%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET587+3 : 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 : n007.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 12:41:14 PM UTC 2026
% Result : Theorem 2.71s 1.34s
% Output : Refutation 2.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 44 ( 8 unt; 0 def)
% Number of atoms : 122 ( 18 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 129 ( 51 ~; 52 |; 18 &)
% ( 6 <=>; 1 =>; 0 <=; 1 <~>)
% 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 76 ( 70 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1,X2] :
( member(X2,difference(X0,X1))
<=> ( member(X2,X0)
& ~ member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_defn) ).
fof(f3,axiom,
! [X0] : ~ member(X0,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_defn) ).
fof(f4,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
fof(f5,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X0,X1)
& subset(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
fof(f9,conjecture,
! [X0,X1] :
( difference(X0,X1) = empty_set
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_difference_empty_set) ).
fof(f10,negated_conjecture,
~ ! [X0,X1] :
( difference(X0,X1) = empty_set
<=> subset(X0,X1) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f11,plain,
? [X0,X1] :
( difference(X0,X1) = empty_set
<~> subset(X0,X1) ),
inference(ennf_transformation,[],[f10]) ).
fof(f13,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f14,plain,
? [X0,X1] :
( ( ~ subset(X0,X1)
| difference(X0,X1) != empty_set )
& ( subset(X0,X1)
| difference(X0,X1) = empty_set ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f15,plain,
( ( ~ subset(sK0,sK1)
| empty_set != difference(sK0,sK1) )
& ( subset(sK0,sK1)
| empty_set = difference(sK0,sK1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f14]) ).
fof(f19,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f20,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(flattening,[],[f19]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ( member(X2,difference(X0,X1))
| ~ member(X2,X0)
| member(X2,X1) )
& ( ( member(X2,X0)
& ~ member(X2,X1) )
| ~ member(X2,difference(X0,X1)) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ( member(X2,difference(X0,X1))
| ~ member(X2,X0)
| member(X2,X1) )
& ( ( member(X2,X0)
& ~ member(X2,X1) )
| ~ member(X2,difference(X0,X1)) ) ),
inference(flattening,[],[f23]) ).
fof(f25,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,[],[f13]) ).
fof(f26,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,[],[f25]) ).
fof(f27,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))],[f26]) ).
fof(f28,plain,
( empty_set = difference(sK0,sK1)
| subset(sK0,sK1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f29,plain,
( empty_set != difference(sK0,sK1)
| ~ subset(sK0,sK1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f36,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f20]) ).
fof(f39,plain,
! [X2,X0,X1] :
( ~ member(X2,difference(X0,X1))
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f40,plain,
! [X2,X0,X1] :
( ~ member(X2,difference(X0,X1))
| member(X2,X0) ),
inference(cnf_transformation,[],[f24]) ).
fof(f41,plain,
! [X2,X0,X1] :
( member(X2,difference(X0,X1))
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f42,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f3]) ).
fof(f44,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f45,plain,
! [X0,X1] :
( member(sK4(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f46,plain,
! [X0,X1] :
( ~ member(sK4(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f54,plain,
! [X0] : subset(empty_set,X0),
inference(resolution,[],[f45,f42]) ).
fof(f55,plain,
! [X2,X0,X1] :
( member(sK4(difference(X0,X1),X2),X0)
| subset(difference(X0,X1),X2) ),
inference(resolution,[],[f45,f40]) ).
fof(f56,plain,
! [X2,X0,X1] :
( ~ member(sK4(difference(X0,X1),X2),X1)
| subset(difference(X0,X1),X2) ),
inference(resolution,[],[f45,f39]) ).
fof(f60,plain,
! [X0] :
( ~ subset(X0,empty_set)
| empty_set = X0 ),
inference(resolution,[],[f36,f54]) ).
fof(f73,plain,
! [X0] :
( member(X0,empty_set)
| ~ member(X0,sK0)
| member(X0,sK1)
| subset(sK0,sK1) ),
inference(superposition,[],[f41,f28]) ).
fof(f74,plain,
! [X0] :
( member(X0,empty_set)
| ~ member(X0,sK0)
| member(X0,sK1) ),
inference(forward_subsumption_resolution,[],[f73,f44]) ).
fof(f75,plain,
! [X0] :
( member(X0,sK1)
| ~ member(X0,sK0) ),
inference(forward_subsumption_resolution,[],[f74,f42]) ).
fof(f79,plain,
! [X0] :
( ~ member(sK4(X0,sK1),sK0)
| subset(X0,sK1) ),
inference(resolution,[],[f75,f46]) ).
