%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET931+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n026.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 12:45:02 PM UTC 2026
% Result : Theorem 0.13s 0.45s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 93 ( 16 unt; 5 def)
% Number of atoms : 271 ( 130 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 300 ( 122 ~; 137 |; 30 &)
% ( 10 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 6 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 65 ( 1 sgn 56 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1,X2] :
( subset(X0,unordered_pair(X1,X2))
<=> ~ ( X0 != empty_set
& X0 != singleton(X1)
& X0 != singleton(X2)
& X0 != unordered_pair(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l46_zfmisc_1) ).
fof(f6,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f7,axiom,
! [X0,X1] :
( set_difference(X0,X1) = empty_set
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_xboole_1) ).
fof(f8,conjecture,
! [X0,X1,X2] :
( set_difference(X0,unordered_pair(X1,X2)) = empty_set
<=> ~ ( X0 != empty_set
& X0 != singleton(X1)
& X0 != singleton(X2)
& X0 != unordered_pair(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t75_zfmisc_1) ).
fof(f9,negated_conjecture,
~ ! [X0,X1,X2] :
( set_difference(X0,unordered_pair(X1,X2)) = empty_set
<=> ~ ( X0 != empty_set
& X0 != singleton(X1)
& X0 != singleton(X2)
& X0 != unordered_pair(X1,X2) ) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f10,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f6]) ).
fof(f11,plain,
! [X0,X1,X2] :
( subset(X0,unordered_pair(X1,X2))
<=> ( empty_set = X0
| singleton(X1) = X0
| singleton(X2) = X0
| unordered_pair(X1,X2) = X0 ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f12,plain,
? [X0,X1,X2] :
( set_difference(X0,unordered_pair(X1,X2)) = empty_set
<~> ( empty_set = X0
| singleton(X1) = X0
| singleton(X2) = X0
| unordered_pair(X1,X2) = X0 ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f13,plain,
! [X0,X1,X2] :
( ( subset(X0,unordered_pair(X1,X2))
| ( empty_set != X0
& singleton(X1) != X0
& singleton(X2) != X0
& unordered_pair(X1,X2) != X0 ) )
& ( empty_set = X0
| singleton(X1) = X0
| singleton(X2) = X0
| unordered_pair(X1,X2) = X0
| ~ subset(X0,unordered_pair(X1,X2)) ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f14,plain,
! [X0,X1,X2] :
( ( subset(X0,unordered_pair(X1,X2))
| ( empty_set != X0
& singleton(X1) != X0
& singleton(X2) != X0
& unordered_pair(X1,X2) != X0 ) )
& ( empty_set = X0
| singleton(X1) = X0
| singleton(X2) = X0
| unordered_pair(X1,X2) = X0
| ~ subset(X0,unordered_pair(X1,X2)) ) ),
inference(flattening,[],[f13]) ).
fof(f17,plain,
! [X0,X1] :
( ( set_difference(X0,X1) = empty_set
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| empty_set != set_difference(X0,X1) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f18,plain,
? [X0,X1,X2] :
( ( ( empty_set != X0
& singleton(X1) != X0
& singleton(X2) != X0
& unordered_pair(X1,X2) != X0 )
| empty_set != set_difference(X0,unordered_pair(X1,X2)) )
& ( empty_set = X0
| singleton(X1) = X0
| singleton(X2) = X0
| unordered_pair(X1,X2) = X0
| set_difference(X0,unordered_pair(X1,X2)) = empty_set ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f19,plain,
? [X0,X1,X2] :
( ( ( empty_set != X0
& singleton(X1) != X0
& singleton(X2) != X0
& unordered_pair(X1,X2) != X0 )
| empty_set != set_difference(X0,unordered_pair(X1,X2)) )
& ( empty_set = X0
| singleton(X1) = X0
| singleton(X2) = X0
| unordered_pair(X1,X2) = X0
| set_difference(X0,unordered_pair(X1,X2)) = empty_set ) ),
inference(flattening,[],[f18]) ).
fof(f20,plain,
( ( ( empty_set != sK2
& sK2 != singleton(sK3)
& sK2 != singleton(sK4)
& sK2 != unordered_pair(sK3,sK4) )
| empty_set != set_difference(sK2,unordered_pair(sK3,sK4)) )
& ( empty_set = sK2
| sK2 = singleton(sK3)
| sK2 = singleton(sK4)
| sK2 = unordered_pair(sK3,sK4)
| empty_set = set_difference(sK2,unordered_pair(sK3,sK4)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f19]) ).
