%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO218^5 : 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 09:53:41 AM UTC 2026
% Result : Theorem 1.57s 1.34s
% Output : Refutation 1.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 2
% Syntax : Number of formulae : 13 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 80 ( 52 equ; 3 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 57 ( 14 ~; 6 |; 4 &; 24 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 21 ( 21 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 3 usr; 4 con; 0-2 aty)
% Number of variables : 41 ( 19 ^; 18 !; 4 ?; 41 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_9,type,
ph3:
!>[X0: $tType] : X0 ).
thf(f14,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f13,f10]) ).
thf(f10,plain,
sK0 != sK1,
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ( sK0 != sK1 )
& ! [X2: ( $i > $o ) > $i] :
( ( sK0
= ( X2
@ ^ [Y0: $i] : ( sK0 = Y0 ) ) )
| ( ( X2
@ ^ [Y0: $i] : ( sK1 = Y0 ) )
!= sK1 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f6,f7]) ).
thf(f7,plain,
( ? [X0: $i,X1: $i] :
( ( X0 != X1 )
& ! [X2: ( $i > $o ) > $i] :
( ( ( X2
@ ^ [Y0: $i] : ( X0 = Y0 ) )
= X0 )
| ( ( X2
@ ^ [Y0: $i] : ( X1 = Y0 ) )
!= X1 ) ) )
=> ( ( sK0 != sK1 )
& ! [X2: ( $i > $o ) > $i] :
( ( sK0
= ( X2
@ ^ [Y0: $i] : ( sK0 = Y0 ) ) )
| ( ( X2
@ ^ [Y0: $i] : ( sK1 = Y0 ) )
!= sK1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f6,plain,
? [X0: $i,X1: $i] :
( ( X0 != X1 )
& ! [X2: ( $i > $o ) > $i] :
( ( ( X2
@ ^ [Y0: $i] : ( X0 = Y0 ) )
= X0 )
| ( ( X2
@ ^ [Y0: $i] : ( X1 = Y0 ) )
!= X1 ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: $i,X1: $i] :
( ! [X2: ( $i > $o ) > $i] :
( ( ( X2
@ ^ [Y0: $i] : ( X1 = Y0 ) )
= X1 )
=> ( ( X2
@ ^ [Y0: $i] : ( X0 = Y0 ) )
= X0 ) )
=> ( X0 = X1 ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: $i,X1: $i] :
( ! [X2: ( $i > $o ) > $i] :
( ( X1
= ( X2
@ ^ [X3: $i] : ( X1 = X3 ) ) )
=> ( X0
= ( X2
@ ^ [X4: $i] : ( X0 = X4 ) ) ) )
=> ( X0 = X1 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X1: $i,X0: $i] :
( ! [X2: ( $i > $o ) > $i] :
( ( X0
= ( X2
@ ^ [X3: $i] : ( X0 = X3 ) ) )
=> ( X1
= ( X2
@ ^ [X3: $i] : ( X1 = X3 ) ) ) )
=> ( X0 = X1 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X1: $i,X0: $i] :
( ! [X2: ( $i > $o ) > $i] :
( ( X0
= ( X2
@ ^ [X3: $i] : ( X0 = X3 ) ) )
=> ( X1
= ( X2
@ ^ [X3: $i] : ( X1 = X3 ) ) ) )
=> ( X0 = X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.5VuCNWtwma/DTF2THF_2240.p',cTHM7B_pme) ).
thf(f13,plain,
sK0 = sK1,
inference(beta_eta_normalization,[status(thm)],[f12]) ).
thf(f12,plain,
( sK0
= ( ^ [Y0: $i > $o] : sK1
@ ( (=) @ sK0 ) ) ),
inference(equality_resolution,[status(thm)],[f11]) ).
thf(f11,plain,
! [X2: ( $i > $o ) > $i] :
( ( sK1
!= ( X2 @ ( (=) @ sK1 ) ) )
| ( sK0
= ( X2 @ ( (=) @ sK0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f9]) ).
thf(f9,plain,
! [X2: ( $i > $o ) > $i] :
( ( ( X2
@ ^ [Y0: $i] : ( sK1 = Y0 ) )
!= sK1 )
| ( sK0
= ( X2
@ ^ [Y0: $i] : ( sK0 = Y0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SYO218^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.10 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.30 % Computer : n021.cluster.edu
% 0.12/0.30 % Model : x86_64 x86_64
% 0.12/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.30 % Memory : 8042.1875MB
% 0.12/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.30 % CPULimit : 300
% 0.12/0.30 % WCLimit : 300
% 0.12/0.30 % DateTime : Tue Feb 24 14:26:08 EST 2026
% 0.12/0.30 % CPUTime :
% 0.12/0.30 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 : SYO218^5 : TPTP v9.2.1. Released v4.0.0.
