%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU124+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 12:47:18 PM UTC 2026
% Result : Theorem 3.47s 1.25s
% Output : Refutation 3.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 23 ( 9 unt; 0 def)
% Number of atoms : 102 ( 10 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 127 ( 48 ~; 48 |; 26 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% 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 : 5 ( 5 usr; 2 con; 0-3 aty)
% Number of variables : 57 ( 50 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0,X1,X2] :
( X2 = set_union2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X0)
| in(X3,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f7,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f30,conjecture,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_xboole_1) ).
fof(f31,negated_conjecture,
~ ! [X0,X1] : subset(X0,set_union2(X0,X1)),
inference(negated_conjecture,[status(cth)],[f30]) ).
fof(f39,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f50,plain,
? [X0,X1] : ~ subset(X0,set_union2(X0,X1)),
inference(ennf_transformation,[],[f31]) ).
fof(f57,plain,
! [X0,X1,X2] :
( ( X2 = set_union2(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_union2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f58,plain,
! [X0,X1,X2] :
( ( X2 = set_union2(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_union2(X0,X1) != X2 ) ),
inference(flattening,[],[f57]) ).
fof(f59,plain,
! [X0,X1,X2] :
( ( X2 = set_union2(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_union2(X0,X1) != X2 ) ),
inference(rectify,[],[f58]) ).
fof(f60,plain,
! [X0,X1,X2] :
( ( X2 = set_union2(X0,X1)
| ( ( ( ~ in(sK1(X0,X1,X2),X0)
& ~ in(sK1(X0,X1,X2),X1) )
| ~ in(sK1(X0,X1,X2),X2) )
& ( in(sK1(X0,X1,X2),X0)
| in(sK1(X0,X1,X2),X1)
| in(sK1(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( ~ in(X4,X0)
& ~ in(X4,X1) ) )
& ( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1,X2))],[f59]) ).
fof(f61,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f39]) ).
fof(f62,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f61]) ).
fof(f63,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK2(X0,X1),X1)
& in(sK2(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f62]) ).
fof(f73,plain,
~ subset(sK8,set_union2(sK8,sK9)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9]),skolemize(X0,sK8),skolemize(X1,sK9)],[f50]) ).
fof(f84,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f60]) ).
fof(f89,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sK2(X0,X1),X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f90,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sK2(X0,X1),X1) ),
inference(cnf_transformation,[],[f63]) ).
fof(f119,plain,
~ subset(sK8,set_union2(sK8,sK9)),
inference(cnf_transformation,[],[f73]) ).
fof(f124,plain,
! [X0,X1,X4] :
( in(X4,set_union2(X0,X1))
| ~ in(X4,X0) ),
inference(equality_resolution,[],[f84]) ).
fof(f157,plain,
in(sK2(sK8,set_union2(sK8,sK9)),sK8),
inference(resolution,[],[f89,f119]) ).
fof(f158,plain,
~ in(sK2(sK8,set_union2(sK8,sK9)),set_union2(sK8,sK9)),
inference(resolution,[],[f90,f119]) ).
fof(f168,plain,
~ in(sK2(sK8,set_union2(sK8,sK9)),sK8),
inference(resolution,[],[f158,f124]) ).
fof(f182,plain,
$false,
inference(resolution,[],[f168,f157]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU124+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n003.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 28 03:40:20 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 3.47/1.25 % (1160337)Detected formulas, will run a generic FOF schedule.
% 3.47/1.25 % (1160347)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2573782931:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.47/1.25 % (1160343)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=418031424:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.47/1.25 % (1160345)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1144288844:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.47/1.25 % (1160346)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1803339121:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.47/1.25 % (1160348)dis-21_1_sil=8000:lcm=predicate:random_seed=292143920: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)
% 3.47/1.25 % (1160342)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=2104976652:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.47/1.25 % (1160344)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=2346610067:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.47/1.25 % (1160348)First to succeed.
% 3.47/1.25 % (1160348)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1160337"
% 3.47/1.25 % (1160347)Instruction limit reached!
% 3.47/1.25 % (1160347)------------------------------
% 3.47/1.25 % (1160347)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.47/1.25 % (1160347)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.47/1.25 % (1160347)CaDiCaL version: 2.1.3
% 3.47/1.25 % (1160347)Termination reason: Instruction limit
% 3.47/1.25 % (1160347)Termination phase: Saturation
% 3.47/1.25 % (1160347)Time elapsed: 0.029 s
% 3.47/1.25 % (1160347)Peak memory usage: 88 MB
% 3.47/1.25 % (1160347)Instructions burned: 140 (million)
% 3.47/1.25 % (1160346)Instruction limit reached!
% 3.47/1.25 % (1160346)------------------------------
% 3.47/1.25 % (1160346)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.47/1.25 % (1160346)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.47/1.25 % (1160346)CaDiCaL version: 2.1.3
% 3.47/1.25 % (1160346)Termination reason: Instruction limit
% 3.47/1.25 % (1160346)Termination phase: Saturation
% 3.47/1.25 % (1160346)Time elapsed: 0.056 s
% 3.47/1.25 % (1160346)Peak memory usage: 88 MB
% 3.47/1.25 % (1160346)Instructions burned: 120 (million)
% 3.47/1.25 % (1160345)Instruction limit reached!
% 3.47/1.25 % (1160345)------------------------------
% 3.47/1.25 % (1160345)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.47/1.25 % (1160345)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.47/1.25 % (1160345)CaDiCaL version: 2.1.3
% 3.47/1.25 % (1160345)Termination reason: Instruction limit
% 3.47/1.25 % (1160345)Termination phase: Saturation
% 3.47/1.25 % (1160345)Time elapsed: 0.065 s
% 3.47/1.25 % (1160345)Peak memory usage: 89 MB
% 3.47/1.25 % (1160345)Instructions burned: 110 (million)
% 3.47/1.25 % (1160356)lrs+10_1_sil=8000:sp=occurrence:random_seed=3625348052:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.47/1.25 % (1160356)Also succeeded, but the first one will report.
% 3.47/1.25 % (1160357)lrs+10_1_sil=32000:urr=on:br=off:random_seed=253072589:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.47/1.25 % (1160357)Also succeeded, but the first one will report.
% 3.47/1.25 % (1160358)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1953307249:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 3.47/1.25 % (1160358)Also succeeded, but the first one will report.
% 3.47/1.25 % (1160348)Refutation found. Thanks to Tanya!
% 3.47/1.25 % SZS status Theorem for theBenchmark
% 3.47/1.25 % SZS output start Proof for theBenchmark
% See solution above
% 3.47/1.25 % (1160348)------------------------------
% 3.47/1.25 % (1160348)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.47/1.25 % (1160348)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.47/1.25 % (1160348)CaDiCaL version: 2.1.3
% 3.47/1.25 % (1160348)Termination reason: Refutation
% 3.47/1.25 % (1160348)Time elapsed: 0.003 s
% 3.47/1.25 % (1160348)Peak memory usage: 88 MB
% 3.47/1.25 % (1160348)Instructions burned: 3 (million)
% 3.47/1.25 % (1160348)------------------------------
% 3.47/1.25 % (1160348)------------------------------
% 3.47/1.25 % (1160337)Success in time 0.437 s
% 3.47/1.25 % Vampire exiting
%------------------------------------------------------------------------------