%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET763+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 12:41:51 PM UTC 2026
% Result : Theorem 3.39s 11.18s
% Output : Refutation 3.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 50 ( 10 unt; 0 def)
% Number of atoms : 193 ( 6 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 228 ( 85 ~; 72 |; 52 &)
% ( 6 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 146 ( 128 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset) ).
fof(f2,axiom,
! [X0,X1] :
( equal_set(X0,X1)
<=> ( subset(X0,X1)
& subset(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_set) ).
fof(f6,axiom,
! [X0] : ~ member(X0,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set) ).
fof(f12,axiom,
! [X0,X1,X2] :
( maps(X0,X1,X2)
<=> ( ! [X3] :
( member(X3,X1)
=> ? [X4] :
( member(X4,X2)
& apply(X0,X3,X4) ) )
& ! [X3,X5,X6] :
( ( member(X3,X1)
& member(X5,X2)
& member(X6,X2) )
=> ( ( apply(X0,X3,X5)
& apply(X0,X3,X6) )
=> X5 = X6 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maps) ).
fof(f22,axiom,
! [X0,X1,X2] :
( member(X2,image2(X0,X1))
<=> ? [X3] :
( member(X3,X1)
& apply(X0,X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',image2) ).
fof(f29,conjecture,
! [X0,X1,X2,X3] :
( ( maps(X0,X1,X2)
& subset(X3,X1)
& equal_set(image2(X0,X3),empty_set) )
=> equal_set(X3,empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIIa13) ).
fof(f30,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( maps(X0,X1,X2)
& subset(X3,X1)
& equal_set(image2(X0,X3),empty_set) )
=> equal_set(X3,empty_set) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f31,plain,
! [X0,X1,X2] :
( maps(X0,X1,X2)
<=> ( ! [X3] :
( member(X3,X1)
=> ? [X4] :
( member(X4,X2)
& apply(X0,X3,X4) ) )
& ! [X5,X6,X7] :
( ( member(X5,X1)
& member(X6,X2)
& member(X7,X2) )
=> ( ( apply(X0,X5,X6)
& apply(X0,X5,X7) )
=> X6 = X7 ) ) ) ),
inference(rectify,[],[f12]) ).
fof(f32,plain,
! [X0,X1,X2] :
( maps(X0,X1,X2)
=> ( ! [X3] :
( member(X3,X1)
=> ? [X4] :
( member(X4,X2)
& apply(X0,X3,X4) ) )
& ! [X5,X6,X7] :
( ( member(X5,X1)
& member(X6,X2)
& member(X7,X2) )
=> ( ( apply(X0,X5,X6)
& apply(X0,X5,X7) )
=> X6 = X7 ) ) ) ),
inference(unused_predicate_definition_removal,[],[f31]) ).
fof(f33,plain,
? [X0,X1,X2,X3] :
( ~ equal_set(X3,empty_set)
& maps(X0,X1,X2)
& subset(X3,X1)
& equal_set(image2(X0,X3),empty_set) ),
inference(ennf_transformation,[],[f30]) ).
fof(f34,plain,
? [X0,X1,X2,X3] :
( ~ equal_set(X3,empty_set)
& maps(X0,X1,X2)
& subset(X3,X1)
& equal_set(image2(X0,X3),empty_set) ),
inference(flattening,[],[f33]) ).
fof(f35,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f36,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ? [X4] :
( member(X4,X2)
& apply(X0,X3,X4) )
| ~ member(X3,X1) )
& ! [X5,X6,X7] :
( X6 = X7
| ~ apply(X0,X5,X6)
| ~ apply(X0,X5,X7)
| ~ member(X5,X1)
| ~ member(X6,X2)
| ~ member(X7,X2) ) )
| ~ maps(X0,X1,X2) ),
inference(ennf_transformation,[],[f32]) ).
fof(f37,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ? [X4] :
( member(X4,X2)
& apply(X0,X3,X4) )
| ~ member(X3,X1) )
& ! [X5,X6,X7] :
( X6 = X7
| ~ apply(X0,X5,X6)
| ~ apply(X0,X5,X7)
| ~ member(X5,X1)
| ~ member(X6,X2)
| ~ member(X7,X2) ) )
| ~ maps(X0,X1,X2) ),
inference(flattening,[],[f36]) ).
fof(f38,plain,
( ~ equal_set(sK3,empty_set)
& maps(sK0,sK1,sK2)
& subset(sK3,sK1)
& equal_set(image2(sK0,sK3),empty_set) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f34]) ).
fof(f39,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f35]) ).
fof(f40,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f39]) ).
fof(f41,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK4(X0,X1),X1)
& member(sK4(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X2,sK4(X0,X1))],[f40]) ).
fof(f42,plain,
! [X0,X1] :
( ( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| ~ equal_set(X0,X1) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f43,plain,
! [X0,X1] :
( ( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| ~ equal_set(X0,X1) ) ),
inference(flattening,[],[f42]) ).