% 0.17/0.39 % Domain : Syntactic
% 0.17/0.39 % Problem : TPS problem THM7B
% 0.17/0.39 % Version : Especial.
% 0.17/0.39 % English : Half-proved version of thm7 for test purposes.
% 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_0135 [Bro09]
% 0.17/0.39 % : THM7B [TPS]
% 0.17/0.39
% 0.17/0.39 % Status : Theorem
% 0.17/0.39 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.38 v8.1.0, 0.36 v7.5.0, 0.14 v7.4.0, 0.00 v6.2.0, 0.29 v6.1.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.17/0.39 % Syntax : Number of formulae : 1 ( 0 unt; 0 typ; 0 def)
% 0.17/0.39 % Number of atoms : 5 ( 5 equ; 0 cnn)
% 0.17/0.39 % Maximal formula atoms : 3 ( 5 avg)
% 0.17/0.39 % Number of connectives : 4 ( 0 ~; 0 |; 0 &; 2 @)
% 0.17/0.39 % ( 0 <=>; 2 =>; 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 : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.17/0.39 % Number of variables : 5 ( 2 ^; 3 !; 0 ?; 5 :)
% 0.17/0.39 % SPC : TH0_THM_EQU_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 % : Polymorphic definitions expanded.
% 0.17/0.39 %------------------------------------------------------------------------------
% 0.17/0.39 thf(cTHM7B_pme,conjecture,
% 0.17/0.39 ! [Xx: $i,Xy: $i] :
% 0.17/0.39 ( ! [Xq: ( $i > $o ) > $i] :
% 0.17/0.39 ( ( Xx
% 0.17/0.39 = ( Xq
% 0.17/0.39 @ ^ [Xz: $i] : ( Xx = Xz ) ) )
% 0.17/0.39 => ( Xy
% 0.17/0.39 = ( Xq
% 0.17/0.39 @ ^ [Xz: $i] : ( Xy = Xz ) ) ) )
% 0.17/0.39 => ( Xx = Xy ) ) ).
% 0.17/0.39
% 0.17/0.39 %------------------------------------------------------------------------------
% 0.17/0.39 ------------------------
% 1.57/1.30 ---- Embedded in THF ---
% 1.57/1.30 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.57/1.30 %%% Generated on Tue Feb 24 14:26:09 EST 2026
% 1.57/1.30 %%% using '$$dhol' embedding, version 1.3.0.
% 1.57/1.30 %%% Logic specification used:
% 1.57/1.30 %%% thf(spec, logic, $$dhol).
% 1.57/1.30
% 1.57/1.30 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.5VuCNWtwma/DTF2DTF2240.p
% See solution above
% 1.57/1.30 ------------------------
% 1.57/1.31 ---- Cleaned THF ---
% 1.57/1.31 thf(cTHM7B_pme,conjecture,
% 1.57/1.31 ! [Xx: $i,Xy: $i] :
% 1.57/1.31 ( ! [Xq: ( $i > $o ) > $i] :
% 1.57/1.31 ( ( Xx
% 1.57/1.31 = ( Xq
% 1.57/1.31 @ ^ [Xz: $i] : ( Xx = Xz ) ) )
% 1.57/1.31 => ( Xy
% 1.57/1.31 = ( Xq
% 1.57/1.31 @ ^ [Xz: $i] : ( Xy = Xz ) ) ) )
% 1.57/1.31 => ( Xx = Xy ) ) ).
