%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET012-2 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 12:39:30 PM UTC 2026
% Result : Unsatisfiable 4.69s 1.75s
% Output : Refutation 4.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of formulae : 34 ( 11 unt; 0 def)
% Number of atoms : 59 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 46 ( 21 ~; 25 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 29 ( 29 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X2,X0,X1] :
( ~ subset(X1,X2)
| ~ member(X0,X1)
| member(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',membership_in_subsets) ).
fof(f3,axiom,
! [X0,X1] :
( member(member_of_1_not_of_2(X0,X1),X0)
| subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsets_axiom1) ).
fof(f4,axiom,
! [X0,X1] :
( ~ member(member_of_1_not_of_2(X0,X1),X1)
| subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsets_axiom2) ).
fof(f5,axiom,
! [X0,X1] :
( member(X0,complement(X1))
| member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_set_or_complement) ).
fof(f6,axiom,
! [X0,X1] :
( ~ member(X0,complement(X1))
| ~ member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_member_of_set_and_complement) ).
fof(f13,axiom,
! [X0,X1] :
( ~ equal_sets(X0,X1)
| subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_equal_sets_are_subsets1) ).
fof(f14,axiom,
! [X0,X1] :
( ~ equal_sets(X0,X1)
| subset(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_equal_sets_are_subsets2) ).
fof(f15,axiom,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_sets(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsets_are_set_equal_sets) ).
fof(f22,axiom,
equal_sets(complement(a),b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement_of_a_is_b) ).
fof(f23,axiom,
equal_sets(complement(b),c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement_of_b_is_c) ).
fof(f24,negated_conjecture,
~ equal_sets(a,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_equals_c) ).
fof(f25,plain,
subset(complement(a),b),
inference(resolution,[],[f22,f13]) ).
fof(f26,plain,
subset(b,complement(a)),
inference(resolution,[],[f22,f14]) ).
fof(f29,plain,
subset(complement(b),c),
inference(resolution,[],[f23,f13]) ).
fof(f30,plain,
subset(c,complement(b)),
inference(resolution,[],[f23,f14]) ).
fof(f33,plain,
! [X0] :
( ~ member(X0,complement(a))
| member(X0,b) ),
inference(resolution,[],[f25,f2]) ).
fof(f35,plain,
! [X0] :
( member(X0,complement(a))
| ~ member(X0,b) ),
inference(resolution,[],[f26,f2]) ).
fof(f42,plain,
! [X0] :
( ~ member(X0,complement(b))
| member(X0,c) ),
inference(resolution,[],[f29,f2]) ).
fof(f44,plain,
! [X0] :
( member(X0,complement(b))
| ~ member(X0,c) ),
inference(resolution,[],[f30,f2]) ).
fof(f55,plain,
! [X0] :
( member(X0,b)
| member(X0,a) ),
inference(resolution,[],[f33,f5]) ).
fof(f59,plain,
! [X0] :
( ~ member(X0,b)
| ~ member(X0,a) ),
inference(resolution,[],[f35,f6]) ).
fof(f68,plain,
! [X0] :
( member(X0,c)
| member(X0,b) ),
inference(resolution,[],[f42,f5]) ).
fof(f70,plain,
! [X0] :
( member(member_of_1_not_of_2(X0,c),b)
| subset(X0,c) ),
inference(resolution,[],[f68,f4]) ).
fof(f72,plain,
! [X0] :
( ~ member(X0,c)
| ~ member(X0,b) ),
inference(resolution,[],[f44,f6]) ).
fof(f75,plain,
! [X0] :
( ~ member(member_of_1_not_of_2(c,X0),b)
| subset(c,X0) ),
inference(resolution,[],[f72,f3]) ).
fof(f99,plain,
! [X0] :
( ~ member(member_of_1_not_of_2(X0,c),a)
| subset(X0,c) ),
inference(resolution,[],[f70,f59]) ).
fof(f148,plain,
! [X0] :
( member(member_of_1_not_of_2(c,X0),a)
| subset(c,X0) ),
inference(resolution,[],[f75,f55]) ).
fof(f156,plain,
( subset(c,a)
| subset(c,a) ),
inference(resolution,[],[f148,f4]) ).
fof(f157,plain,
subset(c,a),
inference(duplicate_literal_removal,[],[f156]) ).
fof(f175,plain,
( subset(a,c)
| subset(a,c) ),
inference(resolution,[],[f99,f3]) ).
fof(f178,plain,
subset(a,c),
inference(duplicate_literal_removal,[],[f175]) ).
fof(f182,plain,
( ~ subset(c,a)
| equal_sets(a,c) ),
inference(resolution,[],[f178,f15]) ).
fof(f183,plain,
equal_sets(a,c),
inference(forward_subsumption_resolution,[],[f182,f157]) ).
fof(f184,plain,
$false,
inference(forward_subsumption_resolution,[],[f183,f24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET012-2 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.59 % Computer : n010.cluster.edu
% 0.11/0.59 % Model : x86_64 x86_64
% 0.11/0.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.59 % Memory : 8046.5625MB
% 0.11/0.59 % OS : Linux 6.8.0-71-generic
% 0.11/0.59 % CPULimit : 300
% 0.11/0.59 % WCLimit : 300
% 0.11/0.59 % DateTime : Mon Sep 28 00:03:33 UTC 2026
% 0.11/0.59 % CPUTime :
% 0.11/0.59 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.17/0.63 Running first-order theorem proving
% 0.17/0.63 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
% 4.69/1.75 % (1445341)Input is clausal, will run a generic CNF schedule.