fof(f44,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ( member(sK5(X0,X2,X3),X2)
& apply(X0,X3,sK5(X0,X2,X3)) )
| ~ member(X3,X1) )
& ! [X5,X6,X7] :
( X6 = X7
| ~ apply(X0,X5,X6)
| ~ apply(X0,X5,X7)
| ~ member(X5,X1)
| ~ member(X6,X2)
| ~ member(X7,X2) ) )
| ~ maps(X0,X1,X2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X4,sK5(X0,X2,X3))],[f37]) ).
fof(f45,plain,
! [X0,X1,X2] :
( ( member(X2,image2(X0,X1))
| ! [X3] :
( ~ member(X3,X1)
| ~ apply(X0,X3,X2) ) )
& ( ? [X3] :
( member(X3,X1)
& apply(X0,X3,X2) )
| ~ member(X2,image2(X0,X1)) ) ),
inference(nnf_transformation,[],[f22]) ).
fof(f46,plain,
! [X0,X1,X2] :
( ( member(X2,image2(X0,X1))
| ! [X3] :
( ~ member(X3,X1)
| ~ apply(X0,X3,X2) ) )
& ( ? [X4] :
( member(X4,X1)
& apply(X0,X4,X2) )
| ~ member(X2,image2(X0,X1)) ) ),
inference(rectify,[],[f45]) ).
fof(f47,plain,
! [X0,X1,X2] :
( ( member(X2,image2(X0,X1))
| ! [X3] :
( ~ member(X3,X1)
| ~ apply(X0,X3,X2) ) )
& ( ( member(sK6(X0,X1,X2),X1)
& apply(X0,sK6(X0,X1,X2),X2) )
| ~ member(X2,image2(X0,X1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X4,sK6(X0,X1,X2))],[f46]) ).
fof(f48,plain,
equal_set(image2(sK0,sK3),empty_set),
inference(cnf_transformation,[],[f38]) ).
fof(f49,plain,
subset(sK3,sK1),
inference(cnf_transformation,[],[f38]) ).
fof(f50,plain,
maps(sK0,sK1,sK2),
inference(cnf_transformation,[],[f38]) ).
fof(f51,plain,
~ equal_set(sK3,empty_set),
inference(cnf_transformation,[],[f38]) ).
fof(f52,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f41]) ).
fof(f53,plain,
! [X0,X1] :
( member(sK4(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f41]) ).
fof(f56,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ equal_set(X0,X1) ),
inference(cnf_transformation,[],[f43]) ).
fof(f57,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(cnf_transformation,[],[f43]) ).
fof(f58,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f6]) ).
fof(f60,plain,
! [X2,X3,X0,X1] :
( apply(X0,X3,sK5(X0,X2,X3))
| ~ member(X3,X1)
| ~ maps(X0,X1,X2) ),
inference(cnf_transformation,[],[f44]) ).
fof(f64,plain,
! [X2,X3,X0,X1] :
( member(X2,image2(X0,X1))
| ~ member(X3,X1)
| ~ apply(X0,X3,X2) ),
inference(cnf_transformation,[],[f47]) ).
fof(f65,plain,
! [X0] : subset(empty_set,X0),
inference(resolution,[],[f53,f58]) ).
fof(f68,plain,
! [X0,X1] :
( ~ member(X0,X1)
| ~ subset(X1,empty_set) ),
inference(resolution,[],[f52,f58]) ).
fof(f72,plain,
( ~ subset(sK3,empty_set)
| ~ subset(empty_set,sK3) ),
inference(resolution,[],[f57,f51]) ).
fof(f73,plain,
~ subset(sK3,empty_set),
inference(forward_subsumption_resolution,[],[f72,f65]) ).
fof(f84,plain,
! [X2,X3,X0,X1] :
( ~ subset(image2(X2,X1),empty_set)
| ~ apply(X2,X0,X3)
| ~ member(X0,X1) ),
inference(resolution,[],[f64,f68]) ).
fof(f147,plain,
! [X2,X3,X0,X1] :
( ~ equal_set(image2(X0,X3),empty_set)
| ~ member(X1,X3)
| ~ apply(X0,X1,X2) ),
inference(resolution,[],[f84,f56]) ).
fof(f287,plain,
! [X0,X1] :
( ~ apply(sK0,X0,X1)
| ~ member(X0,sK3) ),
inference(resolution,[],[f147,f48]) ).
fof(f290,plain,
! [X2,X0,X1] :
( ~ maps(sK0,X1,X2)
| ~ member(X0,X1)
| ~ member(X0,sK3) ),
inference(resolution,[],[f287,f60]) ).
fof(f305,plain,
! [X0] :
( ~ member(X0,sK3)
| ~ member(X0,sK1) ),
inference(resolution,[],[f290,f50]) ).