% 1.57/1.31 ------------------------
% 1.57/1.33 % (2340)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_2240 for (2999ds/2Mi)
% 1.57/1.33 % (2337)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_2240 for (2999ds/183Mi)
% 1.57/1.33 % (2339)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_2240 for (2999ds/27Mi)
% 1.57/1.33 % (2342)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_2240 for (2999ds/275Mi)
% 1.57/1.33 % (2338)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_2240 for (2999ds/4Mi)
% 1.57/1.33 % (2341)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_2240 for (2999ds/2Mi)
% 1.57/1.33 % (2340)Refutation not found, incomplete strategy
% 1.57/1.33 % (2340)------------------------------
% 1.57/1.33 % (2340)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.34 % (2342)Refutation not found, incomplete strategy
% 1.57/1.34 % (2342)------------------------------
% 1.57/1.34 % (2342)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.34 % (2340)Termination reason: Refutation not found, incomplete strategy
% 1.57/1.34
% 1.57/1.34
% 1.57/1.34 % (2340)Memory used [KB]: 5500
% 1.57/1.34 % (2340)Time elapsed: 0.003 s
% 1.57/1.34 % (2340)Instructions burned: 1 (million)
% 1.57/1.34 % (2338)First to succeed.
% 1.57/1.34 % (2340)------------------------------
% 1.57/1.34 % (2340)------------------------------
% 1.57/1.34 % (2342)Termination reason: Refutation not found, incomplete strategy
% 1.57/1.34
% 1.57/1.34
% 1.57/1.34 % (2342)Memory used [KB]: 5500
% 1.57/1.34 % (2342)Time elapsed: 0.003 s
% 1.57/1.34 % (2342)Instructions burned: 1 (million)
% 1.57/1.34 % (2342)------------------------------
% 1.57/1.34 % (2342)------------------------------
% 1.57/1.34 % (2341)Instruction limit reached!
% 1.57/1.34 % (2341)------------------------------
% 1.57/1.34 % (2341)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.34 % (2341)Termination reason: Unknown
% 1.57/1.34 % (2341)Termination phase: Saturation
% 1.57/1.34
% 1.57/1.34 % (2341)Memory used [KB]: 5500
% 1.57/1.34 % (2341)Time elapsed: 0.003 s
% 1.57/1.34 % (2341)Instructions burned: 2 (million)
% 1.57/1.34 % (2341)------------------------------
% 1.57/1.34 % (2341)------------------------------
% 1.57/1.34 % (2343)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_2240 for (2999ds/18Mi)
% 1.57/1.34 % (2337)Also succeeded, but the first one will report.
% 1.57/1.34 % (2339)Refutation not found, incomplete strategy
% 1.57/1.34 % (2339)------------------------------
% 1.57/1.34 % (2339)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.34 % (2339)Termination reason: Refutation not found, incomplete strategy
% 1.57/1.34
% 1.57/1.34
% 1.57/1.34 % (2339)Memory used [KB]: 5500
% 1.57/1.34 % (2339)Time elapsed: 0.004 s
% 1.57/1.34 % (2339)Instructions burned: 2 (million)
% 1.57/1.34 % (2339)------------------------------
% 1.57/1.34 % (2339)------------------------------
% 1.57/1.34 % (2338)Refutation found. Thanks to Tanya!
% 1.57/1.34 % SZS status Theorem for DTF2THF_2240
% 1.57/1.34 % SZS output start Proof for DTF2THF_2240
% 1.57/1.34 thf(func_def_9, type, ph3: !>[X0: $tType]:(X0)).
% 1.57/1.34 thf(f14,plain,(
% 1.57/1.34 $false),
% 1.57/1.34 inference(subsumption_resolution,[status(thm)],[f13,f10])).
% 1.57/1.34 thf(f10,plain,(
% 1.57/1.34 (sK0 != sK1)),
% 1.57/1.34 inference(cnf_transformation,[status(thm)],[f8])).
% 1.57/1.34 thf(f8,plain,(
% 1.57/1.34 (sK0 != sK1) & ! [X2 : ($i > $o) > $i] : ((sK0 = (X2 @ (^[Y0 : $i]: (sK0 = Y0)))) | ((X2 @ (^[Y0 : $i]: (sK1 = Y0))) != sK1))),
% 1.57/1.34 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f6,f7])).
% 1.57/1.34 thf(f7,plain,(
% 1.57/1.34 ? [X0 : $i,X1 : $i] : ((X0 != X1) & ! [X2 : ($i > $o) > $i] : (((X2 @ (^[Y0 : $i]: (X0 = Y0))) = X0) | ((X2 @ (^[Y0 : $i]: (X1 = Y0))) != X1))) => ((sK0 != sK1) & ! [X2 : ($i > $o) > $i] : ((sK0 = (X2 @ (^[Y0 : $i]: (sK0 = Y0)))) | ((X2 @ (^[Y0 : $i]: (sK1 = Y0))) != sK1)))),
% 1.57/1.34 introduced(definition,[],[choice_axiom])).
