%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU126+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n013.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 12:52:00 PM UTC 2026
% Result : Theorem 0.17s 0.49s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 32 ( 7 unt; 0 def)
% Number of atoms : 131 ( 28 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 151 ( 52 ~; 64 |; 28 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 2 ( 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 : 72 ( 65 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f4,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(f5,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f15,conjecture,
! [X0,X1] :
( subset(X0,X1)
=> set_union2(X0,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_xboole_1) ).
fof(f16,negated_conjecture,
~ ! [X0,X1] :
( subset(X0,X1)
=> set_union2(X0,X1) = X1 ),
inference(negated_conjecture,[status(cth)],[f15]) ).
fof(f24,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f27,plain,
? [X0,X1] :
( set_union2(X0,X1) != X1
& subset(X0,X1) ),
inference(ennf_transformation,[],[f16]) ).
fof(f33,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,[],[f4]) ).
fof(f34,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,[],[f33]) ).
fof(f35,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,[],[f34]) ).
fof(f36,plain,
! [X0,X1,X2] :
( ( X2 = set_union2(X0,X1)
| ( ( ( ~ in(sK0(X0,X1,X2),X0)
& ~ in(sK0(X0,X1,X2),X1) )
| ~ in(sK0(X0,X1,X2),X2) )
& ( in(sK0(X0,X1,X2),X0)
| in(sK0(X0,X1,X2),X1)
| in(sK0(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,[sK0]),skolemize(X3,sK0(X0,X1,X2))],[f35]) ).
fof(f37,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,[],[f24]) ).
fof(f38,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,[],[f37]) ).
fof(f39,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK1(X0,X1),X1)
& in(sK1(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0,X1))],[f38]) ).
fof(f42,plain,
( sK5 != set_union2(sK4,sK5)
& subset(sK4,sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5]),skolemize(X0,sK4),skolemize(X1,sK5)],[f27]) ).
fof(f44,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f51,plain,
! [X2,X0,X1] :
( in(sK0(X0,X1,X2),X0)
| in(sK0(X0,X1,X2),X1)
| in(sK0(X0,X1,X2),X2)
| set_union2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f36]) ).
fof(f52,plain,
! [X2,X0,X1] :
( ~ in(sK0(X0,X1,X2),X1)
| set_union2(X0,X1) = X2
| ~ in(sK0(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f36]) ).
fof(f53,plain,
! [X2,X0,X1] :
( ~ in(sK0(X0,X1,X2),X0)
| set_union2(X0,X1) = X2
| ~ in(sK0(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f36]) ).
fof(f54,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f39]) ).
fof(f64,plain,
subset(sK4,sK5),
inference(cnf_transformation,[],[f42]) ).
fof(f65,plain,
sK5 != set_union2(sK4,sK5),
inference(cnf_transformation,[],[f42]) ).
fof(f111,plain,
! [X0] :
( ~ in(X0,sK4)
| in(X0,sK5) ),
inference(resolution,[],[f54,f64]) ).
fof(f156,plain,
! [X0,X1] :
( in(sK0(X0,X1,X0),X0)
| in(sK0(X0,X1,X0),X1)
| set_union2(X0,X1) = X0 ),
inference(factoring,[],[f51]) ).
fof(f207,plain,
! [X0,X1] :
( in(sK0(X0,X1,X0),X1)
| set_union2(X0,X1) = X0
| set_union2(X0,X1) = X0
| ~ in(sK0(X0,X1,X0),X0) ),
inference(resolution,[],[f156,f53]) ).
fof(f222,plain,
! [X0] :
( in(sK0(X0,sK4,X0),X0)
| in(sK0(X0,sK4,X0),sK5)
| set_union2(X0,sK4) = X0 ),
inference(resolution,[],[f156,f111]) ).
fof(f225,plain,
! [X0,X1] :
( in(sK0(X0,X1,X0),X1)
| set_union2(X0,X1) = X0
| ~ in(sK0(X0,X1,X0),X0) ),
inference(duplicate_literal_removal,[],[f207]) ).
fof(f227,plain,
! [X0,X1] :
( set_union2(X0,X1) = X0
| ~ in(sK0(X0,X1,X0),X0) ),
inference(forward_subsumption_resolution,[],[f225,f52]) ).
fof(f618,plain,
( in(sK0(sK5,sK4,sK5),sK5)
| sK5 = set_union2(sK5,sK4) ),
inference(factoring,[],[f222]) ).
fof(f620,plain,
sK5 = set_union2(sK5,sK4),
inference(forward_subsumption_resolution,[],[f618,f227]) ).
fof(f628,plain,
sK5 = set_union2(sK4,sK5),
inference(forward_demodulation,[],[f620,f44]) ).
fof(f631,plain,
$false,
inference(forward_subsumption_resolution,[],[f628,f65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU126+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.39 % Computer : n013.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Mon Sep 28 03:38:07 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.43 Running first-order model finding
% 0.12/0.43 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.49 % (779417)Will run a generic schedule for satisfiability detection.
% 0.17/0.49 % (779422)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=634915644_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.49 % TRYING [1]
% 0.17/0.49 % TRYING [2]
% 0.17/0.49 % TRYING [3]
% 0.17/0.49 % TRYING [4]
% 0.17/0.49 % (779423)% WARNING: option uhcvi not known.
% 0.17/0.49 % TRYING [5]
% 0.17/0.49 % (779426)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2216374454:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.49 % (779423)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1426057567:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.49 % (779424)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1648287445:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.49 % (779425)dis+10_1_sil=32000:sp=arity:random_seed=280370506:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.49 % (779427)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3458597117:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.49 % (779428)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2781034345:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.49 % TRYING [6]
% 0.17/0.49 % (779427) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-779417-779427"...
% 0.17/0.49 % (779427)...printing done.
% 0.17/0.49 % (779427)Refutation found. Thanks to Tanya!
% 0.17/0.49 % SZS status Theorem for theBenchmark
% 0.17/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.49 % (779427)------------------------------
% 0.17/0.49 % (779427)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.49 % (779427)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.49 % (779427)CaDiCaL version: 2.1.3
% 0.17/0.49 % (779427)Termination reason: Refutation
% 0.17/0.49 % (779427)Time elapsed: 0.018 s
% 0.17/0.49 % (779427)Peak memory usage: 12 MB
% 0.17/0.49 % (779427)Instructions burned: 28 (million)
% 0.17/0.49 % (779417)Success in time 0.057 s
% 0.17/0.50 % Vampire exiting
%------------------------------------------------------------------------------