%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET162+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 12:40:21 PM UTC 2026
% Result : Theorem 3.03s 1.42s
% Output : Refutation 3.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 4
% Syntax : Number of formulae : 32 ( 10 unt; 0 def)
% Number of atoms : 101 ( 30 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 105 ( 36 ~; 53 |; 13 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 61 ( 58 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] :
( member(X2,union(X0,X1))
<=> ( member(X2,X0)
| member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_defn) ).
fof(f2,axiom,
! [X0] : ~ member(X0,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_defn) ).
fof(f8,axiom,
! [X0,X1] :
( X0 = X1
<=> ! [X2] :
( member(X2,X0)
<=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_member_defn) ).
fof(f9,conjecture,
! [X0] : union(X0,empty_set) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_union_empty_set) ).
fof(f10,negated_conjecture,
~ ! [X0] : union(X0,empty_set) = X0,
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f12,plain,
? [X0] : union(X0,empty_set) != X0,
inference(ennf_transformation,[],[f10]) ).
fof(f13,plain,
! [X0,X1,X2] :
( ( member(X2,union(X0,X1))
| ( ~ member(X2,X0)
& ~ member(X2,X1) ) )
& ( member(X2,X0)
| member(X2,X1)
| ~ member(X2,union(X0,X1)) ) ),
inference(nnf_transformation,[],[f1]) ).
fof(f14,plain,
! [X0,X1,X2] :
( ( member(X2,union(X0,X1))
| ( ~ member(X2,X0)
& ~ member(X2,X1) ) )
& ( member(X2,X0)
| member(X2,X1)
| ~ member(X2,union(X0,X1)) ) ),
inference(flattening,[],[f13]) ).
fof(f20,plain,
! [X0,X1] :
( ( X0 = X1
| ? [X2] :
( ( ~ member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X1)
| member(X2,X0) ) ) )
& ( ! [X2] :
( ( member(X2,X0)
| ~ member(X2,X1) )
& ( member(X2,X1)
| ~ member(X2,X0) ) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f21,plain,
! [X0,X1] :
( ( X0 = X1
| ? [X2] :
( ( ~ member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X1)
| member(X2,X0) ) ) )
& ( ! [X3] :
( ( member(X3,X0)
| ~ member(X3,X1) )
& ( member(X3,X1)
| ~ member(X3,X0) ) )
| X0 != X1 ) ),
inference(rectify,[],[f20]) ).
fof(f22,plain,
! [X0,X1] :
( ( X0 = X1
| ( ( ~ member(sK1(X0,X1),X1)
| ~ member(sK1(X0,X1),X0) )
& ( member(sK1(X0,X1),X1)
| member(sK1(X0,X1),X0) ) ) )
& ( ! [X3] :
( ( member(X3,X0)
| ~ member(X3,X1) )
& ( member(X3,X1)
| ~ member(X3,X0) ) )
| X0 != X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0,X1))],[f21]) ).
fof(f23,plain,
sK2 != union(sK2,empty_set),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X0,sK2)],[f12]) ).
fof(f24,plain,
! [X2,X0,X1] :
( ~ member(X2,union(X0,X1))
| member(X2,X1)
| member(X2,X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f26,plain,
! [X2,X0,X1] :
( ~ member(X2,X0)
| member(X2,union(X0,X1)) ),
inference(cnf_transformation,[],[f14]) ).
fof(f27,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f2]) ).
fof(f38,plain,
! [X0,X1] :
( member(sK1(X0,X1),X1)
| X0 = X1
| member(sK1(X0,X1),X0) ),
inference(cnf_transformation,[],[f22]) ).
fof(f39,plain,
! [X0,X1] :
( ~ member(sK1(X0,X1),X1)
| X0 = X1
| ~ member(sK1(X0,X1),X0) ),
inference(cnf_transformation,[],[f22]) ).
fof(f40,plain,
sK2 != union(sK2,empty_set),
inference(cnf_transformation,[],[f23]) ).
fof(f56,plain,
! [X2,X0,X1] :
( member(sK1(X0,union(X1,X2)),X2)
| member(sK1(X0,union(X1,X2)),X0)
| union(X1,X2) = X0
| member(sK1(X0,union(X1,X2)),X1) ),
inference(resolution,[],[f38,f24]) ).
fof(f91,plain,
! [X0,X1] :
( member(sK1(X0,union(X1,empty_set)),X1)
| union(X1,empty_set) = X0
| member(sK1(X0,union(X1,empty_set)),X0) ),
inference(resolution,[],[f56,f27]) ).
fof(f229,plain,
! [X2,X0,X1] :
( member(sK1(X1,union(X0,empty_set)),X1)
| union(X0,empty_set) = X1
| member(sK1(X1,union(X0,empty_set)),union(X0,X2)) ),
inference(resolution,[],[f91,f26]) ).