fof(f23,plain,
! [X2,X0,X1] :
( ~ subset(X0,unordered_pair(X1,X2))
| singleton(X1) = X0
| singleton(X2) = X0
| unordered_pair(X1,X2) = X0
| empty_set = X0 ),
inference(cnf_transformation,[],[f14]) ).
fof(f25,plain,
! [X2,X0,X1] :
( subset(X0,unordered_pair(X1,X2))
| singleton(X2) != X0 ),
inference(cnf_transformation,[],[f14]) ).
fof(f26,plain,
! [X2,X0,X1] :
( subset(X0,unordered_pair(X1,X2))
| singleton(X1) != X0 ),
inference(cnf_transformation,[],[f14]) ).
fof(f27,plain,
! [X2,X0,X1] :
( subset(X0,unordered_pair(X1,X2))
| empty_set != X0 ),
inference(cnf_transformation,[],[f14]) ).
fof(f30,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f10]) ).
fof(f31,plain,
! [X0,X1] :
( empty_set != set_difference(X0,X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f32,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| empty_set = set_difference(X0,X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f33,plain,
( empty_set = sK2
| sK2 = singleton(sK3)
| sK2 = singleton(sK4)
| sK2 = unordered_pair(sK3,sK4)
| empty_set = set_difference(sK2,unordered_pair(sK3,sK4)) ),
inference(cnf_transformation,[],[f20]) ).
fof(f34,plain,
( sK2 != unordered_pair(sK3,sK4)
| empty_set != set_difference(sK2,unordered_pair(sK3,sK4)) ),
inference(cnf_transformation,[],[f20]) ).
fof(f35,plain,
( sK2 != singleton(sK4)
| empty_set != set_difference(sK2,unordered_pair(sK3,sK4)) ),
inference(cnf_transformation,[],[f20]) ).
fof(f36,plain,
( sK2 != singleton(sK3)
| empty_set != set_difference(sK2,unordered_pair(sK3,sK4)) ),
inference(cnf_transformation,[],[f20]) ).
fof(f37,plain,
( empty_set != sK2
| empty_set != set_difference(sK2,unordered_pair(sK3,sK4)) ),
inference(cnf_transformation,[],[f20]) ).
fof(f38,plain,
! [X2,X1] : subset(empty_set,unordered_pair(X1,X2)),
inference(equality_resolution,[],[f27]) ).
fof(f39,plain,
! [X2,X1] : subset(singleton(X1),unordered_pair(X1,X2)),
inference(equality_resolution,[],[f26]) ).
fof(f40,plain,
! [X2,X1] : subset(singleton(X2),unordered_pair(X1,X2)),
inference(equality_resolution,[],[f25]) ).
fof(f43,definition,
( spl5_1
<=> empty_set = set_difference(sK2,unordered_pair(sK3,sK4)) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
fof(f44,plain,
( empty_set != set_difference(sK2,unordered_pair(sK3,sK4))
| spl5_1 ),
inference(avatar_component_clause,[],[f43]) ).
fof(f45,plain,
( empty_set = set_difference(sK2,unordered_pair(sK3,sK4))
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f43]) ).
fof(f47,definition,
( spl5_2
<=> sK2 = unordered_pair(sK3,sK4) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
fof(f48,plain,
( sK2 != unordered_pair(sK3,sK4)
| spl5_2 ),
inference(avatar_component_clause,[],[f47]) ).
fof(f49,plain,
( sK2 = unordered_pair(sK3,sK4)
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f47]) ).
fof(f51,definition,
( spl5_3
<=> sK2 = singleton(sK4) ),
introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition]) ).
fof(f52,plain,
( sK2 != singleton(sK4)
| spl5_3 ),
inference(avatar_component_clause,[],[f51]) ).
fof(f53,plain,
( sK2 = singleton(sK4)
| ~ spl5_3 ),
inference(avatar_component_clause,[],[f51]) ).
fof(f55,definition,
( spl5_4
<=> sK2 = singleton(sK3) ),
introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition]) ).
fof(f56,plain,
( sK2 != singleton(sK3)
| spl5_4 ),
inference(avatar_component_clause,[],[f55]) ).
fof(f57,plain,
( sK2 = singleton(sK3)
| ~ spl5_4 ),
inference(avatar_component_clause,[],[f55]) ).
fof(f59,definition,
( spl5_5
<=> empty_set = sK2 ),
introduced(definition,[new_symbols(definition,[spl5_5])],[avatar_definition]) ).
fof(f60,plain,
( empty_set != sK2
| spl5_5 ),
inference(avatar_component_clause,[],[f59]) ).
fof(f61,plain,
( empty_set = sK2
| ~ spl5_5 ),
inference(avatar_component_clause,[],[f59]) ).
