%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET976+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 : n012.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 2.05s 0.87s
% Output : Refutation 2.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 55 ( 6 unt; 3 def)
% Number of atoms : 165 ( 40 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 182 ( 72 ~; 78 |; 23 &)
% ( 8 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 72 ( 0 sgn 58 !; 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(X2,singleton(X3)))
<=> ( in(X0,X2)
& X1 = X3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t129_zfmisc_1) ).
fof(f10,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,singleton(X3)))
<=> ( in(X0,X2)
& X1 = X3 ) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f12,plain,
? [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,singleton(X3)))
<~> ( in(X0,X2)
& X1 = X3 ) ),
inference(ennf_transformation,[],[f10]) ).
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,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(f17,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,[],[f16]) ).
fof(f20,plain,
? [X0,X1,X2,X3] :
( ( ~ in(X0,X2)
| X1 != X3
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,singleton(X3))) )
& ( ( in(X0,X2)
& X1 = X3 )
| in(ordered_pair(X0,X1),cartesian_product2(X2,singleton(X3))) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f21,plain,
? [X0,X1,X2,X3] :
( ( ~ in(X0,X2)
| X1 != X3
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,singleton(X3))) )
& ( ( in(X0,X2)
& X1 = X3 )
| in(ordered_pair(X0,X1),cartesian_product2(X2,singleton(X3))) ) ),
inference(flattening,[],[f20]) ).
fof(f22,plain,
( ( ~ in(sK3,sK5)
| sK4 != sK6
| ~ in(ordered_pair(sK3,sK4),cartesian_product2(sK5,singleton(sK6))) )
& ( ( in(sK3,sK5)
& sK4 = sK6 )
| in(ordered_pair(sK3,sK4),cartesian_product2(sK5,singleton(sK6))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5),skolemize(X3,sK6)],[f21]) ).
fof(f25,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f15]) ).
fof(f26,plain,
! [X3,X0,X1] :
( in(X3,X1)
| X0 != X3
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f15]) ).
fof(f31,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(cnf_transformation,[],[f17]) ).
fof(f32,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(cnf_transformation,[],[f17]) ).
fof(f33,plain,
! [X2,X3,X0,X1] :
( ~ in(X0,X2)
| in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3) ),
inference(cnf_transformation,[],[f17]) ).
fof(f36,plain,
( sK4 = sK6
| in(ordered_pair(sK3,sK4),cartesian_product2(sK5,singleton(sK6))) ),
inference(cnf_transformation,[],[f22]) ).
fof(f37,plain,
( in(sK3,sK5)
| in(ordered_pair(sK3,sK4),cartesian_product2(sK5,singleton(sK6))) ),
inference(cnf_transformation,[],[f22]) ).
fof(f38,plain,
( ~ in(sK3,sK5)
| sK4 != sK6
| ~ in(ordered_pair(sK3,sK4),cartesian_product2(sK5,singleton(sK6))) ),
inference(cnf_transformation,[],[f22]) ).
fof(f39,plain,
! [X3,X1] :
( in(X3,X1)
| singleton(X3) != X1 ),
inference(equality_resolution,[],[f26]) ).
fof(f40,plain,
! [X3] : in(X3,singleton(X3)),
inference(equality_resolution,[],[f39]) ).
fof(f41,plain,
! [X3,X0] :
( ~ in(X3,singleton(X0))
| X0 = X3 ),
inference(equality_resolution,[],[f25]) ).
fof(f43,definition,
( spl7_1
<=> in(ordered_pair(sK3,sK4),cartesian_product2(sK5,singleton(sK6))) ),
introduced(definition,[new_symbols(definition,[spl7_1])],[avatar_definition]) ).
fof(f44,plain,
( ~ in(ordered_pair(sK3,sK4),cartesian_product2(sK5,singleton(sK6)))
| spl7_1 ),
inference(avatar_component_clause,[],[f43]) ).
fof(f45,plain,
( in(ordered_pair(sK3,sK4),cartesian_product2(sK5,singleton(sK6)))
| ~ spl7_1 ),
inference(avatar_component_clause,[],[f43]) ).
fof(f47,definition,
( spl7_2
<=> sK4 = sK6 ),
introduced(definition,[new_symbols(definition,[spl7_2])],[avatar_definition]) ).
fof(f49,plain,
( sK4 = sK6
| ~ spl7_2 ),
inference(avatar_component_clause,[],[f47]) ).
fof(f50,plain,
( spl7_1
| spl7_2 ),
inference(avatar_split_clause,[],[f36,f47,f43]) ).
fof(f52,definition,
( spl7_3
<=> in(sK3,sK5) ),
introduced(definition,[new_symbols(definition,[spl7_3])],[avatar_definition]) ).
fof(f54,plain,
( in(sK3,sK5)
| ~ spl7_3 ),
inference(avatar_component_clause,[],[f52]) ).
fof(f55,plain,
( spl7_1
| spl7_3 ),
inference(avatar_split_clause,[],[f37,f52,f43]) ).
fof(f56,plain,
( ~ spl7_1
| ~ spl7_2
| ~ spl7_3 ),
inference(avatar_split_clause,[],[f38,f52,f47,f43]) ).
fof(f57,plain,
( ~ in(ordered_pair(sK3,sK4),cartesian_product2(sK5,singleton(sK4)))
| spl7_1
| ~ spl7_2 ),
inference(forward_demodulation,[],[f44,f49]) ).
fof(f73,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| in(ordered_pair(sK3,X0),cartesian_product2(sK5,X1)) )
| ~ spl7_3 ),
inference(resolution,[],[f33,f54]) ).
