%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET960+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 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 12:45:05 PM UTC 2026
% Result : Theorem 0.10s 0.43s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 72 ( 14 unt; 5 def)
% Number of atoms : 162 ( 46 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 172 ( 82 ~; 77 |; 2 &)
% ( 10 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 6 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-3 aty)
% Number of variables : 71 ( 0 sgn 67 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( X0 = empty_set
<=> ! [X1] : ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f4,axiom,
! [X0,X1,X2] :
( X2 = cartesian_product2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4,X5] :
( in(X4,X0)
& in(X5,X1)
& X3 = ordered_pair(X4,X5) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_zfmisc_1) ).
fof(f5,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(f10,conjecture,
! [X0,X1] :
( cartesian_product2(X0,X1) = empty_set
<=> ( X0 = empty_set
| X1 = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t113_zfmisc_1) ).
fof(f11,negated_conjecture,
~ ! [X0,X1] :
( cartesian_product2(X0,X1) = empty_set
<=> ( X0 = empty_set
| X1 = empty_set ) ),
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f13,plain,
? [X0,X1] :
( cartesian_product2(X0,X1) = empty_set
<~> ( X0 = empty_set
| X1 = empty_set ) ),
inference(ennf_transformation,[],[f11]) ).
fof(f16,plain,
! [X0] :
( in(sK0(X0),X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f3]) ).
fof(f17,plain,
! [X0,X1] :
( ~ in(X1,X0)
| empty_set != X0 ),
inference(cnf_transformation,[],[f3]) ).
fof(f23,plain,
! [X2,X3,X0,X1] :
( in(sK3(X0,X1,X3),X1)
| ~ in(X3,X2)
| cartesian_product2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f4]) ).
fof(f24,plain,
! [X2,X3,X0,X1] :
( in(sK2(X0,X1,X3),X0)
| ~ in(X3,X2)
| cartesian_product2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f4]) ).
fof(f25,plain,
! [X2,X3,X0,X1,X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X5,X1)
| ~ in(X4,X0)
| in(X3,X2)
| cartesian_product2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f4]) ).
fof(f26,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f5]) ).
fof(f31,plain,
( empty_set != sK9
| empty_set != cartesian_product2(sK8,sK9) ),
inference(cnf_transformation,[],[f13]) ).
fof(f32,plain,
( empty_set != sK8
| empty_set != cartesian_product2(sK8,sK9) ),
inference(cnf_transformation,[],[f13]) ).
fof(f33,plain,
( empty_set = sK9
| empty_set = sK8
| empty_set = cartesian_product2(sK8,sK9) ),
inference(cnf_transformation,[],[f13]) ).
fof(f34,plain,
! [X2,X3,X0,X1,X4,X5] :
( unordered_pair(unordered_pair(X4,X5),singleton(X4)) != X3
| ~ in(X5,X1)
| ~ in(X4,X0)
| in(X3,X2)
| cartesian_product2(X0,X1) != X2 ),
inference(definition_unfolding,[],[f25,f26]) ).
fof(f39,plain,
! [X1] : ~ in(X1,empty_set),
inference(equality_resolution,[],[f17]) ).
fof(f40,plain,
! [X2,X0,X1,X4,X5] :
( ~ in(X5,X1)
| ~ in(X4,X0)
| in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),X2)
| cartesian_product2(X0,X1) != X2 ),
inference(equality_resolution,[],[f34]) ).
fof(f41,plain,
! [X0,X1,X4,X5] :
( in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),cartesian_product2(X0,X1))
| ~ in(X4,X0)
| ~ in(X5,X1) ),
inference(equality_resolution,[],[f40]) ).
fof(f42,plain,
! [X3,X0,X1] :
( in(sK2(X0,X1,X3),X0)
| ~ in(X3,cartesian_product2(X0,X1)) ),
inference(equality_resolution,[],[f24]) ).
fof(f43,plain,
! [X3,X0,X1] :
( in(sK3(X0,X1,X3),X1)
| ~ in(X3,cartesian_product2(X0,X1)) ),
inference(equality_resolution,[],[f23]) ).
fof(f46,definition,
( spl10_1
<=> empty_set = cartesian_product2(sK8,sK9) ),
introduced(definition,[new_symbols(definition,[spl10_1])],[avatar_definition]) ).
