%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU162+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 12:47:30 PM UTC 2026
% Result : Theorem 0.16s 1.40s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 45 ( 6 unt; 0 def)
% Number of atoms : 194 ( 74 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 242 ( 93 ~; 95 |; 44 &)
% ( 7 <=>; 2 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 94 ( 84 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [X0,X1,X2] :
( X2 = unordered_pair(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( X3 = X0
| X3 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
fof(f16,axiom,
! [X0,X1,X2] :
( X2 = set_difference(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X0)
& ~ in(X3,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(f40,axiom,
! [X0,X1] :
( ~ in(X0,X1)
=> disjoint(singleton(X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l28_zfmisc_1) ).
fof(f50,axiom,
! [X0,X1] :
( disjoint(X0,X1)
=> disjoint(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
fof(f82,conjecture,
! [X0,X1] :
( set_difference(X0,singleton(X1)) = X0
<=> ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_zfmisc_1) ).
fof(f83,negated_conjecture,
~ ! [X0,X1] :
( set_difference(X0,singleton(X1)) = X0
<=> ~ in(X1,X0) ),
inference(negated_conjecture,[status(cth)],[f82]) ).
fof(f84,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f89,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> set_difference(X0,X1) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_xboole_1) ).
fof(f103,plain,
! [X0,X1] :
( disjoint(singleton(X0),X1)
| in(X0,X1) ),
inference(ennf_transformation,[],[f40]) ).
fof(f125,plain,
? [X0,X1] :
( set_difference(X0,singleton(X1)) = X0
<~> ~ in(X1,X0) ),
inference(ennf_transformation,[],[f83]) ).
fof(f134,plain,
! [X0,X1] :
( disjoint(X1,X0)
| ~ disjoint(X0,X1) ),
inference(ennf_transformation,[],[f50]) ).
fof(f157,plain,
? [X0,X1] :
( ( in(X1,X0)
| set_difference(X0,singleton(X1)) != X0 )
& ( ~ in(X1,X0)
| set_difference(X0,singleton(X1)) = X0 ) ),
inference(nnf_transformation,[],[f125]) ).
fof(f158,plain,
( ( in(sK3,sK2)
| sK2 != set_difference(sK2,singleton(sK3)) )
& ( ~ in(sK3,sK2)
| sK2 = set_difference(sK2,singleton(sK3)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f157]) ).
fof(f159,plain,
! [X0,X1] :
( ( disjoint(X0,X1)
| set_difference(X0,X1) != X0 )
& ( set_difference(X0,X1) = X0
| ~ disjoint(X0,X1) ) ),
inference(nnf_transformation,[],[f89]) ).
fof(f178,plain,
! [X0,X1,X2] :
( ( X2 = set_difference(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& ~ in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X0)
| in(X3,X1) )
& ( ( in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f16]) ).
fof(f179,plain,
! [X0,X1,X2] :
( ( X2 = set_difference(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& ~ in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X0)
| in(X3,X1) )
& ( ( in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(flattening,[],[f178]) ).
fof(f180,plain,
! [X0,X1,X2] :
( ( X2 = set_difference(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& ~ in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| in(X4,X1) )
& ( ( in(X4,X0)
& ~ in(X4,X1) )
| ~ in(X4,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(rectify,[],[f179]) ).
fof(f181,plain,
! [X0,X1,X2] :
( ( X2 = set_difference(X0,X1)
| ( ( ~ in(sK9(X0,X1,X2),X0)
| in(sK9(X0,X1,X2),X1)
| ~ in(sK9(X0,X1,X2),X2) )
& ( ( in(sK9(X0,X1,X2),X0)
& ~ in(sK9(X0,X1,X2),X1) )
| in(sK9(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| in(X4,X1) )
& ( ( in(X4,X0)
& ~ in(X4,X1) )
| ~ in(X4,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X3,sK9(X0,X1,X2))],[f180]) ).
fof(f188,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,[],[f10]) ).
fof(f189,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,[],[f188]) ).
fof(f190,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,[],[f189]) ).
fof(f191,plain,
! [X0,X1,X2] :
( ( X2 = unordered_pair(X0,X1)
| ( ( ( sK18(X0,X1,X2) != X0
& sK18(X0,X1,X2) != X1 )
| ~ in(sK18(X0,X1,X2),X2) )
& ( sK18(X0,X1,X2) = X0
| sK18(X0,X1,X2) = X1
| in(sK18(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,[sK18]),skolemize(X3,sK18(X0,X1,X2))],[f190]) ).
fof(f204,plain,
! [X0,X1] :
( disjoint(singleton(X0),X1)
| in(X0,X1) ),
inference(cnf_transformation,[],[f103]) ).
fof(f253,plain,
( ~ in(sK3,sK2)
| sK2 = set_difference(sK2,singleton(sK3)) ),
inference(cnf_transformation,[],[f158]) ).
fof(f254,plain,
( in(sK3,sK2)
| sK2 != set_difference(sK2,singleton(sK3)) ),
inference(cnf_transformation,[],[f158]) ).
fof(f255,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f84]) ).
fof(f258,plain,
! [X0,X1] :
( set_difference(X0,X1) = X0
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f159]) ).
fof(f284,plain,
! [X0,X1] :
( disjoint(X1,X0)
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f134]) ).
fof(f293,plain,
! [X2,X0,X1,X4] :
( ~ in(X4,X1)
| ~ in(X4,X2)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f181]) ).
fof(f316,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| X1 != X4
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f191]) ).