% 4.69/1.75 % (1445390)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1398028789:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 4.69/1.75 % (1445392)lrs+10_1_sil=8000:sp=occurrence:random_seed=49202707:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 4.69/1.75 % (1445388)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=1603400444:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 4.69/1.75 % (1445391)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2978475659:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 4.69/1.75 % (1445395)dis-21_1_sil=8000:lcm=predicate:random_seed=2615749035:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 4.69/1.75 % (1445394)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=306703970:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 4.69/1.75 % (1445392)Refutation not found, incomplete strategy
% 4.69/1.75 % (1445392)------------------------------
% 4.69/1.75 % (1445392)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.69/1.75 % (1445392)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.69/1.75 % (1445392)CaDiCaL version: 2.1.3
% 4.69/1.75 % (1445392)Termination reason: Refutation not found, incomplete strategy
% 4.69/1.75 % (1445392)Time elapsed: 0.002 s
% 4.69/1.75 % (1445392)Peak memory usage: 88 MB
% 4.69/1.75 % (1445392)Instructions burned: 2 (million)
% 4.69/1.75 % (1445393)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1661942548:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 4.69/1.75 % (1445395)Instruction limit reached!
% 4.69/1.75 % (1445395)------------------------------
% 4.69/1.75 % (1445395)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.69/1.75 % (1445395)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.69/1.75 % (1445395)CaDiCaL version: 2.1.3
% 4.69/1.75 % (1445395)Termination reason: Instruction limit
% 4.69/1.75 % (1445395)Termination phase: Saturation
% 4.69/1.75 % (1445395)Time elapsed: 0.070 s
% 4.69/1.75 % (1445395)Peak memory usage: 89 MB
% 4.69/1.75 % (1445395)Instructions burned: 117 (million)
% 4.69/1.75 % (1445393)Instruction limit reached!
% 4.69/1.75 % (1445393)------------------------------
% 4.69/1.75 % (1445393)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.69/1.75 % (1445393)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.69/1.75 % (1445393)CaDiCaL version: 2.1.3
% 4.69/1.75 % (1445393)Termination reason: Instruction limit
% 4.69/1.75 % (1445393)Termination phase: Saturation
% 4.69/1.75 % (1445393)Time elapsed: 0.068 s
% 4.69/1.75 % (1445393)Peak memory usage: 88 MB
% 4.69/1.75 % (1445393)Instructions burned: 115 (million)
% 4.69/1.75 % (1445394)Instruction limit reached!
% 4.69/1.75 % (1445394)------------------------------
% 4.69/1.75 % (1445394)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.69/1.75 % (1445394)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.69/1.75 % (1445394)CaDiCaL version: 2.1.3
% 4.69/1.75 % (1445394)Termination reason: Instruction limit
% 4.69/1.75 % (1445394)Termination phase: Saturation
% 4.69/1.75 % (1445394)Time elapsed: 0.120 s
% 4.69/1.75 % (1445394)Peak memory usage: 89 MB
% 4.69/1.75 % (1445394)Instructions burned: 181 (million)
% 4.69/1.75 % (1445407)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=4079199652:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 4.69/1.75 % (1445407)First to succeed.
% 4.69/1.75 % (1445407)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1445341"
% 4.69/1.75 % (1445408)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1229994938:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 4.69/1.75 % (1445408)Refutation not found, incomplete strategy
% 4.69/1.75 % (1445408)------------------------------
% 4.69/1.75 % (1445408)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.69/1.75 % (1445408)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.69/1.75 % (1445408)CaDiCaL version: 2.1.3
% 4.69/1.75 % (1445408)Termination reason: Refutation not found, incomplete strategy
% 4.69/1.75 % (1445408)Time elapsed: 0.002 s
% 4.69/1.75 % (1445408)Peak memory usage: 87 MB
% 4.69/1.75 % (1445408)Instructions burned: 2 (million)
% 4.69/1.75 % (1445392)------------------------------
% 4.69/1.75 % (1445392)------------------------------
% 4.69/1.75 % (1445409)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=2731844040:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 4.69/1.75 % (1445409)Also succeeded, but the first one will report.
% 4.69/1.75 % (1445412)lrs+10_64_to=lpo:sil=8000:random_seed=2798181843:i=126:bd=preordered_2996 on theBenchmark for (2996ds/126Mi)
% 4.69/1.75 % (1445412)Also succeeded, but the first one will report.
% 4.69/1.75 % (1445407)Refutation found. Thanks to Tanya!
% 4.69/1.75 % SZS status Unsatisfiable for theBenchmark
% 4.69/1.75 % SZS output start Proof for theBenchmark
% See solution above
% 4.69/1.75 % (1445407)------------------------------
% 4.69/1.75 % (1445407)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.69/1.75 % (1445407)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.69/1.75 % (1445407)CaDiCaL version: 2.1.3
% 4.69/1.75 % (1445407)Termination reason: Refutation
% 4.69/1.75 % (1445407)Time elapsed: 0.004 s
% 4.69/1.75 % (1445407)Peak memory usage: 88 MB
% 4.69/1.75 % (1445407)Instructions burned: 4 (million)
% 4.69/1.75 % (1445407)------------------------------
% 4.69/1.75 % (1445407)------------------------------
% 4.69/1.75 % (1445341)Success in time 0.593 s
% 4.69/1.75 % Vampire exiting
%------------------------------------------------------------------------------