%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU925^5 : 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 : n012.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 09:37:45 AM UTC 2026
% Result : Theorem 0.83s 0.88s
% Output : Refutation 0.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 2
% Syntax : Number of formulae : 15 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 79 ( 49 equ; 2 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 25 ( 11 ~; 4 |; 4 &; 2 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 3 usr; 5 con; 0-2 aty)
% Number of variables : 30 ( 16 ^; 10 !; 4 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_9,type,
ph3:
!>[X0: $tType] : X0 ).
thf(f20,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f19]) ).
thf(f19,plain,
( ( sK0 != sK0 )
| ( sK1 != sK1 ) ),
inference(superposition,[status(thm)],[f9,f15]) ).
thf(f15,plain,
! [X1: $i] :
( ( sK0 = X1 )
| ( sK1 != X1 ) ),
inference(equality_proxy_clausification,[status(thm)],[f14]) ).
thf(f14,plain,
! [X1: $i] :
( ( sK1 != X1 )
| ( ( sK0 = X1 )
= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
! [X1: $i] :
( ( ( sK1 = X1 )
= $false )
| ( ( sK0 = X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
! [X1: $i] :
( ( sK1 = X1 )
= ( sK0 = X1 ) ),
inference(argument_congruence,[status(thm)],[f10]) ).
thf(f10,plain,
( ( (=) @ sK1 )
= ( (=) @ sK0 ) ),
inference(beta_eta_normalization,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ^ [Y0: $i] : ( sK1 = Y0 ) )
= ( ^ [Y0: $i] : ( sK0 = Y0 ) ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( ( sK1 != sK0 )
& ( ( ^ [Y0: $i] : ( sK1 = Y0 ) )
= ( ^ [Y0: $i] : ( sK0 = Y0 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f5,f6]) ).
thf(f6,plain,
( ? [X0: $i,X1: $i] :
( ( X0 != X1 )
& ( ( ^ [Y0: $i] : ( X1 = Y0 ) )
= ( ^ [Y0: $i] : ( X0 = Y0 ) ) ) )
=> ( ( sK1 != sK0 )
& ( ( ^ [Y0: $i] : ( sK1 = Y0 ) )
= ( ^ [Y0: $i] : ( sK0 = Y0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f5,plain,
? [X0: $i,X1: $i] :
( ( X0 != X1 )
& ( ( ^ [Y0: $i] : ( X1 = Y0 ) )
= ( ^ [Y0: $i] : ( X0 = Y0 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: $i,X1: $i] :
( ( ( ^ [Y0: $i] : ( X1 = Y0 ) )
= ( ^ [Y0: $i] : ( X0 = Y0 ) ) )
=> ( X0 = X1 ) ),
inference(fool_elimination,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: $i,X1: $i] :
( ( ( ^ [X2: $i] : ( X0 = X2 ) )
= ( ^ [X3: $i] : ( X1 = X3 ) ) )
=> ( X0 = X1 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: $i,X1: $i] :
( ( ( ^ [X2: $i] : ( X0 = X2 ) )
= ( ^ [X3: $i] : ( X1 = X3 ) ) )
=> ( X0 = X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.6nEWJ94B30/DTF2THF_3492.p',cTHM7_TPS2_pme) ).
thf(f9,plain,
sK1 != sK0,
inference(cnf_transformation,[status(thm)],[f7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SEU925^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.07 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.25 % Computer : n012.cluster.edu
% 0.07/0.25 % Model : x86_64 x86_64
% 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.25 % Memory : 8042.1875MB
% 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.25 % CPULimit : 300
% 0.07/0.25 % WCLimit : 300
% 0.07/0.25 % DateTime : Tue Feb 24 12:37:15 EST 2026
% 0.07/0.25 % CPUTime :
% 0.07/0.25 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.32 ---- Original DTF file ---
% 0.07/0.32 thf(spec,logic,$$dhol).
% 0.07/0.32 %------------------------------------------------------------------------------
% 0.07/0.32 % File : SEU925^5 : TPTP v9.2.1. Released v4.0.0.
% 0.07/0.32 % Domain : Set Theory (Functions)
% 0.07/0.32 % Problem : TPS problem THM7-TPS2
% 0.07/0.32 % Version : Especial.
% 0.07/0.32 % English : Unitset is injective.
