%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP010+2 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n012.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 11:34:04 AM UTC 2026
% Result : Theorem 0.04s 5.37s
% Output : Refutation 0.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 1
% Syntax : Number of formulae : 11 ( 3 unt; 0 def)
% Number of atoms : 49 ( 0 equ)
% Maximal formula atoms : 8 ( 4 avg)
% Number of connectives : 54 ( 16 ~; 8 |; 19 &)
% ( 2 <=>; 8 =>; 0 <=; 1 <~>)
% Maximal formula depth : 12 ( 7 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 20 ( 8 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f41,conjecture,
! [X0] :
( ne(X0)
=> ! [X1] :
( ne(X1)
=> ! [X2] :
( mem(X2,arr(X0,bool))
=> ! [X3] :
( mem(X3,arr(X1,bool))
=> ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3))
<=> ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Ecardinal_2ECARD__NOT__LE) ).
fof(f42,negated_conjecture,
~ ! [X0] :
( ne(X0)
=> ! [X1] :
( ne(X1)
=> ! [X2] :
( mem(X2,arr(X0,bool))
=> ! [X3] :
( mem(X3,arr(X1,bool))
=> ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3))
<=> ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3)) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f41]) ).
fof(f91,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3))
<~> ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3)) )
& mem(X3,arr(X1,bool)) )
& mem(X2,arr(X0,bool)) )
& ne(X1) )
& ne(X0) ),
inference(ennf_transformation,[],[f42]) ).
fof(f144,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3))
| p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3)) )
& ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3))
| ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3)) )
& mem(X3,arr(X1,bool)) )
& mem(X2,arr(X0,bool)) )
& ne(X1) )
& ne(X0) ),
inference(nnf_transformation,[],[f91]) ).
fof(f145,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3))
| p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3)) )
& ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3))
| ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X0,X1),X2),X3)) )
& mem(X3,arr(X1,bool)) )
& mem(X2,arr(X0,bool)) )
& ne(X1) )
& ne(X0) ),
inference(flattening,[],[f144]) ).
fof(f146,plain,
( ( p(ap(ap(c_2Ecardinal_2Ecardleq(sK10,sK11),sK12),sK13))
| p(ap(ap(c_2Ecardinal_2Ecardleq(sK10,sK11),sK12),sK13)) )
& ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK10,sK11),sK12),sK13))
| ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK10,sK11),sK12),sK13)) )
& mem(sK13,arr(sK11,bool))
& mem(sK12,arr(sK10,bool))
& ne(sK11)
& ne(sK10) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11,sK12,sK13]),skolemize(X0,sK10),skolemize(X1,sK11),skolemize(X2,sK12),skolemize(X3,sK13)],[f145]) ).
fof(f259,plain,
( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK10,sK11),sK12),sK13))
| ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK10,sK11),sK12),sK13)) ),
inference(cnf_transformation,[],[f146]) ).
fof(f260,plain,
( p(ap(ap(c_2Ecardinal_2Ecardleq(sK10,sK11),sK12),sK13))
| p(ap(ap(c_2Ecardinal_2Ecardleq(sK10,sK11),sK12),sK13)) ),
inference(cnf_transformation,[],[f146]) ).
fof(f261,plain,
~ p(ap(ap(c_2Ecardinal_2Ecardleq(sK10,sK11),sK12),sK13)),
inference(duplicate_literal_removal,[],[f259]) ).
fof(f262,plain,
p(ap(ap(c_2Ecardinal_2Ecardleq(sK10,sK11),sK12),sK13)),
inference(duplicate_literal_removal,[],[f260]) ).
fof(f263,plain,
$false,
inference(forward_subsumption_resolution,[],[f262,f261]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : ITP010+2 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.04/5.32 % Computer : n012.cluster.edu
% 0.04/5.32 % Model : x86_64 x86_64
% 0.04/5.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/5.32 % Memory : 8046.5625MB
% 0.04/5.32 % OS : Linux 6.8.0-71-generic
% 0.04/5.32 % CPULimit : 300
% 0.04/5.32 % WCLimit : 300
% 0.04/5.32 % DateTime : Sun Sep 27 11:56:44 UTC 2026
% 0.04/5.32 % CPUTime :
% 0.04/5.32 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.04/5.34 Running first-order model finding
% 0.04/5.34 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
% 0.04/5.37 % (2248665)Will run a generic schedule for satisfiability detection.
% 0.04/5.37 % (2248671)% WARNING: option uhcvi not known.
% 0.04/5.37 % (2248670)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2067755722_2999 on theBenchmark for (2999ds/0Mi)
% 0.04/5.37 % (2248672)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2856100723:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.04/5.37 % (2248676)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1759951901:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.04/5.37 % (2248671)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2573422994:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.04/5.37 % (2248674)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3358534258:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.04/5.37 % (2248673)dis+10_1_sil=32000:sp=arity:random_seed=1111464436:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.04/5.37 % (2248675)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1220053387:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.04/5.37 % (2248672) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2248665-2248672"...
% 0.04/5.37 % (2248675) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2248665-2248675"...
% 0.04/5.37 % (2248671) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2248665-2248671"...
% 0.04/5.37 % (2248673) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2248665-2248673"...
% 0.04/5.37 % (2248676) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2248665-2248676"...
% 0.04/5.37 % (2248674) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2248665-2248674"...
% 0.04/5.37 % (2248675)...printing done.
% 0.04/5.37 % (2248672)...printing done.
% 0.04/5.37 % (2248671)...printing done.
% 0.04/5.37 % (2248673)...printing done.
% 0.04/5.37 % (2248674)...printing done.
% 0.04/5.37 % (2248676)...printing done.
% 0.04/5.37 % (2248675)Refutation found. Thanks to Tanya!
% 0.04/5.37 % SZS status Theorem for theBenchmark
% 0.04/5.37 % SZS output start Proof for theBenchmark
% See solution above
% 0.04/5.37 % (2248675)------------------------------
% 0.04/5.37 % (2248675)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.04/5.37 % (2248675)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.04/5.37 % (2248675)CaDiCaL version: 2.1.3
% 0.04/5.37 % (2248675)Termination reason: Refutation
% 0.04/5.37 % (2248675)Time elapsed: 0.001 s
% 0.04/5.37 % (2248675)Peak memory usage: 11 MB
% 0.04/5.37 % (2248675)Instructions burned: 3 (million)
% 0.04/5.37 % (2248665)Success in time 0.026 s
% 0.04/5.37 % Vampire exiting
%------------------------------------------------------------------------------