%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU142+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 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 12:52:04 PM UTC 2026
% Result : Theorem 0.11s 0.43s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 3
% Syntax : Number of formulae : 32 ( 9 unt; 0 def)
% Number of atoms : 145 ( 104 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 176 ( 63 ~; 80 |; 29 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-3 aty)
% Number of variables : 75 ( 69 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(f4,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(f8,conjecture,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f9,negated_conjecture,
~ ! [X0] : unordered_pair(X0,X0) = singleton(X0),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f12,plain,
? [X0] : singleton(X0) != unordered_pair(X0,X0),
inference(ennf_transformation,[],[f9]) ).
fof(f13,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X2 = X0
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| X0 != X2 )
& ( X2 = X0
| ~ in(X2,X1) ) )
| singleton(X0) != X1 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f14,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X2 = X0
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(rectify,[],[f13]) ).
fof(f15,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ( ( sK0(X0,X1) != X0
| ~ in(sK0(X0,X1),X1) )
& ( sK0(X0,X1) = X0
| in(sK0(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f14]) ).
fof(f16,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,[],[f4]) ).
fof(f17,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,[],[f16]) ).
fof(f18,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,[],[f17]) ).
fof(f19,plain,
! [X0,X1,X2] :
( ( X2 = unordered_pair(X0,X1)
| ( ( ( sK1(X0,X1,X2) != X0
& sK1(X0,X1,X2) != X1 )
| ~ in(sK1(X0,X1,X2),X2) )
& ( sK1(X0,X1,X2) = X0
| sK1(X0,X1,X2) = X1
| in(sK1(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,[sK1]),skolemize(X3,sK1(X0,X1,X2))],[f18]) ).
fof(f22,plain,
singleton(sK3) != unordered_pair(sK3,sK3),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X0,sK3)],[f12]) ).
fof(f27,plain,
! [X0,X1] :
( in(sK0(X0,X1),X1)
| sK0(X0,X1) = X0
| singleton(X0) = X1 ),
inference(cnf_transformation,[],[f15]) ).
fof(f28,plain,
! [X0,X1] :
( sK0(X0,X1) != X0
| singleton(X0) = X1
| ~ in(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f29,plain,
! [X2,X0,X1,X4] :
( X0 = X4
| X1 = X4
| ~ in(X4,X2)
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f19]) ).
fof(f31,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| X0 != X4
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f19]) ).
fof(f37,plain,
singleton(sK3) != unordered_pair(sK3,sK3),
inference(cnf_transformation,[],[f22]) ).
fof(f41,plain,
! [X2,X1,X4] :
( in(X4,X2)
| unordered_pair(X4,X1) != X2 ),
inference(equality_resolution,[],[f31]) ).
fof(f42,plain,
! [X1,X4] : in(X4,unordered_pair(X4,X1)),
inference(equality_resolution,[],[f41]) ).
fof(f45,plain,
! [X0,X1,X4] :
( ~ in(X4,unordered_pair(X0,X1))
| X1 = X4
| X0 = X4 ),
inference(equality_resolution,[],[f29]) ).
fof(f73,plain,
! [X2,X0,X1] :
( sK0(X0,unordered_pair(X1,X2)) = X2
| sK0(X0,unordered_pair(X1,X2)) = X1
| sK0(X0,unordered_pair(X1,X2)) = X0
| singleton(X0) = unordered_pair(X1,X2) ),
inference(resolution,[],[f27,f45]) ).
fof(f137,plain,
! [X2,X0,X1] :
( X1 != X2
| sK0(X0,unordered_pair(X1,X2)) = X1
| sK0(X0,unordered_pair(X1,X2)) = X0
| singleton(X0) = unordered_pair(X1,X2) ),
inference(equality_factoring,[],[f73]) ).
fof(f262,plain,
! [X0,X1] :
( sK0(X0,unordered_pair(X1,X1)) = X1
| sK0(X0,unordered_pair(X1,X1)) = X0
| singleton(X0) = unordered_pair(X1,X1) ),
inference(equality_resolution,[],[f137]) ).
fof(f289,plain,
! [X0,X1] :
( X0 != X1
| sK0(X0,unordered_pair(X1,X1)) = X0
| singleton(X0) = unordered_pair(X1,X1) ),
inference(equality_factoring,[],[f262]) ).
fof(f298,plain,
! [X0] :
( sK0(X0,unordered_pair(X0,X0)) = X0
| singleton(X0) = unordered_pair(X0,X0) ),
inference(equality_resolution,[],[f289]) ).
fof(f300,plain,
! [X0] :
( X0 != X0
| singleton(X0) = unordered_pair(X0,X0)
| ~ in(X0,unordered_pair(X0,X0))
| singleton(X0) = unordered_pair(X0,X0) ),
inference(superposition,[],[f28,f298]) ).
fof(f301,plain,
! [X0] :
( X0 != X0
| singleton(X0) = unordered_pair(X0,X0)
| ~ in(X0,unordered_pair(X0,X0)) ),
inference(duplicate_literal_removal,[],[f300]) ).
fof(f302,plain,
! [X0] :
( singleton(X0) = unordered_pair(X0,X0)
| ~ in(X0,unordered_pair(X0,X0)) ),
inference(trivial_inequality_removal,[],[f301]) ).
fof(f303,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(forward_subsumption_resolution,[],[f302,f42]) ).
fof(f304,plain,
singleton(sK3) != singleton(sK3),
inference(superposition,[],[f37,f303]) ).
fof(f331,plain,
$false,
inference(trivial_inequality_removal,[],[f304]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU142+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.36 % Computer : n004.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 28 03:42:36 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.39 Running first-order model finding
% 0.11/0.39 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.43 % (4125966)Will run a generic schedule for satisfiability detection.
% 0.11/0.43 % (4125974)dis+10_1_sil=32000:sp=arity:random_seed=1834855189:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.11/0.43 % (4125972)% WARNING: option uhcvi not known.
% 0.11/0.43 % (4125974) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4125966-4125974"...
% 0.11/0.43 % (4125974)...printing done.
% 0.11/0.43 % (4125971)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3092980539_2999 on theBenchmark for (2999ds/0Mi)
% 0.11/0.43 % (4125974)Refutation found. Thanks to Tanya!
% 0.11/0.43 % SZS status Theorem for theBenchmark
% 0.11/0.43 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.43 % (4125974)------------------------------
% 0.11/0.43 % (4125974)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.43 % (4125974)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.43 % (4125974)CaDiCaL version: 2.1.3
% 0.11/0.43 % (4125974)Termination reason: Refutation
% 0.11/0.43 % (4125974)Time elapsed: 0.006 s
% 0.11/0.43 % (4125974)Peak memory usage: 11 MB
% 0.11/0.43 % (4125974)Instructions burned: 19 (million)
% 0.11/0.43 % (4125966)Success in time 0.03 s
% 0.11/0.43 % Vampire exiting
%------------------------------------------------------------------------------