% 0.07/0.32
% 0.07/0.32 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.07/0.32 % Source : [Bro09]
% 0.07/0.32 % Names : tps_0194 [Bro09]
% 0.07/0.32 % : tps_0757 [Bro09]
% 0.07/0.32 % : THM7 [TPS]
% 0.07/0.32 % : THM7-TPS2 [TPS]
% 0.07/0.32 % : tps_0341 [Bro09]
% 0.07/0.32 % : THM104 [TPS]
% 0.07/0.32
% 0.07/0.32 % Status : Theorem
% 0.07/0.32 % Rating : 0.00 v9.0.0, 0.10 v8.2.0, 0.08 v8.1.0, 0.00 v6.2.0, 0.14 v6.1.0, 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 v4.0.0
% 0.07/0.32 % Syntax : Number of formulae : 1 ( 0 unt; 0 typ; 0 def)
% 0.07/0.32 % Number of atoms : 4 ( 4 equ; 0 cnn)
% 0.07/0.32 % Maximal formula atoms : 2 ( 4 avg)
% 0.07/0.32 % Number of connectives : 1 ( 0 ~; 0 |; 0 &; 0 @)
% 0.07/0.32 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.07/0.32 % Maximal formula depth : 4 ( 4 avg)
% 0.07/0.32 % Number of types : 1 ( 0 usr)
% 0.07/0.32 % Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% 0.07/0.32 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.07/0.32 % Number of variables : 4 ( 2 ^; 2 !; 0 ?; 4 :)
% 0.07/0.32 % SPC : TH0_THM_EQU_NAR
% 0.07/0.32
% 0.07/0.32 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.07/0.32 % project in the Department of Mathematical Sciences at Carnegie
% 0.07/0.32 % Mellon University. Distributed under the Creative Commons copyleft
% 0.07/0.32 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.07/0.32 % : Polymorphic definitions expanded.
% 0.07/0.32 %------------------------------------------------------------------------------
% 0.07/0.32 thf(cTHM7_TPS2_pme,conjecture,
% 0.07/0.32 ! [Xx: $i,Xy: $i] :
% 0.07/0.32 ( ( ( ^ [Xy0: $i] : ( Xx = Xy0 ) )
% 0.07/0.32 = ( ^ [Xy_2: $i] : ( Xy = Xy_2 ) ) )
% 0.07/0.32 => ( Xx = Xy ) ) ).
% 0.07/0.32
% 0.07/0.32 %------------------------------------------------------------------------------
% 0.07/0.32 ------------------------
% 0.83/0.86 ---- Embedded in THF ---
% 0.83/0.86 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.83/0.86 %%% Generated on Tue Feb 24 12:37:16 EST 2026
% 0.83/0.86 %%% using '$$dhol' embedding, version 1.3.0.
% 0.83/0.86 %%% Logic specification used:
% 0.83/0.86 %%% thf(spec, logic, $$dhol).
% 0.83/0.86
% 0.83/0.86 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.6nEWJ94B30/DTF2DTF3492.p
% See solution above
% 0.83/0.86 ------------------------
% 0.83/0.87 ---- Cleaned THF ---
% 0.83/0.87 thf(cTHM7_TPS2_pme,conjecture,
% 0.83/0.87 ! [Xx: $i,Xy: $i] :
% 0.83/0.87 ( ( ( ^ [Xy0: $i] : ( Xx = Xy0 ) )
% 0.83/0.87 = ( ^ [Xy_2: $i] : ( Xy = Xy_2 ) ) )
% 0.83/0.87 => ( Xx = Xy ) ) ).
% 0.83/0.87 ------------------------
% 0.83/0.88 % (3761)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_3492 for (3000ds/27Mi)
% 0.83/0.88 % (3759)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_3492 for (3000ds/183Mi)
% 0.83/0.88 % (3760)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_3492 for (3000ds/4Mi)
% 0.83/0.88 % (3762)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_3492 for (3000ds/2Mi)
% 0.83/0.88 % (3763)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_3492 for (3000ds/2Mi)
% 0.83/0.88 % (3764)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_3492 for (3000ds/275Mi)
% 0.83/0.88 % (3765)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_3492 for (3000ds/18Mi)
% 0.83/0.88 % (3764)First to succeed.
% 0.83/0.88 % (3763)Instruction limit reached!
% 0.83/0.88 % (3763)------------------------------
% 0.83/0.88 % (3763)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.83/0.88 % (3763)Termination reason: Unknown
% 0.83/0.88 % (3763)Termination phase: Saturation
% 0.83/0.88
% 0.83/0.88 % (3763)Memory used [KB]: 5500
% 0.83/0.88 % (3763)Time elapsed: 0.002 s
% 0.83/0.88 % (3763)Instructions burned: 2 (million)
% 0.83/0.88 % (3763)------------------------------
% 0.83/0.88 % (3763)------------------------------
% 0.83/0.88 % (3759)Also succeeded, but the first one will report.
% 0.83/0.88 % (3762)Also succeeded, but the first one will report.
% 0.83/0.88 % (3764)Refutation found. Thanks to Tanya!
% 0.83/0.88 % SZS status Theorem for DTF2THF_3492
% 0.83/0.88 % SZS output start Proof for DTF2THF_3492
% 0.83/0.88 thf(func_def_9, type, ph3: !>[X0: $tType]:(X0)).
% 0.83/0.88 thf(f20,plain,(
% 0.83/0.88 $false),
% 0.83/0.88 inference(trivial_inequality_removal,[status(thm)],[f19])).
