformation,[status(thm)],[f6])).
% 1.29/1.20 thf(f6,plain,(
% 1.29/1.20 ~! [X0 : a > $o,X1 : a > $o] : (((^[Y0 : a]: ((X1 @ Y0) | (X0 @ Y0))) = X1) => ! [X2 : a] : (((X0 @ X2) = $true) => ((X1 @ X2) = $true)))),
% 1.29/1.20 inference(rectify,[status(thm)],[f5])).
% 1.29/1.20 thf(f5,plain,(
% 1.29/1.20 ~! [X0 : a > $o,X1 : a > $o] : (((^[Y0 : a]: ((X1 @ Y0) | (X0 @ Y0))) = X1) => ! [X3 : a] : (((X0 @ X3) = $true) => ((X1 @ X3) = $true)))),
% 1.29/1.20 inference(fool_elimination,[status(thm)],[f4])).
% 1.29/1.20 thf(f4,plain,(
% 1.29/1.20 ~! [X0 : a > $o,X1 : a > $o] : (((^[X2 : a] : ((X0 @ X2) | (X1 @ X2))) = X1) => ! [X3 : a] : ((X0 @ X3) => (X1 @ X3)))),
% 1.29/1.20 inference(rectify,[status(thm)],[f2])).
% 1.29/1.20 thf(f2,negated_conjecture,(
% 1.29/1.20 ~! [X1 : a > $o,X0 : a > $o] : (((^[X2 : a] : ((X1 @ X2) | (X0 @ X2))) = X0) => ! [X3 : a] : ((X1 @ X3) => (X0 @ X3)))),
% 1.29/1.20 inference(negated_conjecture,[status(cth)],[f1])).
% 1.29/1.20 thf(f1,conjecture,(
% 1.29/1.20 ! [X1 : a > $o,X0 : a > $o] : (((^[X2 : a] : ((X1 @ X2) | (X0 @ X2))) = X0) => ! [X3 : a] : ((X1 @ X3) => (X0 @ X3)))),
% 1.29/1.20 file('/export/starexec/sandbox/tmp/tmp.7gt4ogeqld/DTF2THF_9462.p',cGAZING_THM23_pme)).
% 1.29/1.20 thf(f12,plain,(
% 1.29/1.20 ($true != (sK1 @ sK2))),
% 1.29/1.20 inference(cnf_transformation,[status(thm)],[f10])).
% 1.29/1.20 thf(f13,plain,(
% 1.29/1.20 ($true = (sK0 @ sK2))),
% 1.29/1.20 inference(cnf_transformation,[status(thm)],[f10])).
% 1.29/1.20 % SZS output end Proof for DTF2THF_9462
% 1.29/1.20 % (9565)------------------------------
% 1.29/1.20 % (9565)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.29/1.20 % (9565)Termination reason: Refutation
% 1.29/1.20
% 1.29/1.20 % (9565)Memory used [KB]: 5500
% 1.29/1.20 % (9565)Time elapsed: 0.005 s
% 1.29/1.20 % (9565)Instructions burned: 1 (million)
% 1.29/1.20 % (9565)------------------------------
% 1.29/1.20 % (9565)------------------------------
% 1.29/1.20 % (9558)Success in time 0.022 s
%------------------------------------------------------------------------------