fof(f62,plain,
( spl5_1
| spl5_2
| spl5_3
| spl5_4
| spl5_5 ),
inference(avatar_split_clause,[],[f33,f59,f55,f51,f47,f43]) ).
fof(f63,plain,
( ~ spl5_1
| ~ spl5_2 ),
inference(avatar_split_clause,[],[f34,f47,f43]) ).
fof(f64,plain,
( ~ spl5_1
| ~ spl5_3 ),
inference(avatar_split_clause,[],[f35,f51,f43]) ).
fof(f65,plain,
( ~ spl5_1
| ~ spl5_4 ),
inference(avatar_split_clause,[],[f36,f55,f43]) ).
fof(f66,plain,
( ~ spl5_1
| ~ spl5_5 ),
inference(avatar_split_clause,[],[f37,f59,f43]) ).
fof(f67,plain,
( empty_set != set_difference(sK2,sK2)
| spl5_1
| ~ spl5_2 ),
inference(forward_demodulation,[],[f44,f49]) ).
fof(f77,plain,
! [X0] : empty_set = set_difference(X0,X0),
inference(resolution,[],[f32,f30]) ).
fof(f78,plain,
! [X0,X1] : empty_set = set_difference(empty_set,unordered_pair(X0,X1)),
inference(resolution,[],[f32,f38]) ).
fof(f80,plain,
! [X0,X1] : empty_set = set_difference(singleton(X0),unordered_pair(X0,X1)),
inference(resolution,[],[f32,f39]) ).
fof(f100,plain,
( empty_set != empty_set
| spl5_1
| ~ spl5_2 ),
inference(superposition,[],[f67,f77]) ).
fof(f101,plain,
( $false
| spl5_1
| ~ spl5_2 ),
inference(trivial_inequality_removal,[],[f100]) ).
fof(f102,plain,
( spl5_1
| ~ spl5_2 ),
inference(avatar_contradiction_clause,[],[f101]) ).
fof(f104,plain,
( ! [X0] : subset(sK2,unordered_pair(X0,sK4))
| ~ spl5_3 ),
inference(superposition,[],[f40,f53]) ).
fof(f107,plain,
( ! [X0] : empty_set = set_difference(sK2,unordered_pair(X0,sK4))
| ~ spl5_3 ),
inference(resolution,[],[f104,f32]) ).
fof(f130,plain,
( empty_set != empty_set
| spl5_1
| ~ spl5_3 ),
inference(superposition,[],[f44,f107]) ).
fof(f133,plain,
( $false
| spl5_1
| ~ spl5_3 ),
inference(trivial_inequality_removal,[],[f130]) ).
fof(f134,plain,
( spl5_1
| ~ spl5_3 ),
inference(avatar_contradiction_clause,[],[f133]) ).
fof(f135,plain,
( empty_set != set_difference(empty_set,unordered_pair(sK3,sK4))
| spl5_1
| ~ spl5_5 ),
inference(superposition,[],[f44,f61]) ).
fof(f136,plain,
( $false
| spl5_1
| ~ spl5_5 ),
inference(forward_subsumption_resolution,[],[f135,f78]) ).
fof(f137,plain,
( spl5_1
| ~ spl5_5 ),
inference(avatar_contradiction_clause,[],[f136]) ).
fof(f139,plain,
( ! [X0] : empty_set = set_difference(sK2,unordered_pair(sK3,X0))
| ~ spl5_4 ),
inference(superposition,[],[f80,f57]) ).
fof(f156,plain,
( empty_set != empty_set
| spl5_1
| ~ spl5_4 ),
inference(superposition,[],[f44,f139]) ).
fof(f159,plain,
( $false
| spl5_1
| ~ spl5_4 ),
inference(trivial_inequality_removal,[],[f156]) ).
fof(f160,plain,
( spl5_1
| ~ spl5_4 ),
inference(avatar_contradiction_clause,[],[f159]) ).
fof(f161,plain,
( empty_set != empty_set
| subset(sK2,unordered_pair(sK3,sK4))
| ~ spl5_1 ),
inference(superposition,[],[f31,f45]) ).
fof(f162,plain,
( subset(sK2,unordered_pair(sK3,sK4))
| ~ spl5_1 ),
inference(trivial_inequality_removal,[],[f161]) ).
fof(f163,plain,
( sK2 = singleton(sK3)
| sK2 = singleton(sK4)
| sK2 = unordered_pair(sK3,sK4)
| empty_set = sK2
| ~ spl5_1 ),
inference(resolution,[],[f162,f23]) ).