fof(f77,plain,
( ! [X0] : in(ordered_pair(sK3,X0),cartesian_product2(sK5,singleton(X0)))
| ~ spl7_3 ),
inference(resolution,[],[f73,f40]) ).
fof(f86,plain,
( $false
| spl7_1
| ~ spl7_2
| ~ spl7_3 ),
inference(resolution,[],[f77,f57]) ).
fof(f92,plain,
( spl7_1
| ~ spl7_2
| ~ spl7_3 ),
inference(avatar_contradiction_clause,[],[f86]) ).
fof(f93,plain,
( in(sK3,sK5)
| ~ spl7_1 ),
inference(resolution,[],[f45,f32]) ).
fof(f94,plain,
( in(sK4,singleton(sK6))
| ~ spl7_1 ),
inference(resolution,[],[f45,f31]) ).
fof(f98,plain,
( sK4 = sK6
| ~ spl7_1 ),
inference(resolution,[],[f94,f41]) ).
fof(f104,plain,
( spl7_3
| ~ spl7_1 ),
inference(avatar_split_clause,[],[f93,f43,f52]) ).
fof(f105,plain,
( spl7_2
| ~ spl7_1 ),
inference(avatar_split_clause,[],[f98,f43,f47]) ).
cnf(s1,plain,
( spl7_1
| spl7_2 ),
inference(sat_conversion,[],[f50]) ).
cnf(s2,plain,
( spl7_1
| spl7_3 ),
inference(sat_conversion,[],[f55]) ).
cnf(s3,plain,
( ~ spl7_1
| ~ spl7_2
| ~ spl7_3 ),
inference(sat_conversion,[],[f56]) ).
cnf(s4,plain,
( spl7_1
| ~ spl7_2
| ~ spl7_3 ),
inference(sat_conversion,[],[f92]) ).
cnf(s6,plain,
( ~ spl7_1
| spl7_3 ),
inference(sat_conversion,[],[f104]) ).
cnf(s7,plain,
( ~ spl7_1
| spl7_2 ),
inference(sat_conversion,[],[f105]) ).
cnf(s8,plain,
spl7_1,
inference(rat,[],[s4,s1,s2]) ).
cnf(s9,plain,
spl7_2,
inference(rat,[],[s7,s8]) ).
cnf(s10,plain,
spl7_3,
inference(rat,[],[s6,s8]) ).
cnf(s11,plain,
$false,
inference(rat,[],[s3,s9,s10,s8]) ).
fof(f106,plain,
$false,
inference(avatar_sat_refutation,[],[s11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET976+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.02 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.05/0.30 % Computer : n012.cluster.edu
% 0.05/0.30 % Model : x86_64 x86_64
% 0.05/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.30 % Memory : 8046.5625MB
% 0.05/0.30 % OS : Linux 6.8.0-71-generic
% 0.05/0.30 % CPULimit : 300
% 0.05/0.30 % WCLimit : 300
% 0.05/0.30 % DateTime : Mon Sep 28 03:17:19 UTC 2026
% 0.05/0.30 % CPUTime :
% 0.05/0.30 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.05/0.32 Running first-order theorem proving
% 0.05/0.32 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
% 2.05/0.87 % (2983727)Detected formulas, will run a generic FOF schedule.
% 2.05/0.87 % (2983732)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=1863079973:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.05/0.87 % (2983737)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3665788294:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.05/0.87 % (2983736)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=335659041:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.05/0.87 % (2983735)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=152286451:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.05/0.87 % (2983733)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=2505566620:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.05/0.87 % (2983734)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=2718134093:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.05/0.87 % (2983737)First to succeed.
% 2.05/0.87 % (2983736)Also succeeded, but the first one will report.
% 2.05/0.87 % (2983735)Also succeeded, but the first one will report.
% 2.05/0.87 % (2983737)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2983727"
% 2.05/0.87 % (2983738)dis-21_1_sil=8000:lcm=predicate:random_seed=1446655766: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)
% 2.05/0.87 % (2983738)Instruction limit reached!
% 2.05/0.87 % (2983738)------------------------------
% 2.05/0.87 % (2983738)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.05/0.87 % (2983738)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.05/0.87 % (2983738)CaDiCaL version: 2.1.3
% 2.05/0.87 % (2983738)Termination reason: Instruction limit
% 2.05/0.87 % (2983738)Termination phase: Saturation
% 2.05/0.87 % (2983738)Time elapsed: 0.030 s
% 2.05/0.87 % (2983738)Peak memory usage: 88 MB
% 2.05/0.87 % (2983738)Instructions burned: 130 (million)
% 2.05/0.87 % (2983746)lrs+10_1_sil=8000:sp=occurrence:random_seed=1793396169:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.05/0.87 % (2983746)Also succeeded, but the first one will report.
% 2.05/0.87 % (2983737)Refutation found. Thanks to Tanya!
% 2.05/0.87 % SZS status Theorem for theBenchmark
% 2.05/0.87 % SZS output start Proof for theBenchmark
% See solution above
% 2.05/0.87 % (2983737)------------------------------
% 2.05/0.87 % (2983737)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.05/0.87 % (2983737)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.05/0.87 % (2983737)CaDiCaL version: 2.1.3
% 2.05/0.87 % (2983737)Termination reason: Refutation
% 2.05/0.87 % (2983737)Time elapsed: 0.003 s
% 2.05/0.87 % (2983737)Peak memory usage: 90 MB
% 2.05/0.87 % (2983737)Instructions burned: 5 (million)
% 2.05/0.87 % (2983737)------------------------------
% 2.05/0.87 % (2983737)------------------------------
% 2.05/0.87 % (2983727)Success in time 0.262 s
% 2.05/0.87 % Vampire exiting
%------------------------------------------------------------------------------