%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET185+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 12:40:26 PM UTC 2026
% Result : Theorem 3.50s 1.46s
% Output : Refutation 3.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 37 ( 5 unt; 0 def)
% Number of atoms : 108 ( 14 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 114 ( 43 ~; 47 |; 17 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 78 ( 74 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] :
( member(X2,union(X0,X1))
<=> ( member(X2,X0)
| member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_defn) ).
fof(f2,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
fof(f3,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X0,X1)
& subset(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
fof(f7,conjecture,
! [X0,X1] :
( subset(X0,X1)
=> union(X0,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_subset_union) ).
fof(f8,negated_conjecture,
~ ! [X0,X1] :
( subset(X0,X1)
=> union(X0,X1) = X1 ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,plain,
? [X0,X1] :
( union(X0,X1) != X1
& subset(X0,X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f10,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f11,plain,
( sK1 != union(sK0,sK1)
& subset(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f9]) ).
fof(f12,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f13,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(flattening,[],[f12]) ).
fof(f14,plain,
! [X0,X1,X2] :
( ( member(X2,union(X0,X1))
| ( ~ member(X2,X0)
& ~ member(X2,X1) ) )
& ( member(X2,X0)
| member(X2,X1)
| ~ member(X2,union(X0,X1)) ) ),
inference(nnf_transformation,[],[f1]) ).
fof(f15,plain,
! [X0,X1,X2] :
( ( member(X2,union(X0,X1))
| ( ~ member(X2,X0)
& ~ member(X2,X1) ) )
& ( member(X2,X0)
| member(X2,X1)
| ~ member(X2,union(X0,X1)) ) ),
inference(flattening,[],[f14]) ).
fof(f19,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,[],[f10]) ).
fof(f20,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,[],[f19]) ).
fof(f21,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK3(X0,X1),X1)
& member(sK3(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X2,sK3(X0,X1))],[f20]) ).
fof(f22,plain,
subset(sK0,sK1),
inference(cnf_transformation,[],[f11]) ).
fof(f23,plain,
sK1 != union(sK0,sK1),
inference(cnf_transformation,[],[f11]) ).
fof(f26,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f13]) ).
fof(f28,plain,
! [X2,X0,X1] :
( ~ member(X2,union(X0,X1))
| member(X2,X1)
| member(X2,X0) ),
inference(cnf_transformation,[],[f15]) ).
fof(f29,plain,
! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f36,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f37,plain,
! [X0,X1] :
( member(sK3(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f38,plain,
! [X0,X1] :
( ~ member(sK3(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f49,plain,
! [X2,X0,X1] :
( ~ member(sK3(X0,union(X1,X2)),X2)
| subset(X0,union(X1,X2)) ),
inference(resolution,[],[f38,f29]) ).
fof(f54,plain,
! [X2,X0,X1] :
( ~ member(sK3(X0,X1),X2)
| ~ subset(X2,X1)
| subset(X0,X1) ),
inference(resolution,[],[f36,f38]) ).
fof(f58,plain,
! [X2,X0,X1] :
( member(sK3(union(X0,X1),X2),X1)
| member(sK3(union(X0,X1),X2),X0)
| subset(union(X0,X1),X2) ),
inference(resolution,[],[f28,f37]) ).
fof(f83,plain,
! [X0,X1] :
( subset(X0,union(X1,X0))
| subset(X0,union(X1,X0)) ),
inference(resolution,[],[f49,f37]) ).
fof(f89,plain,
! [X0,X1] : subset(X0,union(X1,X0)),
inference(duplicate_literal_removal,[],[f83]) ).
fof(f90,plain,
! [X0,X1] :
( ~ subset(union(X0,X1),X1)
| union(X0,X1) = X1 ),
inference(resolution,[],[f89,f26]) ).
fof(f106,plain,
! [X0,X1] :
( member(sK3(union(X0,X1),X1),X0)
| subset(union(X0,X1),X1)
| subset(union(X0,X1),X1) ),
inference(resolution,[],[f58,f38]) ).
fof(f116,plain,
! [X0,X1] :
( member(sK3(union(X0,X1),X1),X0)
| subset(union(X0,X1),X1) ),
inference(duplicate_literal_removal,[],[f106]) ).
