%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET351+4 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 12:40:49 PM UTC 2026
% Result : Theorem 5.18s 1.87s
% Output : Refutation 5.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 41 ( 9 unt; 0 def)
% Number of atoms : 101 ( 6 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 103 ( 43 ~; 40 |; 12 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 75 ( 70 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset) ).
fof(f2,axiom,
! [X0,X1] :
( equal_set(X0,X1)
<=> ( subset(X0,X1)
& subset(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_set) ).
fof(f8,axiom,
! [X0,X1] :
( member(X0,singleton(X1))
<=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton) ).
fof(f10,axiom,
! [X0,X1] :
( member(X0,sum(X1))
<=> ? [X2] :
( member(X2,X1)
& member(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum) ).
fof(f12,conjecture,
! [X0] : equal_set(sum(singleton(X0)),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI39) ).
fof(f13,negated_conjecture,
~ ! [X0] : equal_set(sum(singleton(X0)),X0),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [X0,X1] :
( ( subset(X0,X1)
& subset(X1,X0) )
=> equal_set(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f15,plain,
! [X0,X1] :
( ! [X2] :
( member(X2,X0)
=> member(X2,X1) )
=> subset(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f1]) ).
fof(f16,plain,
? [X0] : ~ equal_set(sum(singleton(X0)),X0),
inference(ennf_transformation,[],[f13]) ).
fof(f17,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f18,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(flattening,[],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f20,plain,
~ equal_set(sum(singleton(sK0)),sK0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f16]) ).
fof(f21,plain,
! [X0,X1] :
( ( member(X0,singleton(X1))
| X0 != X1 )
& ( X0 = X1
| ~ member(X0,singleton(X1)) ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f22,plain,
! [X0,X1] :
( ( member(X0,sum(X1))
| ! [X2] :
( ~ member(X2,X1)
| ~ member(X0,X2) ) )
& ( ? [X2] :
( member(X2,X1)
& member(X0,X2) )
| ~ member(X0,sum(X1)) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f23,plain,
! [X0,X1] :
( ( member(X0,sum(X1))
| ! [X2] :
( ~ member(X2,X1)
| ~ member(X0,X2) ) )
& ( ? [X3] :
( member(X3,X1)
& member(X0,X3) )
| ~ member(X0,sum(X1)) ) ),
inference(rectify,[],[f22]) ).
fof(f24,plain,
! [X0,X1] :
( ( member(X0,sum(X1))
| ! [X2] :
( ~ member(X2,X1)
| ~ member(X0,X2) ) )
& ( ( member(sK1(X0,X1),X1)
& member(X0,sK1(X0,X1)) )
| ~ member(X0,sum(X1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1))],[f23]) ).
fof(f25,plain,
! [X0,X1] :
( subset(X0,X1)
| ( ~ member(sK2(X0,X1),X1)
& member(sK2(X0,X1),X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f19]) ).
fof(f26,plain,
~ equal_set(sum(singleton(sK0)),sK0),
inference(cnf_transformation,[],[f20]) ).
fof(f27,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(cnf_transformation,[],[f18]) ).
fof(f28,plain,
! [X0,X1] :
( ~ member(X0,singleton(X1))
| X0 = X1 ),
inference(cnf_transformation,[],[f21]) ).
fof(f29,plain,
! [X0,X1] :
( member(X0,singleton(X1))
| X0 != X1 ),
inference(cnf_transformation,[],[f21]) ).
fof(f30,plain,
! [X0,X1] :
( member(X0,sK1(X0,X1))
| ~ member(X0,sum(X1)) ),
inference(cnf_transformation,[],[f24]) ).
fof(f31,plain,
! [X0,X1] :
( member(sK1(X0,X1),X1)
| ~ member(X0,sum(X1)) ),
inference(cnf_transformation,[],[f24]) ).
fof(f32,plain,
! [X2,X0,X1] :
( member(X0,sum(X1))
| ~ member(X2,X1)
| ~ member(X0,X2) ),
inference(cnf_transformation,[],[f24]) ).
fof(f33,plain,
! [X0,X1] :
( member(sK2(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f34,plain,
! [X0,X1] :
( ~ member(sK2(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f35,plain,
! [X1] : member(X1,singleton(X1)),
inference(equality_resolution,[],[f29]) ).
fof(f40,plain,
( ~ subset(sK0,sum(singleton(sK0)))
| ~ subset(sum(singleton(sK0)),sK0) ),
inference(resolution,[],[f27,f26]) ).
fof(f41,plain,
! [X0,X1] :
( sK1(X0,singleton(X1)) = X1
| ~ member(X0,sum(singleton(X1))) ),
inference(resolution,[],[f31,f28]) ).
fof(f42,plain,
! [X2,X0,X1] :
( ~ member(sK2(X2,sum(X1)),X0)
| ~ member(X0,X1)
| subset(X2,sum(X1)) ),
inference(resolution,[],[f32,f34]) ).
fof(f48,plain,
! [X0,X1] :
( member(X1,X0)
| ~ member(X1,sum(singleton(X0)))
| ~ member(X1,sum(singleton(X0))) ),
inference(superposition,[],[f30,f41]) ).
fof(f49,plain,
! [X0,X1] :
( ~ member(X1,sum(singleton(X0)))
| member(X1,X0) ),
inference(duplicate_literal_removal,[],[f48]) ).
fof(f52,plain,
! [X0,X1] :
( member(sK2(sum(singleton(X0)),X1),X0)
| subset(sum(singleton(X0)),X1) ),
inference(resolution,[],[f49,f33]) ).
