%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET012-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 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 12:42:34 PM UTC 2026
% Result : Unsatisfiable 0.19s 0.50s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 23 ( 8 unt; 0 def)
% Number of atoms : 50 ( 23 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 40 ( 13 ~; 27 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 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 : 28 ( 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( little_set(f1(X0,X1))
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',extensionality1) ).
fof(f3,axiom,
! [X0,X1] :
( member(f1(X0,X1),X0)
| member(f1(X0,X1),X1)
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',extensionality2) ).
fof(f4,axiom,
! [X0,X1] :
( ~ member(f1(X0,X1),X0)
| ~ member(f1(X0,X1),X1)
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',extensionality3) ).
fof(f5,axiom,
! [X0,X1] :
( ~ member(X0,complement(X1))
| ~ member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement1) ).
fof(f6,axiom,
! [X0,X1] :
( ~ little_set(X0)
| member(X0,complement(X1))
| member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement2) ).
fof(f9,axiom,
complement(as) = bs,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement_of_a_is_b) ).
fof(f10,axiom,
complement(bs) = cs,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement_of_b_is_c) ).
fof(f11,negated_conjecture,
as != cs,
file('/export/starexec/sandbox2/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(forward_demodulation,[],[f12,f9]) ).
fof(f15,plain,
! [X2,X0,X1] :
( member(f1(X0,X1),complement(X2))
| member(f1(X0,X1),X2)
| X0 = X1 ),
inference(resolution,[],[f6,f2]) ).
fof(f19,plain,
! [X0,X1] :
( ~ member(f1(complement(X0),X1),X0)
| complement(X0) = X1
| member(f1(complement(X0),X1),X1) ),
inference(resolution,[],[f3,f5]) ).
fof(f38,plain,
! [X0,X1] :
( member(f1(complement(X0),X1),X0)
| complement(X0) = X1
| ~ member(f1(complement(X0),X1),X1)
| complement(X0) = X1 ),
inference(resolution,[],[f15,f4]) ).
fof(f41,plain,
! [X0,X1] :
( ~ member(f1(complement(X0),X1),X1)
| complement(X0) = X1
| member(f1(complement(X0),X1),X0) ),
inference(duplicate_literal_removal,[],[f38]) ).
fof(f48,plain,
! [X0,X1] :
( complement(complement(X0)) = X1
| member(f1(complement(complement(X0)),X1),X1)
| member(f1(complement(complement(X0)),X1),X0)
| complement(complement(X0)) = X1 ),
inference(resolution,[],[f19,f15]) ).
fof(f51,plain,
! [X0,X1] :
( member(f1(complement(complement(X0)),X1),X1)
| member(f1(complement(complement(X0)),X1),X0)
| complement(complement(X0)) = X1 ),
inference(duplicate_literal_removal,[],[f48]) ).
fof(f108,plain,
! [X0] :
( member(f1(complement(complement(X0)),X0),X0)
| complement(complement(X0)) = X0 ),
inference(factoring,[],[f51]) ).
fof(f219,plain,
! [X0] :
( complement(complement(X0)) = X0
| complement(complement(X0)) = X0
| member(f1(complement(complement(X0)),X0),complement(X0)) ),
inference(resolution,[],[f108,f41]) ).
fof(f224,plain,
! [X0] :
( member(f1(complement(complement(X0)),X0),complement(X0))
| complement(complement(X0)) = X0 ),
inference(duplicate_literal_removal,[],[f219]) ).
fof(f363,plain,
! [X0] :
( complement(complement(X0)) = X0
| ~ member(f1(complement(complement(X0)),X0),X0) ),
inference(resolution,[],[f224,f5]) ).
fof(f368,plain,
! [X0] : complement(complement(X0)) = X0,
inference(forward_subsumption_resolution,[],[f363,f108]) ).
fof(f411,plain,
as != as,
inference(superposition,[],[f13,f368]) ).
fof(f440,plain,
$false,
inference(trivial_inequality_removal,[],[f411]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET012-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.38 % Computer : n004.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Mon Sep 28 00:03:24 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.43 Running first-order model finding
% 0.13/0.43 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.50 % (4021425)Will run a generic schedule for satisfiability detection.
% 0.19/0.50 % (4021432)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1721424855:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.50 % (4021431)% WARNING: option uhcvi not known.
% 0.19/0.50 % (4021430)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=502217765_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.50 % (4021436)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3285508723:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.50 % (4021435)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2946087125:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.50 % (4021433)dis+10_1_sil=32000:sp=arity:random_seed=852018407:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.50 % (4021434)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3779503553:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.50 % TRYING [1]
% 0.19/0.50 % TRYING [2]
% 0.19/0.50 % TRYING [3]
% 0.19/0.50 % TRYING [4]
% 0.19/0.50 % TRYING [5]
% 0.19/0.50 % (4021431)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2874405429:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.50 % (4021435) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4021425-4021435"...
% 0.19/0.50 % (4021435)...printing done.
% 0.19/0.50 % (4021435)Refutation found. Thanks to Tanya!
% 0.19/0.50 % SZS status Unsatisfiable for theBenchmark
% 0.19/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.50 % (4021435)------------------------------
% 0.19/0.50 % (4021435)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.50 % (4021435)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.50 % (4021435)CaDiCaL version: 2.1.3
% 0.19/0.50 % (4021435)Termination reason: Refutation
% 0.19/0.50 % (4021435)Time elapsed: 0.009 s
% 0.19/0.50 % (4021435)Peak memory usage: 11 MB
% 0.19/0.50 % (4021435)Instructions burned: 13 (million)
% 0.19/0.50 % (4021425)Success in time 0.059 s
% 0.19/0.50 % Vampire exiting
%------------------------------------------------------------------------------