%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET975+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 12:42:27 PM UTC 2026
% Result : Theorem 4.21s 1.73s
% Output : Refutation 4.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 7
% Syntax : Number of formulae : 58 ( 8 unt; 4 def)
% Number of atoms : 166 ( 41 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 181 ( 73 ~; 76 |; 23 &)
% ( 8 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 69 ( 0 sgn 55 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(f6,axiom,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X0,X2)
& in(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l55_zfmisc_1) ).
fof(f9,conjecture,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),X3))
<=> ( X0 = X2
& in(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t128_zfmisc_1) ).
fof(f10,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),X3))
<=> ( X0 = X2
& in(X1,X3) ) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f11,plain,
? [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),X3))
<~> ( X0 = X2
& in(X1,X3) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f13,plain,
? [X0,X1,X2,X3] :
( ( X0 != X2
| ~ in(X1,X3)
| ~ in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),X3)) )
& ( ( X0 = X2
& in(X1,X3) )
| in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),X3)) ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f14,plain,
? [X0,X1,X2,X3] :
( ( X0 != X2
| ~ in(X1,X3)
| ~ in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),X3)) )
& ( ( X0 = X2
& in(X1,X3) )
| in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),X3)) ) ),
inference(flattening,[],[f13]) ).
fof(f15,plain,
( ( sK0 != sK2
| ~ in(sK1,sK3)
| ~ in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK2),sK3)) )
& ( ( sK0 = sK2
& in(sK1,sK3) )
| in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK2),sK3)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f14]) ).
fof(f16,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(f17,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,[],[f16]) ).
fof(f18,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ( ( sK4(X0,X1) != X0
| ~ in(sK4(X0,X1),X1) )
& ( sK4(X0,X1) = X0
| in(sK4(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X2,sK4(X0,X1))],[f17]) ).
fof(f19,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) )
& ( ( in(X0,X2)
& in(X1,X3) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f20,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) )
& ( ( in(X0,X2)
& in(X1,X3) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(flattening,[],[f19]) ).
fof(f21,plain,
( in(sK1,sK3)
| in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK2),sK3)) ),
inference(cnf_transformation,[],[f15]) ).
fof(f22,plain,
( sK0 = sK2
| in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK2),sK3)) ),
inference(cnf_transformation,[],[f15]) ).
fof(f23,plain,
( sK0 != sK2
| ~ in(sK1,sK3)
| ~ in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK2),sK3)) ),
inference(cnf_transformation,[],[f15]) ).
fof(f25,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f18]) ).
fof(f26,plain,
! [X3,X0,X1] :
( in(X3,X1)
| X0 != X3
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f18]) ).
fof(f29,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(cnf_transformation,[],[f20]) ).
fof(f30,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(cnf_transformation,[],[f20]) ).
fof(f31,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) ),
inference(cnf_transformation,[],[f20]) ).
fof(f32,definition,
~ sP5(sK0),
introduced(definition,[new_symbols(definition,[sP5])],[inequality_splitting_name_introduction]) ).
fof(f33,plain,
( sP5(sK2)
| ~ in(sK1,sK3)
| ~ in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK2),sK3)) ),
inference(inequality_splitting,[],[f23,f32]) ).
fof(f34,plain,
! [X3,X1] :
( in(X3,X1)
| singleton(X3) != X1 ),
inference(equality_resolution,[],[f26]) ).
fof(f35,plain,
! [X3] : in(X3,singleton(X3)),
inference(equality_resolution,[],[f34]) ).
fof(f36,plain,
! [X3,X0] :
( ~ in(X3,singleton(X0))
| X0 = X3 ),
inference(equality_resolution,[],[f25]) ).
fof(f37,plain,
in(sK1,sK3),
inference(forward_subsumption_resolution,[],[f21,f29]) ).
fof(f39,definition,
( spl6_1
<=> in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK2),sK3)) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
fof(f40,plain,
( ~ in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK2),sK3))
| spl6_1 ),
inference(avatar_component_clause,[],[f39]) ).
fof(f41,plain,
( in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK2),sK3))
| ~ spl6_1 ),
inference(avatar_component_clause,[],[f39]) ).
fof(f43,definition,
( spl6_2
<=> sK0 = sK2 ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
fof(f44,plain,
( sK0 != sK2
| spl6_2 ),
inference(avatar_component_clause,[],[f43]) ).
fof(f45,plain,
( sK0 = sK2
| ~ spl6_2 ),
inference(avatar_component_clause,[],[f43]) ).
fof(f46,plain,
( spl6_1
| spl6_2 ),
inference(avatar_split_clause,[],[f22,f43,f39]) ).
fof(f47,plain,
( sP5(sK2)
| ~ in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK2),sK3)) ),
inference(forward_subsumption_resolution,[],[f33,f29]) ).
fof(f49,definition,
( spl6_3
<=> sP5(sK2) ),
introduced(definition,[new_symbols(definition,[spl6_3])],[avatar_definition]) ).
fof(f52,plain,
( ~ spl6_1
| spl6_3 ),
inference(avatar_split_clause,[],[f47,f49,f39]) ).
fof(f54,plain,
( ~ sP5(sK2)
| ~ spl6_2 ),
inference(superposition,[],[f32,f45]) ).
fof(f55,plain,
( ~ spl6_3
| ~ spl6_2 ),
inference(avatar_split_clause,[],[f54,f43,f49]) ).