fof(f311,plain,
! [X0] :
( ~ member(sK4(sK3,X0),sK1)
| subset(sK3,X0) ),
inference(resolution,[],[f305,f53]) ).
fof(f314,plain,
! [X0,X1] :
( ~ member(sK4(sK3,X0),X1)
| subset(sK3,X0)
| ~ subset(X1,sK1) ),
inference(resolution,[],[f311,f52]) ).
fof(f556,plain,
! [X0] :
( subset(sK3,X0)
| ~ subset(sK3,sK1)
| subset(sK3,X0) ),
inference(resolution,[],[f314,f53]) ).
fof(f559,plain,
! [X0] :
( subset(sK3,X0)
| ~ subset(sK3,sK1) ),
inference(duplicate_literal_removal,[],[f556]) ).
fof(f560,plain,
! [X0] : subset(sK3,X0),
inference(forward_subsumption_resolution,[],[f559,f49]) ).
fof(f579,plain,
$false,
inference(resolution,[],[f560,f73]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET763+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/10.40 % Computer : n006.cluster.edu
% 0.11/10.40 % Model : x86_64 x86_64
% 0.11/10.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.40 % Memory : 8046.5625MB
% 0.11/10.40 % OS : Linux 6.8.0-71-generic
% 0.11/10.40 % CPULimit : 300
% 0.11/10.40 % WCLimit : 300
% 0.11/10.40 % DateTime : Mon Sep 28 02:44:52 UTC 2026
% 0.11/10.40 % CPUTime :
% 0.11/10.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/10.44 Running first-order theorem proving
% 0.11/10.44 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
% 3.39/11.18 % (3536521)Detected formulas, will run a generic FOF schedule.
% 3.39/11.18 % (3536528)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=4058504311:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.39/11.18 % (3536532)dis-21_1_sil=8000:lcm=predicate:random_seed=3365215951: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)
% 3.39/11.18 % (3536527)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=1599256683:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.39/11.18 % (3536526)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=534783927:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.39/11.18 % (3536530)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2542999607:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.39/11.18 % (3536529)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=707138804:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.39/11.18 % (3536529)Refutation not found, incomplete strategy
% 3.39/11.18 % (3536529)------------------------------
% 3.39/11.18 % (3536529)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.39/11.18 % (3536529)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.39/11.18 % (3536529)CaDiCaL version: 2.1.3
% 3.39/11.18 % (3536529)Termination reason: Refutation not found, incomplete strategy
% 3.39/11.18 % (3536529)Time elapsed: 0.003 s
% 3.39/11.18 % (3536529)Peak memory usage: 88 MB
% 3.39/11.18 % (3536529)Instructions burned: 3 (million)
% 3.39/11.18 % (3536530)First to succeed.
% 3.39/11.18 % (3536530)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3536521"
% 3.39/11.18 % (3536531)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=6998752:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.39/11.18 % (3536531)Also succeeded, but the first one will report.
% 3.39/11.18 % (3536532)Instruction limit reached!
% 3.39/11.18 % (3536532)------------------------------
% 3.39/11.18 % (3536532)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.39/11.18 % (3536532)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.39/11.18 % (3536532)CaDiCaL version: 2.1.3
% 3.39/11.18 % (3536532)Termination reason: Instruction limit
% 3.39/11.18 % (3536532)Termination phase: Saturation
% 3.39/11.18 % (3536532)Time elapsed: 0.080 s
% 3.39/11.18 % (3536532)Peak memory usage: 89 MB
% 3.39/11.18 % (3536532)Instructions burned: 130 (million)
% 3.39/11.18 % (3536540)lrs+10_1_sil=8000:sp=occurrence:random_seed=1514043445:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.39/11.18 % (3536529)------------------------------
% 3.39/11.18 % (3536529)------------------------------
% 3.39/11.18 % (3536540)Also succeeded, but the first one will report.
% 3.39/11.18 % (3536530)Refutation found. Thanks to Tanya!
% 3.39/11.18 % SZS status Theorem for theBenchmark
% 3.39/11.18 % SZS output start Proof for theBenchmark
% See solution above
% 3.39/11.18 % (3536530)------------------------------
% 3.39/11.18 % (3536530)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.39/11.18 % (3536530)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.39/11.18 % (3536530)CaDiCaL version: 2.1.3
% 3.39/11.18 % (3536530)Termination reason: Refutation
% 3.39/11.18 % (3536530)Time elapsed: 0.020 s
% 3.39/11.18 % (3536530)Peak memory usage: 88 MB
% 3.39/11.18 % (3536530)Instructions burned: 31 (million)
% 3.39/11.18 % (3536530)------------------------------
% 3.39/11.18 % (3536530)------------------------------
% 3.39/11.18 % (3536521)Success in time 0.44 s
% 3.39/11.18 % Vampire exiting
%------------------------------------------------------------------------------