%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET242-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 12:40:35 PM UTC 2026
% Result : Unsatisfiable 2.56s 1.33s
% Output : Refutation 2.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 12 ( 10 unt; 0 def)
% Number of atoms : 15 ( 3 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 11 ( 8 ~; 3 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 12 ( 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f23,axiom,
! [X2,X0,X1] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection3) ).
fof(f28,axiom,
! [X2,X0,X1] : intersection(X0,cross_product(X1,X2)) = restrict(X0,X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',restriction1) ).
fof(f29,axiom,
! [X2,X0,X1] : intersection(cross_product(X0,X1),X2) = restrict(X2,X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',restriction2) ).
fof(f122,negated_conjecture,
member(z,xr),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_restriction_alternate_defn5_1) ).
fof(f123,negated_conjecture,
member(z,cross_product(x,y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_restriction_alternate_defn5_2) ).
fof(f124,negated_conjecture,
~ member(z,restrict(xr,x,y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_restriction_alternate_defn5_3) ).
fof(f125,plain,
~ member(z,intersection(cross_product(x,y),xr)),
inference(definition_unfolding,[],[f124,f29]) ).
fof(f128,plain,
! [X2,X0,X1] : intersection(X0,cross_product(X1,X2)) = intersection(cross_product(X1,X2),X0),
inference(definition_unfolding,[],[f28,f29]) ).
fof(f129,plain,
~ member(z,intersection(xr,cross_product(x,y))),
inference(forward_demodulation,[],[f125,f128]) ).
fof(f130,plain,
( ~ member(z,cross_product(x,y))
| ~ member(z,xr) ),
inference(resolution,[],[f23,f129]) ).
fof(f133,plain,
~ member(z,xr),
inference(forward_subsumption_resolution,[],[f130,f123]) ).
fof(f134,plain,
$false,
inference(forward_subsumption_resolution,[],[f133,f122]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET242-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 % Computer : n026.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 01:14:57 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.42 Running first-order theorem proving
% 0.13/0.42 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
% 2.56/1.33 % (3380610)Input is clausal, will run a generic CNF schedule.
% 2.56/1.33 % (3380618)lrs+10_1_sil=8000:sp=occurrence:random_seed=2210413516:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.56/1.33 % (3380618)First to succeed.
% 2.56/1.33 % (3380618)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3380610"
% 2.56/1.33 % (3380616)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3061446091:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.56/1.33 % (3380620)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=876704323:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.56/1.33 % (3380617)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3274915437:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.56/1.33 % (3380615)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=512357967:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.56/1.33 % (3380621)dis-21_1_sil=8000:lcm=predicate:random_seed=1809982931: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)
% 2.56/1.33 % (3380619)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=4094579321:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.56/1.33 % (3380619)Also succeeded, but the first one will report.
% 2.56/1.33 % (3380621)Also succeeded, but the first one will report.
% 2.56/1.33 % (3380620)Also succeeded, but the first one will report.
% 2.56/1.33 % (3380618)Refutation found. Thanks to Tanya!
% 2.56/1.33 % SZS status Unsatisfiable for theBenchmark
% 2.56/1.33 % SZS output start Proof for theBenchmark
% See solution above
% 2.56/1.33 % (3380618)------------------------------
% 2.56/1.33 % (3380618)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.56/1.33 % (3380618)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.56/1.33 % (3380618)CaDiCaL version: 2.1.3
% 2.56/1.33 % (3380618)Termination reason: Refutation
% 2.56/1.33 % (3380618)Time elapsed: 0.001 s
% 2.56/1.33 % (3380618)Peak memory usage: 88 MB
% 2.56/1.33 % (3380618)Instructions burned: 1 (million)
% 2.56/1.33 % (3380618)------------------------------
% 2.56/1.33 % (3380618)------------------------------
% 2.56/1.33 % (3380610)Success in time 0.278 s
% 2.56/1.33 % Vampire exiting
%------------------------------------------------------------------------------