%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET468-6 : 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 : 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 12:41:00 PM UTC 2026
% Result : Unsatisfiable 5.03s 1.35s
% Output : Refutation 5.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 26 ( 13 unt; 0 def)
% Number of atoms : 40 ( 16 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 28 ( 14 ~; 14 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-2 aty)
% Number of variables : 35 ( 35 !; 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(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_set) ).
fof(f13,axiom,
! [X0,X1] : unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) = ordered_pair(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pair) ).
fof(f14,axiom,
! [X2,X3,X0,X1] :
( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| member(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartesian_product1) ).
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(f21,axiom,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection1) ).
fof(f24,axiom,
! [X0,X1] :
( ~ member(X0,complement(X1))
| ~ member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement1) ).
fof(f69,axiom,
! [X0] :
( X0 = null_class
| intersection(X0,regular(X0)) = null_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',regularity2) ).
fof(f70,plain,
! [X0] :
( null_class = X0
| null_class = intersection(X0,regular(X0)) ),
inference(reorient_equations,[],[f69]) ).
fof(f122,negated_conjecture,
x = null_class,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_sets_with_one_member2_1) ).
fof(f123,plain,
null_class = x,
inference(reorient_equations,[],[f122]) ).
fof(f124,negated_conjecture,
~ subclass(cross_product(x,x),identity_relation),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_sets_with_one_member2_2) ).
fof(f129,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),
inference(definition_unfolding,[],[f13,f12,f12]) ).
fof(f138,plain,
! [X2,X3,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3))
| member(X0,X2) ),
inference(definition_unfolding,[],[f14,f129]) ).
fof(f141,plain,
! [X2,X0,X1] :
( ~ member(X0,cross_product(X1,X2))
| unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))) = X0 ),
inference(definition_unfolding,[],[f17,f129]) ).
fof(f166,plain,
! [X0] :
( intersection(X0,regular(X0)) = x
| x = X0 ),
inference(definition_unfolding,[],[f70,f123,f123]) ).
fof(f195,plain,
member(not_subclass_element(cross_product(x,x),identity_relation),cross_product(x,x)),
inference(unit_resulting_resolution,[],[f2,f124]) ).
fof(f200,plain,
not_subclass_element(cross_product(x,x),identity_relation) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(x,x),identity_relation)),first(not_subclass_element(cross_product(x,x),identity_relation))),unordered_pair(first(not_subclass_element(cross_product(x,x),identity_relation)),unordered_pair(second(not_subclass_element(cross_product(x,x),identity_relation)),second(not_subclass_element(cross_product(x,x),identity_relation))))),
inference(unit_resulting_resolution,[],[f141,f195]) ).
fof(f202,plain,
! [X0,X1] :
( ~ member(not_subclass_element(cross_product(x,x),identity_relation),cross_product(X0,X1))
| member(first(not_subclass_element(cross_product(x,x),identity_relation)),X0) ),
inference(superposition,[],[f138,f200]) ).
fof(f204,plain,
member(first(not_subclass_element(cross_product(x,x),identity_relation)),x),
inference(unit_resulting_resolution,[],[f202,f195]) ).
fof(f218,plain,
! [X0,X1] :
( ~ member(X0,x)
| member(X0,X1)
| x = X1 ),
inference(superposition,[],[f21,f166]) ).
fof(f378,plain,
~ member(first(not_subclass_element(cross_product(x,x),identity_relation)),complement(x)),
inference(unit_resulting_resolution,[],[f24,f204]) ).
fof(f385,plain,
x = complement(x),
inference(unit_resulting_resolution,[],[f218,f204,f378]) ).
fof(f395,plain,
! [X0] :
( ~ member(X0,x)
| ~ member(X0,x) ),
inference(superposition,[],[f24,f385]) ).
fof(f396,plain,
! [X0] : ~ member(X0,x),
inference(duplicate_literal_removal,[],[f395]) ).
fof(f397,plain,
$false,
inference(unit_resulting_resolution,[],[f396,f204]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET468-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.04/0.32 % Computer : n012.cluster.edu
% 0.04/0.32 % Model : x86_64 x86_64
% 0.04/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.32 % Memory : 8046.5625MB
% 0.04/0.32 % OS : Linux 6.8.0-71-generic
% 0.04/0.32 % CPULimit : 300
% 0.04/0.32 % WCLimit : 300
% 0.04/0.32 % DateTime : Mon Sep 28 01:53:34 UTC 2026
% 0.04/0.32 % CPUTime :
% 0.04/0.32 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.34 Running first-order theorem proving
% 0.08/0.34 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
% 4.19/1.25 % (2933527)Input is clausal, will run a generic CNF schedule.