fof(f58,plain,
! [X0,X1] :
( ~ member(X0,X1)
| subset(X0,sum(X1))
| subset(X0,sum(X1)) ),
inference(resolution,[],[f42,f33]) ).
fof(f64,plain,
! [X0,X1] :
( subset(X0,sum(X1))
| ~ member(X0,X1) ),
inference(duplicate_literal_removal,[],[f58]) ).
fof(f65,plain,
( ~ member(sK0,singleton(sK0))
| ~ subset(sum(singleton(sK0)),sK0) ),
inference(resolution,[],[f64,f40]) ).
fof(f66,plain,
~ subset(sum(singleton(sK0)),sK0),
inference(forward_subsumption_resolution,[],[f65,f35]) ).
fof(f70,plain,
! [X0] :
( subset(sum(singleton(X0)),X0)
| subset(sum(singleton(X0)),X0) ),
inference(resolution,[],[f52,f34]) ).
fof(f76,plain,
! [X0] : subset(sum(singleton(X0)),X0),
inference(duplicate_literal_removal,[],[f70]) ).
fof(f87,plain,
$false,
inference(resolution,[],[f76,f66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET351+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.41 % Computer : n011.cluster.edu
% 0.13/0.41 % Model : x86_64 x86_64
% 0.13/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.41 % Memory : 8046.5625MB
% 0.13/0.41 % OS : Linux 6.8.0-71-generic
% 0.13/0.41 % CPULimit : 300
% 0.13/0.41 % WCLimit : 300
% 0.13/0.41 % DateTime : Mon Sep 28 01:32:46 UTC 2026
% 0.13/0.41 % CPUTime :
% 0.13/0.41 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.45 Running first-order theorem proving
% 0.13/0.46 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.18/1.87 % (2935404)Detected formulas, will run a generic FOF schedule.
% 5.18/1.87 % (2935418)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=2816574606:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.18/1.87 % (2935422)dis-21_1_sil=8000:lcm=predicate:random_seed=3074849813: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)
% 5.18/1.87 % (2935422)Instruction limit reached!
% 5.18/1.87 % (2935422)------------------------------
% 5.18/1.87 % (2935422)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.18/1.87 % (2935422)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.18/1.87 % (2935422)CaDiCaL version: 2.1.3
% 5.18/1.87 % (2935422)Termination reason: Instruction limit
% 5.18/1.87 % (2935422)Termination phase: Saturation
% 5.18/1.87 % (2935422)Time elapsed: 0.070 s
% 5.18/1.87 % (2935422)Peak memory usage: 89 MB
% 5.18/1.87 % (2935422)Instructions burned: 130 (million)
% 5.18/1.87 % (2935419)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3414007869:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.18/1.87 % (2935416)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=3750807967:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.18/1.87 % (2935420)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1730370750:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.18/1.87 % (2935421)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2600962604:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.18/1.87 % (2935417)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=2736806162:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.18/1.87 % (2935419)Refutation not found, incomplete strategy
% 5.18/1.87 % (2935419)------------------------------
% 5.18/1.87 % (2935419)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.18/1.87 % (2935419)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.18/1.87 % (2935419)CaDiCaL version: 2.1.3
% 5.18/1.87 % (2935419)Termination reason: Refutation not found, incomplete strategy
% 5.18/1.87 % (2935419)Time elapsed: 0.001 s
% 5.18/1.87 % (2935419)Peak memory usage: 88 MB
% 5.18/1.87 % (2935420)First to succeed.
% 5.18/1.87 % (2935420)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2935404"
% 5.18/1.87 % (2935421)Also succeeded, but the first one will report.
% 5.18/1.87 % (2935434)lrs+10_1_sil=8000:sp=occurrence:random_seed=2422077182:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 5.18/1.87 % (2935434)Instruction limit reached!
% 5.18/1.87 % (2935434)------------------------------
% 5.18/1.87 % (2935434)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.18/1.87 % (2935434)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.18/1.87 % (2935434)CaDiCaL version: 2.1.3
% 5.18/1.87 % (2935434)Termination reason: Instruction limit
% 5.18/1.87 % (2935434)Termination phase: Saturation
% 5.18/1.87 % (2935434)Time elapsed: 0.147 s
% 5.18/1.87 % (2935434)Peak memory usage: 91 MB
% 5.18/1.87 % (2935434)Instructions burned: 287 (million)
% 5.18/1.87 % (2935419)------------------------------
% 5.18/1.87 % (2935419)------------------------------
% 5.18/1.87 % (2935420)Refutation found. Thanks to Tanya!
% 5.18/1.87 % SZS status Theorem for theBenchmark
% 5.18/1.87 % SZS output start Proof for theBenchmark
% See solution above
% 5.18/1.87 % (2935420)------------------------------
% 5.18/1.87 % (2935420)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.18/1.87 % (2935420)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.18/1.87 % (2935420)CaDiCaL version: 2.1.3
% 5.18/1.87 % (2935420)Termination reason: Refutation
% 5.18/1.87 % (2935420)Time elapsed: 0.005 s
% 5.18/1.87 % (2935420)Peak memory usage: 88 MB
% 5.18/1.87 % (2935420)Instructions burned: 3 (million)
% 5.18/1.87 % (2935420)------------------------------
% 5.18/1.87 % (2935420)------------------------------
% 5.18/1.87 % (2935404)Success in time 0.63 s
% 5.18/1.87 % Vampire exiting
%------------------------------------------------------------------------------