%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU151+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:47:26 PM UTC 2026
% Result : Theorem 3.34s 1.35s
% Output : Refutation 3.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 2
% Syntax : Number of formulae : 34 ( 12 unt; 0 def)
% Number of atoms : 119 ( 86 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 140 ( 55 ~; 55 |; 28 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-3 aty)
% Number of variables : 65 ( 58 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1,X2] :
( X2 = unordered_pair(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( X3 = X0
| X3 = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
fof(f6,conjecture,
! [X0,X1,X2,X3] :
~ ( unordered_pair(X0,X1) = unordered_pair(X2,X3)
& X0 != X2
& X0 != X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_zfmisc_1) ).
fof(f7,negated_conjecture,
~ ! [X0,X1,X2,X3] :
~ ( unordered_pair(X0,X1) = unordered_pair(X2,X3)
& X0 != X2
& X0 != X3 ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f9,plain,
? [X0,X1,X2,X3] :
( unordered_pair(X0,X1) = unordered_pair(X2,X3)
& X0 != X2
& X0 != X3 ),
inference(ennf_transformation,[],[f7]) ).
fof(f10,plain,
! [X0,X1,X2] :
( ( X2 = unordered_pair(X0,X1)
| ? [X3] :
( ( ( X0 != X3
& X1 != X3 )
| ~ in(X3,X2) )
& ( X3 = X0
| X3 = X1
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( X0 != X3
& X1 != X3 ) )
& ( X3 = X0
| X3 = X1
| ~ in(X3,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f11,plain,
! [X0,X1,X2] :
( ( X2 = unordered_pair(X0,X1)
| ? [X3] :
( ( ( X0 != X3
& X1 != X3 )
| ~ in(X3,X2) )
& ( X3 = X0
| X3 = X1
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( X0 != X3
& X1 != X3 ) )
& ( X3 = X0
| X3 = X1
| ~ in(X3,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(flattening,[],[f10]) ).
fof(f12,plain,
! [X0,X1,X2] :
( ( X2 = unordered_pair(X0,X1)
| ? [X3] :
( ( ( X0 != X3
& X1 != X3 )
| ~ in(X3,X2) )
& ( X3 = X0
| X3 = X1
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( X0 != X4
& X1 != X4 ) )
& ( X0 = X4
| X1 = X4
| ~ in(X4,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(rectify,[],[f11]) ).
fof(f13,plain,
! [X0,X1,X2] :
( ( X2 = unordered_pair(X0,X1)
| ( ( ( sK0(X0,X1,X2) != X0
& sK0(X0,X1,X2) != X1 )
| ~ in(sK0(X0,X1,X2),X2) )
& ( sK0(X0,X1,X2) = X0
| sK0(X0,X1,X2) = X1
| in(sK0(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( X0 != X4
& X1 != X4 ) )
& ( X0 = X4
| X1 = X4
| ~ in(X4,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1,X2))],[f12]) ).
fof(f16,plain,
( unordered_pair(sK3,sK4) = unordered_pair(sK5,sK6)
& sK3 != sK5
& sK3 != sK6 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5),skolemize(X3,sK6)],[f9]) ).
fof(f19,plain,
! [X2,X0,X1,X4] :
( X0 = X4
| X1 = X4
| ~ in(X4,X2)
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f13]) ).
fof(f20,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| X1 != X4
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f13]) ).
fof(f21,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| X0 != X4
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f13]) ).
fof(f27,plain,
sK3 != sK6,
inference(cnf_transformation,[],[f16]) ).
fof(f28,plain,
sK3 != sK5,
inference(cnf_transformation,[],[f16]) ).
fof(f29,plain,
unordered_pair(sK3,sK4) = unordered_pair(sK5,sK6),
inference(cnf_transformation,[],[f16]) ).
fof(f30,plain,
! [X2,X1,X4] :
( in(X4,X2)
| unordered_pair(X4,X1) != X2 ),
inference(equality_resolution,[],[f21]) ).
fof(f31,plain,
! [X1,X4] : in(X4,unordered_pair(X4,X1)),
inference(equality_resolution,[],[f30]) ).
fof(f32,plain,
! [X2,X0,X4] :
( in(X4,X2)
| unordered_pair(X0,X4) != X2 ),
inference(equality_resolution,[],[f20]) ).
fof(f33,plain,
! [X0,X4] : in(X4,unordered_pair(X0,X4)),
inference(equality_resolution,[],[f32]) ).
fof(f34,plain,
! [X0,X1,X4] :
( ~ in(X4,unordered_pair(X0,X1))
| X1 = X4
| X0 = X4 ),
inference(equality_resolution,[],[f19]) ).
fof(f35,plain,
in(sK5,unordered_pair(sK3,sK4)),
inference(superposition,[],[f31,f29]) ).
fof(f36,plain,
in(sK6,unordered_pair(sK3,sK4)),
inference(superposition,[],[f33,f29]) ).
fof(f43,plain,
( sK4 = sK5
| sK3 = sK5 ),
inference(resolution,[],[f34,f35]) ).
fof(f44,plain,
( sK4 = sK6
| sK3 = sK6 ),
inference(resolution,[],[f34,f36]) ).