fof(f47,plain,
( empty_set = cartesian_product2(sK8,sK9)
| ~ spl10_1 ),
inference(avatar_component_clause,[],[f46]) ).
fof(f48,plain,
( empty_set != cartesian_product2(sK8,sK9)
| spl10_1 ),
inference(avatar_component_clause,[],[f46]) ).
fof(f50,definition,
( spl10_2
<=> empty_set = sK9 ),
introduced(definition,[new_symbols(definition,[spl10_2])],[avatar_definition]) ).
fof(f51,plain,
( empty_set = sK9
| ~ spl10_2 ),
inference(avatar_component_clause,[],[f50]) ).
fof(f52,plain,
( empty_set != sK9
| spl10_2 ),
inference(avatar_component_clause,[],[f50]) ).
fof(f53,plain,
( ~ spl10_1
| ~ spl10_2 ),
inference(avatar_split_clause,[],[f31,f50,f46]) ).
fof(f55,definition,
( spl10_3
<=> empty_set = sK8 ),
introduced(definition,[new_symbols(definition,[spl10_3])],[avatar_definition]) ).
fof(f56,plain,
( empty_set = sK8
| ~ spl10_3 ),
inference(avatar_component_clause,[],[f55]) ).
fof(f57,plain,
( empty_set != sK8
| spl10_3 ),
inference(avatar_component_clause,[],[f55]) ).
fof(f58,plain,
( ~ spl10_1
| ~ spl10_3 ),
inference(avatar_split_clause,[],[f32,f55,f46]) ).
fof(f59,plain,
( spl10_1
| spl10_3
| spl10_2 ),
inference(avatar_split_clause,[],[f33,f50,f55,f46]) ).
fof(f60,plain,
( empty_set != cartesian_product2(sK8,empty_set)
| spl10_1
| ~ spl10_2 ),
inference(superposition,[],[f48,f51]) ).
fof(f70,plain,
! [X0,X1] : ~ in(X0,cartesian_product2(empty_set,X1)),
inference(resolution,[],[f42,f39]) ).
fof(f73,plain,
! [X0] : empty_set = cartesian_product2(empty_set,X0),
inference(resolution,[],[f70,f16]) ).
fof(f75,plain,
! [X0,X1] : ~ in(X0,cartesian_product2(X1,empty_set)),
inference(resolution,[],[f43,f39]) ).
fof(f80,plain,
! [X0] : empty_set = cartesian_product2(X0,empty_set),
inference(resolution,[],[f75,f16]) ).
fof(f118,plain,
( empty_set != empty_set
| spl10_1
| ~ spl10_2 ),
inference(superposition,[],[f60,f80]) ).
fof(f122,plain,
( $false
| spl10_1
| ~ spl10_2 ),
inference(trivial_inequality_removal,[],[f118]) ).
fof(f123,plain,
( spl10_1
| ~ spl10_2 ),
inference(avatar_contradiction_clause,[],[f122]) ).
fof(f124,plain,
( empty_set != cartesian_product2(empty_set,sK9)
| spl10_1
| ~ spl10_3 ),
inference(superposition,[],[f48,f56]) ).
fof(f125,plain,
( $false
| spl10_1
| ~ spl10_3 ),
inference(forward_subsumption_resolution,[],[f124,f73]) ).
fof(f126,plain,
( spl10_1
| ~ spl10_3 ),
inference(avatar_contradiction_clause,[],[f125]) ).
fof(f127,plain,
( ! [X0,X1] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),empty_set)
| ~ in(X0,sK8)
| ~ in(X1,sK9) )
| ~ spl10_1 ),
inference(superposition,[],[f41,f47]) ).
fof(f128,plain,
( ! [X0,X1] :
( ~ in(X0,sK8)
| ~ in(X1,sK9) )
| ~ spl10_1 ),
inference(forward_subsumption_resolution,[],[f127,f39]) ).
fof(f130,definition,
( spl10_4
<=> ! [X1] : ~ in(X1,sK9) ),
introduced(definition,[new_symbols(definition,[spl10_4])],[avatar_definition]) ).
fof(f131,plain,
( ! [X1] : ~ in(X1,sK9)
| ~ spl10_4 ),
inference(avatar_component_clause,[],[f130]) ).