fof(f165,plain,
( sK2 = singleton(sK4)
| sK2 = unordered_pair(sK3,sK4)
| empty_set = sK2
| ~ spl5_1
| spl5_4 ),
inference(forward_subsumption_resolution,[],[f163,f56]) ).
fof(f166,plain,
( sK2 = unordered_pair(sK3,sK4)
| empty_set = sK2
| ~ spl5_1
| spl5_3
| spl5_4 ),
inference(forward_subsumption_resolution,[],[f165,f52]) ).
fof(f167,plain,
( empty_set = sK2
| ~ spl5_1
| spl5_2
| spl5_3
| spl5_4 ),
inference(forward_subsumption_resolution,[],[f166,f48]) ).
fof(f168,plain,
( $false
| ~ spl5_1
| spl5_2
| spl5_3
| spl5_4
| spl5_5 ),
inference(forward_subsumption_resolution,[],[f167,f60]) ).
fof(f169,plain,
( ~ spl5_1
| spl5_2
| spl5_3
| spl5_4
| spl5_5 ),
inference(avatar_contradiction_clause,[],[f168]) ).
cnf(s1,plain,
( spl5_1
| spl5_2
| spl5_3
| spl5_4
| spl5_5 ),
inference(sat_conversion,[],[f62]) ).
cnf(s2,plain,
( ~ spl5_1
| ~ spl5_2 ),
inference(sat_conversion,[],[f63]) ).
cnf(s3,plain,
( ~ spl5_1
| ~ spl5_3 ),
inference(sat_conversion,[],[f64]) ).
cnf(s4,plain,
( ~ spl5_1
| ~ spl5_4 ),
inference(sat_conversion,[],[f65]) ).
cnf(s5,plain,
( ~ spl5_1
| ~ spl5_5 ),
inference(sat_conversion,[],[f66]) ).
cnf(s6,plain,
( spl5_1
| ~ spl5_2 ),
inference(sat_conversion,[],[f102]) ).
cnf(s7,plain,
( spl5_1
| ~ spl5_3 ),
inference(sat_conversion,[],[f134]) ).
cnf(s8,plain,
( spl5_1
| ~ spl5_5 ),
inference(sat_conversion,[],[f137]) ).
cnf(s9,plain,
( spl5_1
| ~ spl5_4 ),
inference(sat_conversion,[],[f160]) ).
cnf(s10,plain,
( ~ spl5_1
| spl5_2
| spl5_3
| spl5_4
| spl5_5 ),
inference(sat_conversion,[],[f169]) ).
cnf(s11,plain,
spl5_1,
inference(rat,[],[s1,s6,s7,s8,s9]) ).
cnf(s12,plain,
~ spl5_5,
inference(rat,[],[s5,s11]) ).
cnf(s13,plain,
~ spl5_4,
inference(rat,[],[s4,s11]) ).
cnf(s14,plain,
~ spl5_3,
inference(rat,[],[s3,s11]) ).
cnf(s15,plain,
~ spl5_2,
inference(rat,[],[s2,s11]) ).
cnf(s16,plain,
$false,
inference(rat,[],[s10,s12,s13,s14,s11,s15]) ).
fof(f170,plain,
$false,
inference(avatar_sat_refutation,[],[s16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET931+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.38 % Computer : n026.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Mon Sep 28 03:14:12 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.41 Running first-order model finding
% 0.13/0.41 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
% 0.13/0.45 % (3432691)Will run a generic schedule for satisfiability detection.
% 0.13/0.45 % (3432699)dis+10_1_sil=32000:sp=arity:random_seed=198571289:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.13/0.45 % (3432699) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3432691-3432699"...
% 0.13/0.45 % (3432697)% WARNING: option uhcvi not known.
% 0.13/0.45 % (3432699)...printing done.
% 0.13/0.45 % (3432699)Refutation found. Thanks to Tanya!
% 0.13/0.45 % SZS status Theorem for theBenchmark
% 0.13/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.46 % (3432699)------------------------------
% 0.13/0.46 % (3432699)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.13/0.46 % (3432699)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.13/0.46 % (3432699)CaDiCaL version: 2.1.3
% 0.13/0.46 % (3432699)Termination reason: Refutation
% 0.13/0.46 % (3432699)Time elapsed: 0.004 s
% 0.13/0.46 % (3432699)Peak memory usage: 12 MB
% 0.13/0.46 % (3432699)Instructions burned: 8 (million)
% 0.13/0.46 % (3432691)Success in time 0.032 s
% 0.13/0.46 % Vampire exiting
%------------------------------------------------------------------------------