fof(f150,plain,
! [X0,X1] :
( subset(union(X0,X1),X1)
| ~ subset(X0,X1)
| subset(union(X0,X1),X1) ),
inference(resolution,[],[f116,f54]) ).
fof(f158,plain,
! [X0,X1] :
( subset(union(X0,X1),X1)
| ~ subset(X0,X1) ),
inference(duplicate_literal_removal,[],[f150]) ).
fof(f200,plain,
! [X0,X1] :
( union(X0,X1) = X1
| ~ subset(X0,X1) ),
inference(resolution,[],[f158,f90]) ).
fof(f217,plain,
( sK1 != sK1
| ~ subset(sK0,sK1) ),
inference(superposition,[],[f23,f200]) ).
fof(f239,plain,
~ subset(sK0,sK1),
inference(trivial_inequality_removal,[],[f217]) ).
fof(f243,plain,
$false,
inference(forward_subsumption_resolution,[],[f239,f22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET185+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n004.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 28 01:02:22 UTC 2026
% 0.15/0.37 % CPUTime :
% 0.15/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.41 Running first-order theorem proving
% 0.15/0.41 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
% 3.50/1.46 % (4049367)Detected formulas, will run a generic FOF schedule.
% 3.50/1.46 % (4049377)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3426572683:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.50/1.46 % (4049376)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=661064264:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.50/1.46 % (4049375)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3588510403:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.50/1.46 % (4049375)Refutation not found, incomplete strategy
% 3.50/1.46 % (4049375)------------------------------
% 3.50/1.46 % (4049375)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.50/1.46 % (4049375)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.50/1.46 % (4049375)CaDiCaL version: 2.1.3
% 3.50/1.46 % (4049375)Termination reason: Refutation not found, incomplete strategy
% 3.50/1.46 % (4049375)Time elapsed: 0.001 s
% 3.50/1.46 % (4049375)Peak memory usage: 88 MB
% 3.50/1.46 % (4049376)First to succeed.
% 3.50/1.46 % (4049373)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=1238251834:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.50/1.46 % (4049374)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=818073911:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.50/1.46 % (4049372)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=1045953603:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.50/1.46 % (4049376)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4049367"
% 3.50/1.46 % (4049378)dis-21_1_sil=8000:lcm=predicate:random_seed=2246150296: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)
% 3.50/1.46 % (4049378)Also succeeded, but the first one will report.
% 3.50/1.46 % (4049377)Instruction limit reached!
% 3.50/1.46 % (4049377)------------------------------
% 3.50/1.46 % (4049377)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.50/1.46 % (4049377)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.50/1.46 % (4049377)CaDiCaL version: 2.1.3
% 3.50/1.46 % (4049377)Termination reason: Instruction limit
% 3.50/1.46 % (4049377)Termination phase: Saturation
% 3.50/1.46 % (4049377)Time elapsed: 0.049 s
% 3.50/1.46 % (4049377)Peak memory usage: 89 MB
% 3.50/1.46 % (4049377)Instructions burned: 142 (million)
% 3.50/1.46 % (4049386)lrs+10_1_sil=8000:sp=occurrence:random_seed=1138467424:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.50/1.46 % (4049386)Also succeeded, but the first one will report.
% 3.50/1.46 % (4049375)------------------------------
% 3.50/1.46 % (4049375)------------------------------
% 3.50/1.46 % (4049376)Refutation found. Thanks to Tanya!
% 3.50/1.46 % SZS status Theorem for theBenchmark
% 3.50/1.46 % SZS output start Proof for theBenchmark
% See solution above
% 3.50/1.46 % (4049376)------------------------------
% 3.50/1.46 % (4049376)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.50/1.46 % (4049376)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.50/1.46 % (4049376)CaDiCaL version: 2.1.3
% 3.50/1.46 % (4049376)Termination reason: Refutation
% 3.50/1.46 % (4049376)Time elapsed: 0.006 s
% 3.50/1.46 % (4049376)Peak memory usage: 88 MB
% 3.50/1.46 % (4049376)Instructions burned: 7 (million)
% 3.50/1.46 % (4049376)------------------------------
% 3.50/1.46 % (4049376)------------------------------
% 3.50/1.46 % (4049367)Success in time 0.411 s
% 3.50/1.46 % Vampire exiting
%------------------------------------------------------------------------------