% 1.57/1.34 thf(f6,plain,(
% 1.57/1.34 ? [X0 : $i,X1 : $i] : ((X0 != X1) & ! [X2 : ($i > $o) > $i] : (((X2 @ (^[Y0 : $i]: (X0 = Y0))) = X0) | ((X2 @ (^[Y0 : $i]: (X1 = Y0))) != X1)))),
% 1.57/1.34 inference(ennf_transformation,[status(thm)],[f5])).
% 1.57/1.34 thf(f5,plain,(
% 1.57/1.34 ~! [X0 : $i,X1 : $i] : (! [X2 : ($i > $o) > $i] : (((X2 @ (^[Y0 : $i]: (X1 = Y0))) = X1) => ((X2 @ (^[Y0 : $i]: (X0 = Y0))) = X0)) => (X0 = X1))),
% 1.57/1.34 inference(fool_elimination,[status(thm)],[f4])).
% 1.57/1.34 thf(f4,plain,(
% 1.57/1.34 ~! [X0 : $i,X1 : $i] : (! [X2 : ($i > $o) > $i] : ((X1 = (X2 @ (^[X3 : $i] : ((X1 = X3))))) => (X0 = (X2 @ (^[X4 : $i] : ((X0 = X4)))))) => (X0 = X1))),
% 1.57/1.34 inference(rectify,[status(thm)],[f2])).
% 1.57/1.34 thf(f2,negated_conjecture,(
% 1.57/1.34 ~! [X1 : $i,X0 : $i] : (! [X2 : ($i > $o) > $i] : ((X0 = (X2 @ (^[X3 : $i] : ((X0 = X3))))) => (X1 = (X2 @ (^[X3 : $i] : ((X1 = X3)))))) => (X0 = X1))),
% 1.57/1.34 inference(negated_conjecture,[status(cth)],[f1])).
% 1.57/1.34 thf(f1,conjecture,(
% 1.57/1.34 ! [X1 : $i,X0 : $i] : (! [X2 : ($i > $o) > $i] : ((X0 = (X2 @ (^[X3 : $i] : ((X0 = X3))))) => (X1 = (X2 @ (^[X3 : $i] : ((X1 = X3)))))) => (X0 = X1))),
% 1.57/1.34 file('/export/starexec/sandbox/tmp/tmp.5VuCNWtwma/DTF2THF_2240.p',cTHM7B_pme)).
% 1.57/1.34 thf(f13,plain,(
% 1.57/1.34 (sK0 = sK1)),
% 1.57/1.34 inference(beta_eta_normalization,[status(thm)],[f12])).
% 1.57/1.34 thf(f12,plain,(
% 1.57/1.34 (sK0 = ((^[Y0 : $i > $o]: (sK1)) @ (= @ sK0)))),
% 1.57/1.34 inference(equality_resolution,[status(thm)],[f11])).
% 1.57/1.34 thf(f11,plain,(
% 1.57/1.34 ( ! [X2 : ($i > $o) > $i] : ((sK1 != (X2 @ (= @ sK1))) | (sK0 = (X2 @ (= @ sK0)))) )),
% 1.57/1.34 inference(beta_eta_normalization,[status(thm)],[f9])).
% 1.57/1.34 thf(f9,plain,(
% 1.57/1.34 ( ! [X2 : ($i > $o) > $i] : (((X2 @ (^[Y0 : $i]: (sK1 = Y0))) != sK1) | (sK0 = (X2 @ (^[Y0 : $i]: (sK0 = Y0))))) )),
% 1.57/1.34 inference(cnf_transformation,[status(thm)],[f8])).
% 1.57/1.34 % SZS output end Proof for DTF2THF_2240
% 1.57/1.34 % (2338)------------------------------
% 1.57/1.34 % (2338)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.34 % (2338)Termination reason: Refutation
% 1.57/1.34
% 1.57/1.34 % (2338)Memory used [KB]: 5500
% 1.57/1.34 % (2338)Time elapsed: 0.004 s
% 1.57/1.34 % (2338)Instructions burned: 1 (million)
% 1.57/1.34 % (2338)------------------------------
% 1.57/1.34 % (2338)------------------------------
% 1.57/1.34 % (2336)Success in time 0.008 s
%------------------------------------------------------------------------------