fof(f86,plain,
( subset(sK0,sK1)
| subset(sK0,sK1) ),
inference(resolution,[],[f79,f45]) ).
fof(f88,plain,
subset(sK0,sK1),
inference(duplicate_literal_removal,[],[f86]) ).
fof(f167,plain,
! [X0,X1] :
( ~ member(sK4(difference(X0,sK1),X1),sK0)
| subset(difference(X0,sK1),X1) ),
inference(resolution,[],[f56,f75]) ).
fof(f298,plain,
! [X0] :
( subset(difference(sK0,sK1),X0)
| subset(difference(sK0,sK1),X0) ),
inference(resolution,[],[f167,f55]) ).
fof(f304,plain,
! [X0] : subset(difference(sK0,sK1),X0),
inference(duplicate_literal_removal,[],[f298]) ).
fof(f307,plain,
empty_set = difference(sK0,sK1),
inference(resolution,[],[f304,f60]) ).
fof(f345,plain,
( empty_set != empty_set
| ~ subset(sK0,sK1) ),
inference(superposition,[],[f29,f307]) ).
fof(f367,plain,
~ subset(sK0,sK1),
inference(trivial_inequality_removal,[],[f345]) ).
fof(f368,plain,
$false,
inference(forward_subsumption_resolution,[],[f367,f88]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET587+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n007.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 28 02:11:25 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.39 Running first-order theorem proving
% 0.10/0.39 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
% 2.71/1.34 % (1964247)Detected formulas, will run a generic FOF schedule.
% 2.71/1.34 % (1964256)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2918610360:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.71/1.34 % (1964256)First to succeed.
% 2.71/1.34 % (1964256)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1964247"
% 2.71/1.34 % (1964258)dis-21_1_sil=8000:lcm=predicate:random_seed=917391148: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)
% 2.71/1.34 % (1964252)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=1905718003:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.71/1.34 % (1964254)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=1023905686:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.71/1.34 % (1964253)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=1349404147:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.71/1.34 % (1964255)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2541181606:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.71/1.34 % (1964257)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4098734761:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.71/1.34 % (1964255)Refutation not found, incomplete strategy
% 2.71/1.34 % (1964255)------------------------------
% 2.71/1.34 % (1964255)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.71/1.34 % (1964255)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.71/1.34 % (1964255)CaDiCaL version: 2.1.3
% 2.71/1.34 % (1964255)Termination reason: Refutation not found, incomplete strategy
% 2.71/1.34 % (1964255)Time elapsed: 0.002 s
% 2.71/1.34 % (1964255)Peak memory usage: 88 MB
% 2.71/1.34 % (1964255)Instructions burned: 1 (million)
% 2.71/1.34 % (1964257)Also succeeded, but the first one will report.
% 2.71/1.34 % (1964258)Instruction limit reached!
% 2.71/1.34 % (1964258)------------------------------
% 2.71/1.34 % (1964258)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.71/1.34 % (1964258)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.71/1.34 % (1964258)CaDiCaL version: 2.1.3
% 2.71/1.34 % (1964258)Termination reason: Instruction limit
% 2.71/1.34 % (1964258)Termination phase: Saturation
% 2.71/1.34 % (1964258)Time elapsed: 0.076 s
% 2.71/1.34 % (1964258)Peak memory usage: 89 MB
% 2.71/1.34 % (1964258)Instructions burned: 130 (million)
% 2.71/1.34 % (1964256)Refutation found. Thanks to Tanya!
% 2.71/1.34 % SZS status Theorem for theBenchmark
% 2.71/1.34 % SZS output start Proof for theBenchmark
% See solution above
% 2.71/1.34 % (1964256)------------------------------
% 2.71/1.34 % (1964256)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.71/1.34 % (1964256)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.71/1.34 % (1964256)CaDiCaL version: 2.1.3
% 2.71/1.34 % (1964256)Termination reason: Refutation
% 2.71/1.34 % (1964256)Time elapsed: 0.005 s
% 2.71/1.34 % (1964256)Peak memory usage: 88 MB
% 2.71/1.34 % (1964256)Instructions burned: 11 (million)
% 2.71/1.34 % (1964256)------------------------------
% 2.71/1.34 % (1964256)------------------------------
% 2.71/1.34 % (1964247)Success in time 0.298 s
% 2.71/1.34 % Vampire exiting
%------------------------------------------------------------------------------