fof(f350,plain,
! [X0,X1] :
( disjoint(unordered_pair(X0,X0),X1)
| in(X0,X1) ),
inference(definition_unfolding,[],[f204,f255]) ).
fof(f375,plain,
( sK2 != set_difference(sK2,unordered_pair(sK3,sK3))
| in(sK3,sK2) ),
inference(definition_unfolding,[],[f254,f255]) ).
fof(f376,plain,
( sK2 = set_difference(sK2,unordered_pair(sK3,sK3))
| ~ in(sK3,sK2) ),
inference(definition_unfolding,[],[f253,f255]) ).
fof(f415,plain,
! [X0,X1,X4] :
( ~ in(X4,set_difference(X0,X1))
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f293]) ).
fof(f426,plain,
! [X2,X0,X4] :
( in(X4,X2)
| unordered_pair(X0,X4) != X2 ),
inference(equality_resolution,[],[f316]) ).
fof(f427,plain,
! [X0,X4] : in(X4,unordered_pair(X0,X4)),
inference(equality_resolution,[],[f426]) ).
fof(f615,plain,
( sK2 != sK2
| in(sK3,sK2)
| ~ disjoint(sK2,unordered_pair(sK3,sK3)) ),
inference(superposition,[],[f375,f258]) ).
fof(f621,plain,
( ~ disjoint(sK2,unordered_pair(sK3,sK3))
| in(sK3,sK2) ),
inference(trivial_inequality_removal,[],[f615]) ).
fof(f623,plain,
( ~ disjoint(unordered_pair(sK3,sK3),sK2)
| in(sK3,sK2) ),
inference(resolution,[],[f621,f284]) ).
fof(f643,plain,
( in(sK3,sK2)
| in(sK3,sK2) ),
inference(resolution,[],[f350,f623]) ).
fof(f646,plain,
in(sK3,sK2),
inference(duplicate_literal_removal,[],[f643]) ).
fof(f753,plain,
! [X0] :
( ~ in(X0,sK2)
| ~ in(X0,unordered_pair(sK3,sK3))
| ~ in(sK3,sK2) ),
inference(superposition,[],[f415,f376]) ).
fof(f759,plain,
! [X0] :
( ~ in(X0,unordered_pair(sK3,sK3))
| ~ in(X0,sK2) ),
inference(forward_subsumption_resolution,[],[f753,f646]) ).
fof(f762,plain,
~ in(sK3,sK2),
inference(resolution,[],[f759,f427]) ).
fof(f768,plain,
$false,
inference(forward_subsumption_resolution,[],[f762,f646]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU162+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n014.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Mon Sep 28 03:49:16 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/1.40 % (1415340)Detected formulas, will run a generic FOF schedule.
% 0.16/1.40 % (1415345)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=181904672:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.16/1.40 % (1415346)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=2807446498:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.16/1.40 % (1415348)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2788713129:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.16/1.40 % (1415349)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1352961666:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.16/1.40 % (1415351)dis-21_1_sil=8000:lcm=predicate:random_seed=1755672029: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)
% 0.16/1.40 % (1415347)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=933993566:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.16/1.40 % (1415350)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=222516043:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.16/1.40 % (1415349)First to succeed.
% 0.16/1.40 % (1415349)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1415340"
% 0.16/1.40 % (1415351)Also succeeded, but the first one will report.
% 0.16/1.40 % (1415348)Instruction limit reached!
% 0.16/1.40 % (1415348)------------------------------
% 0.16/1.40 % (1415348)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/1.40 % (1415348)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/1.40 % (1415348)CaDiCaL version: 2.1.3
% 0.16/1.40 % (1415348)Termination reason: Instruction limit
% 0.16/1.40 % (1415348)Termination phase: Saturation
% 0.16/1.40 % (1415348)Time elapsed: 0.070 s
% 0.16/1.40 % (1415348)Peak memory usage: 89 MB
% 0.16/1.40 % (1415348)Instructions burned: 109 (million)
% 0.16/1.40 % (1415350)Instruction limit reached!
% 0.16/1.40 % (1415350)------------------------------
% 0.16/1.40 % (1415350)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/1.40 % (1415350)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/1.40 % (1415350)CaDiCaL version: 2.1.3
% 0.16/1.40 % (1415350)Termination reason: Instruction limit
% 0.16/1.40 % (1415350)Termination phase: Saturation
% 0.16/1.40 % (1415350)Time elapsed: 0.097 s
% 0.16/1.40 % (1415350)Peak memory usage: 90 MB
% 0.16/1.40 % (1415350)Instructions burned: 140 (million)
% 0.16/1.40 % (1415359)lrs+10_1_sil=8000:sp=occurrence:random_seed=2989037411:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 0.16/1.40 % (1415360)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2594609912:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 0.16/1.40 % (1415349)Refutation found. Thanks to Tanya!
% 0.16/1.40 % SZS status Theorem for theBenchmark
% 0.16/1.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/1.40 % (1415349)------------------------------
% 0.16/1.40 % (1415349)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/1.40 % (1415349)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/1.40 % (1415349)CaDiCaL version: 2.1.3
% 0.16/1.40 % (1415349)Termination reason: Refutation
% 0.16/1.40 % (1415349)Time elapsed: 0.013 s
% 0.16/1.40 % (1415349)Peak memory usage: 88 MB
% 0.16/1.40 % (1415349)Instructions burned: 17 (million)
% 0.16/1.40 % (1415349)------------------------------
% 0.16/1.40 % (1415349)------------------------------
% 0.16/1.40 % (1415340)Success in time 0.442 s
% 0.16/1.40 % Vampire exiting
%------------------------------------------------------------------------------