fof(f133,definition,
( spl10_5
<=> ! [X0] : ~ in(X0,sK8) ),
introduced(definition,[new_symbols(definition,[spl10_5])],[avatar_definition]) ).
fof(f134,plain,
( ! [X0] : ~ in(X0,sK8)
| ~ spl10_5 ),
inference(avatar_component_clause,[],[f133]) ).
fof(f135,plain,
( spl10_4
| spl10_5
| ~ spl10_1 ),
inference(avatar_split_clause,[],[f128,f46,f133,f130]) ).
fof(f156,plain,
( empty_set = sK8
| ~ spl10_5 ),
inference(resolution,[],[f134,f16]) ).
fof(f161,plain,
( $false
| spl10_3
| ~ spl10_5 ),
inference(forward_subsumption_resolution,[],[f156,f57]) ).
fof(f162,plain,
( spl10_3
| ~ spl10_5 ),
inference(avatar_contradiction_clause,[],[f161]) ).
fof(f183,plain,
( empty_set = sK9
| ~ spl10_4 ),
inference(resolution,[],[f131,f16]) ).
fof(f188,plain,
( $false
| spl10_2
| ~ spl10_4 ),
inference(forward_subsumption_resolution,[],[f183,f52]) ).
fof(f189,plain,
( spl10_2
| ~ spl10_4 ),
inference(avatar_contradiction_clause,[],[f188]) ).
cnf(s1,plain,
( ~ spl10_1
| ~ spl10_2 ),
inference(sat_conversion,[],[f53]) ).
cnf(s2,plain,
( ~ spl10_1
| ~ spl10_3 ),
inference(sat_conversion,[],[f58]) ).
cnf(s3,plain,
( spl10_1
| spl10_2
| spl10_3 ),
inference(sat_conversion,[],[f59]) ).
cnf(s4,plain,
( spl10_1
| ~ spl10_2 ),
inference(sat_conversion,[],[f123]) ).
cnf(s5,plain,
( spl10_1
| ~ spl10_3 ),
inference(sat_conversion,[],[f126]) ).
cnf(s6,plain,
( ~ spl10_1
| spl10_4
| spl10_5 ),
inference(sat_conversion,[],[f135]) ).
cnf(s7,plain,
( spl10_3
| ~ spl10_5 ),
inference(sat_conversion,[],[f162]) ).
cnf(s8,plain,
( spl10_2
| ~ spl10_4 ),
inference(sat_conversion,[],[f189]) ).
cnf(s9,plain,
spl10_1,
inference(rat,[],[s3,s4,s5]) ).
cnf(s10,plain,
~ spl10_3,
inference(rat,[],[s2,s9]) ).
cnf(s11,plain,
~ spl10_2,
inference(rat,[],[s1,s9]) ).
cnf(s12,plain,
~ spl10_5,
inference(rat,[],[s7,s10]) ).
cnf(s13,plain,
~ spl10_4,
inference(rat,[],[s8,s11]) ).
cnf(s14,plain,
$false,
inference(rat,[],[s6,s9,s13,s12]) ).
fof(f190,plain,
$false,
inference(avatar_sat_refutation,[],[s14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET960+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.36 % Computer : n014.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 28 03:16:01 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.39 Running first-order model finding
% 0.10/0.40 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
% 0.10/0.43 % (1403838)Will run a generic schedule for satisfiability detection.
% 0.10/0.43 % (1403847)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=637900191:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.10/0.43 % (1403847) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1403838-1403847"...
% 0.10/0.43 % (1403844)% WARNING: option uhcvi not known.
% 0.10/0.43 % (1403847)...printing done.
% 0.10/0.43 % (1403847)Refutation found. Thanks to Tanya!
% 0.10/0.43 % SZS status Theorem for theBenchmark
% 0.10/0.43 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.43 % (1403847)------------------------------
% 0.10/0.43 % (1403847)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.43 % (1403847)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.43 % (1403847)CaDiCaL version: 2.1.3
% 0.10/0.43 % (1403847)Termination reason: Refutation
% 0.10/0.43 % (1403847)Time elapsed: 0.004 s
% 0.10/0.43 % (1403847)Peak memory usage: 12 MB
% 0.10/0.43 % (1403847)Instructions burned: 7 (million)
% 0.10/0.43 % (1403838)Success in time 0.028 s
% 0.10/0.43 % Vampire exiting
%------------------------------------------------------------------------------