fof(f465,plain,
! [X2,X3,X0,X1] :
( member(sK1(X1,union(X0,empty_set)),union(X1,X3))
| member(sK1(X1,union(X0,empty_set)),union(X0,X2))
| union(X0,empty_set) = X1 ),
inference(resolution,[],[f229,f26]) ).
fof(f1587,plain,
! [X0,X1] :
( member(sK1(X0,union(X0,empty_set)),union(X0,X1))
| union(X0,empty_set) = X0
| union(X0,empty_set) = X0
| ~ member(sK1(X0,union(X0,empty_set)),X0) ),
inference(resolution,[],[f465,f39]) ).
fof(f1598,plain,
! [X0,X1] :
( member(sK1(X0,union(X0,empty_set)),union(X0,X1))
| union(X0,empty_set) = X0
| ~ member(sK1(X0,union(X0,empty_set)),X0) ),
inference(duplicate_literal_removal,[],[f1587]) ).
fof(f1599,plain,
! [X0,X1] :
( member(sK1(X0,union(X0,empty_set)),union(X0,X1))
| union(X0,empty_set) = X0 ),
inference(forward_subsumption_resolution,[],[f1598,f229]) ).
fof(f1794,plain,
! [X0] :
( union(X0,empty_set) = X0
| union(X0,empty_set) = X0
| ~ member(sK1(X0,union(X0,empty_set)),X0) ),
inference(resolution,[],[f1599,f39]) ).
fof(f1803,plain,
! [X0] :
( ~ member(sK1(X0,union(X0,empty_set)),X0)
| union(X0,empty_set) = X0 ),
inference(duplicate_literal_removal,[],[f1794]) ).
fof(f1830,plain,
! [X0] :
( union(X0,empty_set) = X0
| union(X0,empty_set) = X0
| member(sK1(X0,union(X0,empty_set)),X0) ),
inference(resolution,[],[f1803,f91]) ).
fof(f1863,plain,
! [X0] :
( union(X0,empty_set) = X0
| member(sK1(X0,union(X0,empty_set)),X0) ),
inference(duplicate_literal_removal,[],[f1830]) ).
fof(f1881,plain,
! [X0] : union(X0,empty_set) = X0,
inference(forward_subsumption_resolution,[],[f1863,f1803]) ).
fof(f2087,plain,
sK2 != sK2,
inference(superposition,[],[f40,f1881]) ).
fof(f2088,plain,
$false,
inference(trivial_inequality_removal,[],[f2087]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET162+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.40 % Computer : n020.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Mon Sep 28 00:58:34 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.43 Running first-order theorem proving
% 0.13/0.43 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
% 3.03/1.42 % (3934754)Detected formulas, will run a generic FOF schedule.
% 3.03/1.42 % (3934799)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=332473528:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.03/1.42 % (3934799)First to succeed.
% 3.03/1.42 % (3934799)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3934754"
% 3.03/1.42 % (3934794)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=2625681761:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.03/1.42 % (3934796)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=388917178:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.03/1.42 % (3934798)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=633115533:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.03/1.42 % (3934797)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1637457354:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.03/1.42 % (3934797)Refutation not found, incomplete strategy
% 3.03/1.42 % (3934797)------------------------------
% 3.03/1.42 % (3934797)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.03/1.42 % (3934797)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.03/1.42 % (3934797)CaDiCaL version: 2.1.3
% 3.03/1.42 % (3934797)Termination reason: Refutation not found, incomplete strategy
% 3.03/1.42 % (3934797)Time elapsed: 0.001 s
% 3.03/1.42 % (3934797)Peak memory usage: 88 MB
% 3.03/1.42 % (3934798)Also succeeded, but the first one will report.
% 3.03/1.42 % (3934800)dis-21_1_sil=8000:lcm=predicate:random_seed=3526148049: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)
% 3.03/1.42 % (3934800)Also succeeded, but the first one will report.
% 3.03/1.42 % (3934795)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=3969581634:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.03/1.42 % (3934799)Refutation found. Thanks to Tanya!
% 3.03/1.42 % SZS status Theorem for theBenchmark
% 3.03/1.42 % SZS output start Proof for theBenchmark
% See solution above
% 3.03/1.42 % (3934799)------------------------------
% 3.03/1.42 % (3934799)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.03/1.42 % (3934799)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.03/1.42 % (3934799)CaDiCaL version: 2.1.3
% 3.03/1.42 % (3934799)Termination reason: Refutation
% 3.03/1.42 % (3934799)Time elapsed: 0.041 s
% 3.03/1.42 % (3934799)Peak memory usage: 89 MB
% 3.03/1.42 % (3934799)Instructions burned: 117 (million)
% 3.03/1.42 % (3934799)------------------------------
% 3.03/1.42 % (3934799)------------------------------
% 3.03/1.42 % (3934754)Success in time 0.345 s
% 3.03/1.42 % Vampire exiting
%------------------------------------------------------------------------------