%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET204-6 : 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 : n001.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 12:40:30 PM UTC 2026
% Result : Unsatisfiable 3.79s 1.51s
% Output : Refutation 3.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 5
% Syntax : Number of formulae : 10 ( 6 unt; 0 def)
% Number of atoms : 15 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 13 ( 8 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 12 ( 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f14,axiom,
! [X2,X3,X0,X1] :
( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| member(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartesian_product1) ).
fof(f15,axiom,
! [X2,X3,X0,X1] :
( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| member(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartesian_product2) ).
fof(f16,axiom,
! [X2,X3,X0,X1] :
( member(ordered_pair(X0,X2),cross_product(X1,X3))
| ~ member(X2,X3)
| ~ member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartesian_product3) ).
fof(f122,negated_conjecture,
member(ordered_pair(u,v),cross_product(x,y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_cross_product_property2_1) ).
fof(f123,negated_conjecture,
~ member(ordered_pair(v,u),cross_product(y,x)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_cross_product_property2_2) ).
fof(f124,plain,
member(u,x),
inference(resolution,[],[f14,f122]) ).
fof(f125,plain,
member(v,y),
inference(resolution,[],[f15,f122]) ).
fof(f126,plain,
( ~ member(u,x)
| ~ member(v,y) ),
inference(resolution,[],[f16,f123]) ).
fof(f129,plain,
~ member(v,y),
inference(forward_subsumption_resolution,[],[f126,f124]) ).
fof(f130,plain,
$false,
inference(forward_subsumption_resolution,[],[f129,f125]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET204-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n001.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % 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 01:12:03 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 3.79/1.51 % (4128314)Input is clausal, will run a generic CNF schedule.
% 3.79/1.51 % (4128319)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=3974230115:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.79/1.51 % (4128320)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1434288587:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.79/1.51 % (4128322)lrs+10_1_sil=8000:sp=occurrence:random_seed=1362145958:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.79/1.51 % (4128324)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2211478085:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.79/1.51 % (4128323)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3225554881:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.79/1.51 % (4128321)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=138075286:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.79/1.51 % (4128325)dis-21_1_sil=8000:lcm=predicate:random_seed=1131346647: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)
% 3.79/1.51 % (4128322)Also succeeded, but the first one will report.
% 3.79/1.51 % (4128323)First to succeed.
% 3.79/1.51 % (4128323)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4128314"
% 3.79/1.51 % (4128324)Also succeeded, but the first one will report.
% 3.79/1.51 % (4128325)Instruction limit reached!
% 3.79/1.51 % (4128325)------------------------------
% 3.79/1.51 % (4128325)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.79/1.51 % (4128325)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.79/1.51 % (4128325)CaDiCaL version: 2.1.3
% 3.79/1.51 % (4128325)Termination reason: Instruction limit
% 3.79/1.51 % (4128325)Termination phase: Saturation
% 3.79/1.51 % (4128325)Time elapsed: 0.074 s
% 3.79/1.51 % (4128325)Peak memory usage: 89 MB
% 3.79/1.51 % (4128325)Instructions burned: 118 (million)
% 3.79/1.51 % (4128333)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=3867431967:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.79/1.51 % (4128333)Also succeeded, but the first one will report.
% 3.79/1.51 % (4128323)Refutation found. Thanks to Tanya!
% 3.79/1.51 % SZS status Unsatisfiable for theBenchmark
% 3.79/1.51 % SZS output start Proof for theBenchmark
% See solution above
% 3.79/1.51 % (4128323)------------------------------
% 3.79/1.51 % (4128323)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.79/1.51 % (4128323)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.79/1.51 % (4128323)CaDiCaL version: 2.1.3
% 3.79/1.51 % (4128323)Termination reason: Refutation
% 3.79/1.51 % (4128323)Time elapsed: 0.002 s
% 3.79/1.51 % (4128323)Peak memory usage: 88 MB
% 3.79/1.51 % (4128323)Instructions burned: 1 (million)
% 3.79/1.51 % (4128323)------------------------------
% 3.79/1.51 % (4128323)------------------------------
% 3.79/1.51 % (4128314)Success in time 0.449 s
% 3.79/1.51 % Vampire exiting
%------------------------------------------------------------------------------