%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET231-6 : 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 : n016.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 12:40:34 PM UTC 2026
% Result : Unsatisfiable 2.85s 1.39s
% Output : Refutation 2.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of formulae : 8 ( 5 unt; 0 def)
% Number of atoms : 11 ( 5 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 7 ( 4 ~; 3 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 8 ( 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( member(not_subclass_element(X0,X1),X0)
| subclass(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_subclass_members1) ).
fof(f17,axiom,
! [X2,X0,X1] :
( ~ member(X0,cross_product(X1,X2))
| ordered_pair(first(X0),second(X0)) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartesian_product4) ).
fof(f122,negated_conjecture,
~ subclass(cross_product(x,y),z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_cross_product_property6_1) ).
fof(f123,negated_conjecture,
ordered_pair(first(not_subclass_element(cross_product(x,y),z)),second(not_subclass_element(cross_product(x,y),z))) != not_subclass_element(cross_product(x,y),z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_cross_product_property6_2) ).
fof(f124,plain,
not_subclass_element(cross_product(x,y),z) != ordered_pair(first(not_subclass_element(cross_product(x,y),z)),second(not_subclass_element(cross_product(x,y),z))),
inference(reorient_equations,[],[f123]) ).
fof(f218,plain,
! [X2,X0,X1] :
( subclass(cross_product(X0,X1),X2)
| not_subclass_element(cross_product(X0,X1),X2) = ordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),second(not_subclass_element(cross_product(X0,X1),X2))) ),
inference(resolution,[],[f17,f2]) ).
fof(f744,plain,
not_subclass_element(cross_product(x,y),z) = ordered_pair(first(not_subclass_element(cross_product(x,y),z)),second(not_subclass_element(cross_product(x,y),z))),
inference(resolution,[],[f218,f122]) ).
fof(f749,plain,
$false,
inference(forward_subsumption_resolution,[],[f744,f124]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET231-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n016.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Mon Sep 28 01:15:40 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 2.85/1.39 % (3164334)Input is clausal, will run a generic CNF schedule.
% 2.85/1.39 % (3164342)lrs+10_1_sil=8000:sp=occurrence:random_seed=3054645797:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.85/1.39 % (3164342)First to succeed.
% 2.85/1.39 % (3164342)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3164334"
% 2.85/1.39 % (3164340)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=140840614:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.85/1.39 % (3164343)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1382461628:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.85/1.39 % (3164345)dis-21_1_sil=8000:lcm=predicate:random_seed=2915675444: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)
% 2.85/1.39 % (3164344)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1162050863:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.85/1.39 % (3164339)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=4085715260:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.85/1.39 % (3164341)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=547816689:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.85/1.39 % (3164343)Also succeeded, but the first one will report.
% 2.85/1.39 % (3164344)Also succeeded, but the first one will report.
% 2.85/1.39 % (3164345)Instruction limit reached!
% 2.85/1.39 % (3164345)------------------------------
% 2.85/1.39 % (3164345)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.85/1.39 % (3164345)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.85/1.39 % (3164345)CaDiCaL version: 2.1.3
% 2.85/1.39 % (3164345)Termination reason: Instruction limit
% 2.85/1.39 % (3164345)Termination phase: Saturation
% 2.85/1.39 % (3164345)Time elapsed: 0.072 s
% 2.85/1.39 % (3164345)Peak memory usage: 89 MB
% 2.85/1.39 % (3164345)Instructions burned: 117 (million)
% 2.85/1.39 % (3164342)Refutation found. Thanks to Tanya!
% 2.85/1.39 % SZS status Unsatisfiable for theBenchmark
% 2.85/1.39 % SZS output start Proof for theBenchmark
% See solution above
% 2.85/1.39 % (3164342)------------------------------
% 2.85/1.39 % (3164342)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.85/1.39 % (3164342)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.85/1.39 % (3164342)CaDiCaL version: 2.1.3
% 2.85/1.39 % (3164342)Termination reason: Refutation
% 2.85/1.39 % (3164342)Time elapsed: 0.012 s
% 2.85/1.39 % (3164342)Peak memory usage: 89 MB
% 2.85/1.39 % (3164342)Instructions burned: 27 (million)
% 2.85/1.39 % (3164342)------------------------------
% 2.85/1.39 % (3164342)------------------------------
% 2.85/1.39 % (3164334)Success in time 0.327 s
% 2.85/1.39 % Vampire exiting
%------------------------------------------------------------------------------