% 4.19/1.25 % (2933535)lrs+10_1_sil=8000:sp=occurrence:random_seed=1770377981:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 4.19/1.25 % (2933538)dis-21_1_sil=8000:lcm=predicate:random_seed=990894663: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)
% 4.19/1.25 % (2933532)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=1123772387:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 4.19/1.25 % (2933534)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3656014191:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 4.19/1.25 % (2933537)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=983518491:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 4.19/1.25 % (2933533)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2687112171:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 4.19/1.25 % (2933536)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=830741017:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 4.19/1.25 % (2933535)Refutation not found, incomplete strategy
% 4.19/1.25 % (2933535)------------------------------
% 4.19/1.25 % (2933535)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.19/1.25 % (2933535)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.19/1.25 % (2933535)CaDiCaL version: 2.1.3
% 4.19/1.25 % (2933535)Termination reason: Refutation not found, incomplete strategy
% 4.19/1.25 % (2933535)Time elapsed: 0.001 s
% 4.19/1.25 % (2933535)Peak memory usage: 88 MB
% 4.19/1.25 % (2933535)Instructions burned: 1 (million)
% 4.19/1.25 % (2933536)Instruction limit reached!
% 4.19/1.25 % (2933536)------------------------------
% 4.19/1.25 % (2933536)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.19/1.25 % (2933536)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.19/1.25 % (2933536)CaDiCaL version: 2.1.3
% 4.19/1.25 % (2933536)Termination reason: Instruction limit
% 4.19/1.25 % (2933536)Termination phase: Saturation
% 4.19/1.25 % (2933536)Time elapsed: 0.035 s
% 4.19/1.25 % (2933536)Peak memory usage: 89 MB
% 4.19/1.25 % (2933536)Instructions burned: 116 (million)
% 4.19/1.25 % (2933538)Instruction limit reached!
% 4.19/1.25 % (2933538)------------------------------
% 4.19/1.25 % (2933538)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.19/1.25 % (2933538)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.19/1.25 % (2933538)CaDiCaL version: 2.1.3
% 4.19/1.25 % (2933538)Termination reason: Instruction limit
% 4.19/1.25 % (2933538)Termination phase: Saturation
% 4.19/1.25 % (2933538)Time elapsed: 0.040 s
% 4.19/1.25 % (2933538)Peak memory usage: 89 MB
% 4.19/1.25 % (2933538)Instructions burned: 117 (million)
% 4.19/1.25 % (2933537)Instruction limit reached!
% 4.19/1.25 % (2933537)------------------------------
% 4.19/1.25 % (2933537)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.19/1.25 % (2933537)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.19/1.25 % (2933537)CaDiCaL version: 2.1.3
% 4.19/1.25 % (2933537)Termination reason: Instruction limit
% 4.19/1.25 % (2933537)Termination phase: Saturation
% 4.19/1.25 % (2933537)Time elapsed: 0.074 s
% 4.19/1.25 % (2933537)Peak memory usage: 90 MB
% 4.19/1.25 % (2933537)Instructions burned: 182 (million)
% 4.19/1.25 % (2933535)------------------------------
% 4.19/1.25 % (2933535)------------------------------
% 4.19/1.25 % (2933546)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=705288696:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 4.19/1.25 % (2933547)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2902311792:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2998 on theBenchmark for (2998ds/189Mi)
% 4.19/1.25 % (2933546)Refutation not found, incomplete strategy
% 4.19/1.25 % (2933546)------------------------------
% 4.19/1.25 % (2933546)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.19/1.25 % (2933546)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.03/1.35 % (2933546)CaDiCaL version: 2.1.3
% 5.03/1.35 % (2933546)Termination reason: Refutation not found, incomplete strategy
% 5.03/1.35 % (2933546)Time elapsed: 0.002 s
% 5.03/1.35 % (2933546)Peak memory usage: 88 MB
% 5.03/1.35 % (2933546)Instructions burned: 4 (million)
% 5.03/1.35 % (2933548)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=77571688:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 5.03/1.35 % (2933548)Refutation not found, incomplete strategy
% 5.03/1.35 % (2933548)------------------------------
% 5.03/1.35 % (2933548)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.03/1.35 % (2933548)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.03/1.35 % (2933548)CaDiCaL version: 2.1.3
% 5.03/1.35 % (2933548)Termination reason: Refutation not found, incomplete strategy
% 5.03/1.35 % (2933548)Time elapsed: 0.002 s
% 5.03/1.35 % (2933548)Peak memory usage: 88 MB
% 5.03/1.35 % (2933548)Instructions burned: 4 (million)
% 5.03/1.35 % (2933547)Instruction limit reached!
% 5.03/1.35 % (2933547)------------------------------
% 5.03/1.35 % (2933547)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.03/1.35 % (2933547)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.03/1.35 % (2933547)CaDiCaL version: 2.1.3
% 5.03/1.35 % (2933547)Termination reason: Instruction limit
% 5.03/1.35 % (2933547)Termination phase: Saturation
% 5.03/1.35 % (2933547)Time elapsed: 0.053 s
% 5.03/1.35 % (2933547)Peak memory usage: 90 MB
% 5.03/1.35 % (2933547)Instructions burned: 190 (million)
% 5.03/1.35 % (2933551)lrs+10_64_to=lpo:sil=8000:random_seed=1913098614:i=126:bd=preordered_2997 on theBenchmark for (2997ds/126Mi)
% 5.03/1.35 % (2933546)------------------------------
% 5.03/1.35 % (2933546)------------------------------
% 5.03/1.35 % (2933553)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=4216987858:avsq=on:i=194:fgj=on:bd=preordered_2996 on theBenchmark for (2996ds/194Mi)
% 5.03/1.35 % (2933551)Instruction limit reached!