fof(f56,plain,
( ~ in(sK0,singleton(sK2))
| ~ in(sK1,sK3)
| spl6_1 ),
inference(resolution,[],[f40,f31]) ).
fof(f58,plain,
( ~ in(sK0,singleton(sK2))
| spl6_1 ),
inference(forward_subsumption_resolution,[],[f56,f37]) ).
fof(f59,plain,
( ~ in(sK2,singleton(sK2))
| spl6_1
| ~ spl6_2 ),
inference(forward_demodulation,[],[f58,f45]) ).
fof(f60,plain,
( $false
| spl6_1
| ~ spl6_2 ),
inference(forward_subsumption_resolution,[],[f59,f35]) ).
fof(f61,plain,
( spl6_1
| ~ spl6_2 ),
inference(avatar_contradiction_clause,[],[f60]) ).
fof(f63,plain,
( in(sK0,singleton(sK2))
| ~ spl6_1 ),
inference(resolution,[],[f41,f30]) ).
fof(f65,plain,
( sK0 = sK2
| ~ spl6_1 ),
inference(resolution,[],[f63,f36]) ).
fof(f67,plain,
( $false
| ~ spl6_1
| spl6_2 ),
inference(forward_subsumption_resolution,[],[f65,f44]) ).
fof(f68,plain,
( ~ spl6_1
| spl6_2 ),
inference(avatar_contradiction_clause,[],[f67]) ).
cnf(s1,plain,
( spl6_1
| spl6_2 ),
inference(sat_conversion,[],[f46]) ).
cnf(s2,plain,
( ~ spl6_1
| spl6_3 ),
inference(sat_conversion,[],[f52]) ).
cnf(s3,plain,
( ~ spl6_2
| ~ spl6_3 ),
inference(sat_conversion,[],[f55]) ).
cnf(s4,plain,
( spl6_1
| ~ spl6_2 ),
inference(sat_conversion,[],[f61]) ).
cnf(s5,plain,
( ~ spl6_1
| spl6_2 ),
inference(sat_conversion,[],[f68]) ).
cnf(s6,plain,
spl6_1,
inference(rat,[],[s1,s4]) ).
cnf(s7,plain,
spl6_2,
inference(rat,[],[s5,s6]) ).
cnf(s8,plain,
spl6_3,
inference(rat,[],[s2,s6]) ).
cnf(s9,plain,
$false,
inference(rat,[],[s3,s8,s7]) ).
fof(f69,plain,
$false,
inference(avatar_sat_refutation,[],[s9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET975+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.44 % Computer : n016.cluster.edu
% 0.15/0.44 % Model : x86_64 x86_64
% 0.15/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.44 % Memory : 8046.5625MB
% 0.15/0.44 % OS : Linux 6.8.0-71-generic
% 0.15/0.44 % CPULimit : 300
% 0.15/0.44 % WCLimit : 300
% 0.15/0.44 % DateTime : Mon Sep 28 03:22:02 UTC 2026
% 0.15/0.44 % CPUTime :
% 0.15/0.44 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.20/0.50 Running first-order theorem proving
% 0.20/0.50 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
% 4.21/1.73 % (3226067)Detected formulas, will run a generic FOF schedule.
% 4.21/1.73 % (3226077)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=334859217:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.21/1.73 % (3226077)First to succeed.
% 4.21/1.73 % (3226077)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3226067"
% 4.21/1.73 % (3226074)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=572238578:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.21/1.73 % (3226080)dis-21_1_sil=8000:lcm=predicate:random_seed=4143315898: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)
% 4.21/1.73 % (3226075)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=2801380890:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.21/1.73 % (3226078)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1825637157:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.21/1.73 % (3226076)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=2410296001:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.21/1.73 % (3226078)Also succeeded, but the first one will report.
% 4.21/1.73 % (3226079)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1099721041:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.21/1.73 % (3226079)Also succeeded, but the first one will report.
% 4.21/1.73 % (3226080)Instruction limit reached!
% 4.21/1.73 % (3226080)------------------------------
% 4.21/1.73 % (3226080)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.21/1.73 % (3226080)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.21/1.73 % (3226080)CaDiCaL version: 2.1.3
% 4.21/1.73 % (3226080)Termination reason: Instruction limit
% 4.21/1.73 % (3226080)Termination phase: Saturation
% 4.21/1.73 % (3226080)Time elapsed: 0.088 s
% 4.21/1.73 % (3226080)Peak memory usage: 88 MB
% 4.21/1.73 % (3226080)Instructions burned: 129 (million)
% 4.21/1.73 % (3226077)Refutation found. Thanks to Tanya!
% 4.21/1.73 % SZS status Theorem for theBenchmark
% 4.21/1.73 % SZS output start Proof for theBenchmark
% See solution above
% 4.21/1.73 % (3226077)------------------------------
% 4.21/1.73 % (3226077)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.21/1.73 % (3226077)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.21/1.73 % (3226077)CaDiCaL version: 2.1.3
% 4.21/1.73 % (3226077)Termination reason: Refutation
% 4.21/1.73 % (3226077)Time elapsed: 0.003 s
% 4.21/1.73 % (3226077)Peak memory usage: 89 MB
% 4.21/1.73 % (3226077)Instructions burned: 2 (million)
% 4.21/1.73 % (3226077)------------------------------
% 4.21/1.73 % (3226077)------------------------------
% 4.21/1.73 % (3226067)Success in time 0.481 s
% 4.21/1.73 % Vampire exiting
%------------------------------------------------------------------------------