% 0.83/0.88 thf(f19,plain,(
% 0.83/0.88 (sK0 != sK0) | (sK1 != sK1)),
% 0.83/0.88 inference(superposition,[status(thm)],[f9,f15])).
% 0.83/0.88 thf(f15,plain,(
% 0.83/0.88 ( ! [X1 : $i] : ((sK0 = X1) | (sK1 != X1)) )),
% 0.83/0.88 inference(equality_proxy_clausification,[status(thm)],[f14])).
% 0.83/0.88 thf(f14,plain,(
% 0.83/0.88 ( ! [X1 : $i] : ((sK1 != X1) | ((sK0 = X1) = $true)) )),
% 0.83/0.88 inference(equality_proxy_clausification,[status(thm)],[f13])).
% 0.83/0.88 thf(f13,plain,(
% 0.83/0.88 ( ! [X1 : $i] : (((sK1 = X1) = $false) | ((sK0 = X1) = $true)) )),
% 0.83/0.88 inference(binary_proxy_clausification,[status(thm)],[f11])).
% 0.83/0.88 thf(f11,plain,(
% 0.83/0.88 ( ! [X1 : $i] : (((sK1 = X1) = (sK0 = X1))) )),
% 0.83/0.88 inference(argument_congruence,[status(thm)],[f10])).
% 0.83/0.88 thf(f10,plain,(
% 0.83/0.88 ((= @ sK1) = (= @ sK0))),
% 0.83/0.88 inference(beta_eta_normalization,[status(thm)],[f8])).
% 0.83/0.88 thf(f8,plain,(
% 0.83/0.88 ((^[Y0 : $i]: (sK1 = Y0)) = (^[Y0 : $i]: (sK0 = Y0)))),
% 0.83/0.88 inference(cnf_transformation,[status(thm)],[f7])).
% 0.83/0.88 thf(f7,plain,(
% 0.83/0.88 (sK1 != sK0) & ((^[Y0 : $i]: (sK1 = Y0)) = (^[Y0 : $i]: (sK0 = Y0)))),
% 0.83/0.88 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f5,f6])).
% 0.83/0.88 thf(f6,plain,(
% 0.83/0.88 ? [X0 : $i,X1 : $i] : ((X0 != X1) & ((^[Y0 : $i]: (X1 = Y0)) = (^[Y0 : $i]: (X0 = Y0)))) => ((sK1 != sK0) & ((^[Y0 : $i]: (sK1 = Y0)) = (^[Y0 : $i]: (sK0 = Y0))))),
% 0.83/0.88 introduced(definition,[],[choice_axiom])).
% 0.83/0.88 thf(f5,plain,(
% 0.83/0.88 ? [X0 : $i,X1 : $i] : ((X0 != X1) & ((^[Y0 : $i]: (X1 = Y0)) = (^[Y0 : $i]: (X0 = Y0))))),
% 0.83/0.88 inference(ennf_transformation,[status(thm)],[f4])).
% 0.83/0.88 thf(f4,plain,(
% 0.83/0.88 ~! [X0 : $i,X1 : $i] : (((^[Y0 : $i]: (X1 = Y0)) = (^[Y0 : $i]: (X0 = Y0))) => (X0 = X1))),
% 0.83/0.88 inference(fool_elimination,[status(thm)],[f2])).
% 0.83/0.88 thf(f2,negated_conjecture,(
% 0.83/0.88 ~! [X0 : $i,X1 : $i] : (((^[X2 : $i] : ((X0 = X2))) = (^[X3 : $i] : ((X1 = X3)))) => (X0 = X1))),
% 0.83/0.88 inference(negated_conjecture,[status(cth)],[f1])).
% 0.83/0.88 thf(f1,conjecture,(
% 0.83/0.88 ! [X0 : $i,X1 : $i] : (((^[X2 : $i] : ((X0 = X2))) = (^[X3 : $i] : ((X1 = X3)))) => (X0 = X1))),
% 0.83/0.88 file('/export/starexec/sandbox/tmp/tmp.6nEWJ94B30/DTF2THF_3492.p',cTHM7_TPS2_pme)).
% 0.83/0.88 thf(f9,plain,(
% 0.83/0.88 (sK1 != sK0)),
% 0.83/0.88 inference(cnf_transformation,[status(thm)],[f7])).
% 0.83/0.88 % SZS output end Proof for DTF2THF_3492
% 0.83/0.88 % (3764)------------------------------
% 0.83/0.88 % (3764)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.83/0.88 % (3764)Termination reason: Refutation
% 0.83/0.88
% 0.83/0.88 % (3764)Memory used [KB]: 5500
% 0.83/0.88 % (3764)Time elapsed: 0.002 s
% 0.83/0.88 % (3764)Instructions burned: 1 (million)
% 0.83/0.88 % (3764)------------------------------
% 0.83/0.88 % (3764)------------------------------
% 0.83/0.88 % (3758)Success in time 0.01 s
%------------------------------------------------------------------------------