% 5.03/1.35 % (2933551)------------------------------
% 5.03/1.35 % (2933551)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.03/1.35 % (2933551)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.03/1.35 % (2933551)CaDiCaL version: 2.1.3
% 5.03/1.35 % (2933551)Termination reason: Instruction limit
% 5.03/1.35 % (2933551)Termination phase: Saturation
% 5.03/1.35 % (2933551)Time elapsed: 0.039 s
% 5.03/1.35 % (2933551)Peak memory usage: 89 MB
% 5.03/1.35 % (2933551)Instructions burned: 129 (million)
% 5.03/1.35 % (2933548)------------------------------
% 5.03/1.35 % (2933548)------------------------------
% 5.03/1.35 % (2933533)First to succeed.
% 5.03/1.35 % (2933533)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2933527"
% 5.03/1.35 % (2933553)Instruction limit reached!
% 5.03/1.35 % (2933553)------------------------------
% 5.03/1.35 % (2933553)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.03/1.35 % (2933553)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.03/1.35 % (2933553)CaDiCaL version: 2.1.3
% 5.03/1.35 % (2933553)Termination reason: Instruction limit
% 5.03/1.35 % (2933553)Termination phase: Saturation
% 5.03/1.35 % (2933553)Time elapsed: 0.061 s
% 5.03/1.35 % (2933553)Peak memory usage: 90 MB
% 5.03/1.35 % (2933553)Instructions burned: 195 (million)
% 5.03/1.35 % (2933532)Also succeeded, but the first one will report.
% 5.03/1.35 % (2933555)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=2478353909:i=157:gtg=all_2995 on theBenchmark for (2995ds/157Mi)
% 5.03/1.35 % (2933557)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=1879564877:i=3394:sd=4:ss=included:sgt=64_2995 on theBenchmark for (2995ds/3394Mi)
% 5.03/1.35 % (2933555)Instruction limit reached!
% 5.03/1.35 % (2933555)------------------------------
% 5.03/1.35 % (2933555)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.03/1.35 % (2933555)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.03/1.35 % (2933555)CaDiCaL version: 2.1.3
% 5.03/1.35 % (2933555)Termination reason: Instruction limit
% 5.03/1.35 % (2933555)Termination phase: Saturation
% 5.03/1.35 % (2933555)Time elapsed: 0.045 s
% 5.03/1.35 % (2933555)Peak memory usage: 90 MB
% 5.03/1.35 % (2933555)Instructions burned: 159 (million)
% 5.03/1.35 % (2933558)lrs+1011_5_to=lpo:sil=8000:tgt=full:plsq=on:prc=on:drc=off:plsqr=31,4:sp=occurrence:urr=on:nwc=0.8:s2agt=16:br=off:random_seed=4057677340:cts=off:s2a=on:i=106:fsr=off:gsp=on:ss=axioms:sgt=16:rawr=on_2995 on theBenchmark for (2995ds/106Mi)
% 5.03/1.35 % (2933558)Instruction limit reached!
% 5.03/1.35 % (2933558)------------------------------
% 5.03/1.35 % (2933558)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.03/1.35 % (2933558)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.03/1.35 % (2933558)CaDiCaL version: 2.1.3
% 5.03/1.35 % (2933558)Termination reason: Instruction limit
% 5.03/1.35 % (2933558)Termination phase: Saturation
% 5.03/1.35 % (2933558)Time elapsed: 0.035 s
% 5.03/1.35 % (2933558)Peak memory usage: 89 MB
% 5.03/1.35 % (2933558)Instructions burned: 109 (million)
% 5.03/1.35 % (2933559)lrs+2_4096_sil=8000:plsq=on:plsqr=12672147,131072:sos=on:spb=goal:lcm=predicate:random_seed=3042531237:i=107_2994 on theBenchmark for (2994ds/107Mi)
% 5.03/1.35 % (2933533)Refutation found. Thanks to Tanya!
% 5.03/1.35 % SZS status Unsatisfiable for theBenchmark
% 5.03/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 5.03/1.35 % (2933533)------------------------------
% 5.03/1.35 % (2933533)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.03/1.35 % (2933533)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.03/1.35 % (2933533)CaDiCaL version: 2.1.3
% 5.03/1.35 % (2933533)Termination reason: Refutation
% 5.03/1.35 % (2933533)Time elapsed: 0.384 s
% 5.03/1.35 % (2933533)Peak memory usage: 127 MB
% 5.03/1.35 % (2933533)Instructions burned: 1018 (million)
% 5.03/1.35 % (2933533)------------------------------
% 5.03/1.35 % (2933533)------------------------------
% 5.03/1.35 % (2933527)Success in time 0.688 s
% 5.03/1.35 % Vampire exiting
%------------------------------------------------------------------------------