fof(f45,plain,
! [X0] :
( ~ in(X0,unordered_pair(sK3,sK4))
| sK6 = X0
| sK5 = X0 ),
inference(superposition,[],[f34,f29]) ).
fof(f48,plain,
sK4 = sK6,
inference(forward_subsumption_resolution,[],[f44,f27]) ).
fof(f49,plain,
sK4 = sK5,
inference(forward_subsumption_resolution,[],[f43,f28]) ).
fof(f52,plain,
sK5 = sK6,
inference(superposition,[],[f49,f48]) ).
fof(f67,plain,
! [X0] :
( ~ in(X0,unordered_pair(sK3,sK6))
| sK6 = X0
| sK5 = X0 ),
inference(forward_demodulation,[],[f45,f48]) ).
fof(f68,plain,
! [X0] :
( ~ in(X0,unordered_pair(sK3,sK5))
| sK6 = X0
| sK5 = X0 ),
inference(forward_demodulation,[],[f67,f52]) ).
fof(f69,plain,
! [X0] :
( sK5 = X0
| ~ in(X0,unordered_pair(sK3,sK5))
| sK5 = X0 ),
inference(forward_demodulation,[],[f68,f52]) ).
fof(f70,plain,
! [X0] :
( ~ in(X0,unordered_pair(sK3,sK5))
| sK5 = X0 ),
inference(duplicate_literal_removal,[],[f69]) ).
fof(f72,plain,
sK3 = sK5,
inference(resolution,[],[f70,f31]) ).
fof(f74,plain,
$false,
inference(forward_subsumption_resolution,[],[f72,f28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU151+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n004.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Mon Sep 28 03:45:52 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.34/1.35 % (4126776)Detected formulas, will run a generic FOF schedule.
% 3.34/1.35 % (4126781)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=4199294824:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.34/1.35 % (4126786)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3180110147:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.34/1.35 % (4126787)dis-21_1_sil=8000:lcm=predicate:random_seed=4110144816:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 3.34/1.35 % (4126784)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=898168970:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.34/1.35 % (4126785)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2164287940:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.34/1.35 % (4126782)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3643211501:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.34/1.35 % (4126783)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=1555740386:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.34/1.35 % (4126784)Refutation not found, incomplete strategy
% 3.34/1.35 % (4126784)------------------------------
% 3.34/1.35 % (4126784)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.34/1.35 % (4126784)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.34/1.35 % (4126784)CaDiCaL version: 2.1.3
% 3.34/1.35 % (4126784)Termination reason: Refutation not found, incomplete strategy
% 3.34/1.35 % (4126784)Time elapsed: 0.001 s
% 3.34/1.35 % (4126784)Peak memory usage: 88 MB
% 3.34/1.35 % (4126785)Refutation not found, incomplete strategy
% 3.34/1.35 % (4126785)------------------------------
% 3.34/1.35 % (4126785)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.34/1.35 % (4126785)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.34/1.35 % (4126785)CaDiCaL version: 2.1.3
% 3.34/1.35 % (4126785)Termination reason: Refutation not found, incomplete strategy
% 3.34/1.35 % (4126785)Time elapsed: 0.001 s
% 3.34/1.35 % (4126785)Peak memory usage: 88 MB
% 3.34/1.35 % (4126786)First to succeed.
% 3.34/1.35 % (4126786)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4126776"
% 3.34/1.35 % (4126787)Instruction limit reached!
% 3.34/1.35 % (4126787)------------------------------
% 3.34/1.35 % (4126787)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.34/1.35 % (4126787)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.34/1.35 % (4126787)CaDiCaL version: 2.1.3
% 3.34/1.35 % (4126787)Termination reason: Instruction limit
% 3.34/1.35 % (4126787)Termination phase: Saturation
% 3.34/1.35 % (4126787)Time elapsed: 0.073 s
% 3.34/1.35 % (4126787)Peak memory usage: 89 MB
% 3.34/1.35 % (4126787)Instructions burned: 129 (million)
% 3.34/1.35 % (4126795)lrs+10_1_sil=8000:sp=occurrence:random_seed=3121524526:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.34/1.35 % (4126795)Also succeeded, but the first one will report.
% 3.34/1.35 % (4126784)------------------------------
% 3.34/1.35 % (4126784)------------------------------
% 3.34/1.35 % (4126785)------------------------------
% 3.34/1.35 % (4126785)------------------------------
% 3.34/1.35 % (4126786)Refutation found. Thanks to Tanya!
% 3.34/1.35 % SZS status Theorem for theBenchmark
% 3.34/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 3.34/1.35 % (4126786)------------------------------
% 3.34/1.35 % (4126786)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.34/1.35 % (4126786)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.34/1.35 % (4126786)CaDiCaL version: 2.1.3
% 3.34/1.35 % (4126786)Termination reason: Refutation
% 3.34/1.35 % (4126786)Time elapsed: 0.004 s
% 3.34/1.35 % (4126786)Peak memory usage: 89 MB
% 3.34/1.35 % (4126786)Instructions burned: 3 (million)
% 3.34/1.35 % (4126786)------------------------------
% 3.34/1.35 % (4126786)------------------------------
% 3.34/1.35 % (4126776)Success in time 0.402 s
% 3.34/1.35 % Vampire exiting
%------------------------------------------------------------------------------