%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET012-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 3.47s 12.03s
% Output : Refutation 3.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 23 ( 8 unt; 0 def)
% Number of atoms : 48 ( 20 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 46 ( 21 ~; 25 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 2 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 : 26 ( 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( ~ member(X0,X1)
| little_set(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2) ).
fof(f2,axiom,
! [X0,X1] :
( little_set(f1(X0,X1))
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',extensionality1) ).
fof(f3,axiom,
! [X0,X1] :
( member(f1(X0,X1),X1)
| member(f1(X0,X1),X0)
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',extensionality2) ).
fof(f4,axiom,
! [X0,X1] :
( ~ member(f1(X0,X1),X1)
| ~ member(f1(X0,X1),X0)
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',extensionality3) ).
fof(f5,axiom,
! [X0,X1] :
( ~ member(X0,complement(X1))
| ~ member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement1) ).
fof(f6,axiom,
! [X0,X1] :
( member(X0,complement(X1))
| ~ little_set(X0)
| member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement2) ).
fof(f9,axiom,
complement(as) = bs,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement_of_a_is_b) ).
fof(f10,axiom,
complement(bs) = cs,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement_of_b_is_c) ).
fof(f11,negated_conjecture,
as != cs,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_equals_c) ).
fof(f12,plain,
as != complement(bs),
inference(superposition,[],[f11,f10]) ).
fof(f13,plain,
as != complement(complement(as)),
inference(superposition,[],[f12,f9]) ).
fof(f17,plain,
! [X0,X1] :
( member(f1(X0,complement(X1)),X0)
| complement(X1) = X0
| ~ member(f1(X0,complement(X1)),X1) ),
inference(resolution,[],[f3,f5]) ).
fof(f19,plain,
! [X0,X1] :
( ~ member(f1(X0,complement(X1)),X0)
| complement(X1) = X0
| ~ little_set(f1(X0,complement(X1)))
| member(f1(X0,complement(X1)),X1) ),
inference(resolution,[],[f4,f6]) ).
fof(f22,plain,
! [X0,X1] :
( member(f1(X0,complement(X1)),X1)
| complement(X1) = X0
| ~ member(f1(X0,complement(X1)),X0) ),
inference(forward_subsumption_resolution,[],[f19,f1]) ).
fof(f28,plain,
! [X0,X1] :
( ~ member(f1(X1,complement(complement(X0))),X1)
| complement(complement(X0)) = X1
| ~ member(f1(X1,complement(complement(X0))),X0) ),
inference(resolution,[],[f22,f5]) ).
fof(f40,plain,
! [X0] :
( ~ member(f1(X0,complement(complement(X0))),X0)
| complement(complement(X0)) = X0 ),
inference(factoring,[],[f28]) ).
fof(f45,plain,
! [X0] :
( complement(complement(X0)) = X0
| complement(complement(X0)) = X0
| ~ member(f1(X0,complement(complement(X0))),complement(X0)) ),
inference(resolution,[],[f40,f17]) ).
fof(f47,plain,
! [X0] :
( ~ member(f1(X0,complement(complement(X0))),complement(X0))
| complement(complement(X0)) = X0 ),
inference(duplicate_literal_removal,[],[f45]) ).
fof(f50,plain,
! [X0] :
( complement(complement(X0)) = X0
| ~ little_set(f1(X0,complement(complement(X0))))
| member(f1(X0,complement(complement(X0))),X0) ),
inference(resolution,[],[f47,f6]) ).
fof(f52,plain,
! [X0] :
( complement(complement(X0)) = X0
| ~ little_set(f1(X0,complement(complement(X0)))) ),
inference(forward_subsumption_resolution,[],[f50,f40]) ).
fof(f53,plain,
! [X0] : complement(complement(X0)) = X0,
inference(forward_subsumption_resolution,[],[f52,f2]) ).
fof(f59,plain,
as != as,
inference(superposition,[],[f13,f53]) ).
fof(f71,plain,
$false,
inference(trivial_inequality_removal,[],[f59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET012-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/10.41 % Computer : n003.cluster.edu
% 0.11/10.41 % Model : x86_64 x86_64
% 0.11/10.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.41 % Memory : 8046.5625MB
% 0.11/10.41 % OS : Linux 6.8.0-71-generic
% 0.11/10.41 % CPULimit : 300
% 0.11/10.41 % WCLimit : 300
% 0.11/10.41 % DateTime : Mon Sep 28 00:05:23 UTC 2026
% 0.11/10.42 % CPUTime :
% 0.11/10.42 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/10.45 Running first-order theorem proving
% 0.11/10.45 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
% 3.47/12.03 % (1066328)Input is clausal, will run a generic CNF schedule.
% 3.47/12.03 % (1066339)dis-21_1_sil=8000:lcm=predicate:random_seed=1765174419: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)
% 3.47/12.03 % (1066339)Refutation not found, incomplete strategy
% 3.47/12.03 % (1066339)------------------------------
% 3.47/12.03 % (1066339)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.47/12.03 % (1066339)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.47/12.03 % (1066339)CaDiCaL version: 2.1.3
% 3.47/12.03 % (1066339)Termination reason: Refutation not found, incomplete strategy
% 3.47/12.03 % (1066339)Time elapsed: 0.001 s
% 3.47/12.03 % (1066339)Peak memory usage: 88 MB
% 3.47/12.03 % (1066339)Instructions burned: 1 (million)
% 3.47/12.03 % (1066333)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=316887096:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.47/12.03 % (1066334)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=302289220:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.47/12.03 % (1066338)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=211683028:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.47/12.03 % (1066337)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3030092236:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.47/12.03 % (1066335)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2688199127:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.47/12.03 % (1066336)lrs+10_1_sil=8000:sp=occurrence:random_seed=4195872820:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.47/12.03 % (1066337)First to succeed.
% 3.47/12.03 % (1066337)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1066328"
% 3.47/12.03 % (1066338)Also succeeded, but the first one will report.
% 3.47/12.03 % (1066336)Also succeeded, but the first one will report.
% 3.47/12.03 % (1066339)------------------------------
% 3.47/12.03 % (1066339)------------------------------
% 3.47/12.03 % (1066347)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=347127543:i=143:sd=2:aac=none:ss=axioms:sgt=16_2992 on theBenchmark for (2992ds/143Mi)
% 3.47/12.03 % (1066347)Also succeeded, but the first one will report.
% 3.47/12.03 % (1066337)Refutation found. Thanks to Tanya!
% 3.47/12.03 % SZS status Unsatisfiable for theBenchmark
% 3.47/12.03 % SZS output start Proof for theBenchmark
% See solution above
% 3.47/12.03 % (1066337)------------------------------
% 3.47/12.03 % (1066337)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.47/12.03 % (1066337)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.47/12.03 % (1066337)CaDiCaL version: 2.1.3
% 3.47/12.03 % (1066337)Termination reason: Refutation
% 3.47/12.03 % (1066337)Time elapsed: 0.003 s
% 3.47/12.03 % (1066337)Peak memory usage: 88 MB
% 3.47/12.03 % (1066337)Instructions burned: 3 (million)
% 3.47/12.03 % (1066337)------------------------------
% 3.47/12.03 % (1066337)------------------------------
% 3.47/12.03 % (1066328)Success in time 0.93 s
% 3.47/12.03 % Vampire exiting
%------------------------------------------------------------------------------