%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET214-6 : 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 : n004.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 12:40:32 PM UTC 2026
% Result : Unsatisfiable 5.57s 1.79s
% Output : Refutation 5.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 13
% Syntax : Number of formulae : 41 ( 13 unt; 3 def)
% Number of atoms : 84 ( 11 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 86 ( 43 ~; 43 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-2 aty)
% Number of variables : 73 ( 73 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( member(not_subclass_element(X0,X1),X0)
| subclass(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_subclass_members1) ).
fof(f3,axiom,
! [X0,X1] :
( ~ member(not_subclass_element(X0,X1),X1)
| subclass(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_subclass_members2) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/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/sandbox2/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/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(X0,X1)
| ~ member(X2,X3)
| member(ordered_pair(X0,X2),cross_product(X1,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartesian_product3) ).
fof(f17,axiom,
! [X2,X0,X1] :
( ~ member(X0,cross_product(X1,X2))
| ordered_pair(first(X0),second(X0)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartesian_product4) ).
fof(f21,axiom,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection1) ).
fof(f122,negated_conjecture,
~ subclass(cross_product(intersection(x,y),z),cross_product(x,z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_5_to_X_product_monotonicity_1) ).
fof(f127,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(f136,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,f127]) ).
fof(f137,plain,
! [X2,X3,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3))
| member(X1,X3) ),
inference(definition_unfolding,[],[f15,f127]) ).
fof(f138,plain,
! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(X1,X3))
| ~ member(X2,X3)
| ~ member(X0,X1) ),
inference(definition_unfolding,[],[f16,f127]) ).
fof(f139,plain,
! [X2,X0,X1] :
( unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))) = X0
| ~ member(X0,cross_product(X1,X2)) ),
inference(definition_unfolding,[],[f17,f127]) ).
fof(f189,definition,
sF0 = intersection(x,y),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f190,plain,
intersection(x,y) = sF0,
inference(reorient_equations,[],[f189]) ).
fof(f191,definition,
sF1 = cross_product(sF0,z),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f192,plain,
cross_product(sF0,z) = sF1,
inference(reorient_equations,[],[f191]) ).
fof(f193,definition,
sF2 = cross_product(x,z),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f194,plain,
cross_product(x,z) = sF2,
inference(reorient_equations,[],[f193]) ).
fof(f195,plain,
~ subclass(sF1,sF2),
inference(definition_folding,[],[f122,f194,f192,f190]) ).
fof(f201,plain,
! [X0] :
( member(X0,x)
| ~ member(X0,sF0) ),
inference(superposition,[],[f21,f190]) ).
fof(f208,plain,
! [X2,X3,X0,X1,X4] :
( ~ member(X0,cross_product(X3,X4))
| member(second(X0),X2)
| ~ member(X0,cross_product(X1,X2)) ),
inference(superposition,[],[f137,f139]) ).
fof(f209,plain,
! [X2,X3,X0,X1,X4] :
( ~ member(X0,cross_product(X3,X4))
| member(first(X0),X1)
| ~ member(X0,cross_product(X1,X2)) ),
inference(superposition,[],[f136,f139]) ).
fof(f212,plain,
! [X2,X0,X1] :
( ~ member(X0,cross_product(X2,X1))
| member(second(X0),X1)
| ~ member(X0,sF1) ),
inference(superposition,[],[f208,f192]) ).
fof(f215,plain,
! [X2,X0,X1] :
( ~ member(X0,cross_product(X1,X2))
| member(first(X0),X1)
| ~ member(X0,sF1) ),
inference(superposition,[],[f209,f192]) ).
fof(f218,plain,
! [X0] :
( ~ member(X0,sF1)
| member(first(X0),sF0)
| ~ member(X0,sF1) ),
inference(superposition,[],[f215,f192]) ).
fof(f219,plain,
! [X0] :
( member(first(X0),sF0)
| ~ member(X0,sF1) ),
inference(duplicate_literal_removal,[],[f218]) ).
fof(f222,plain,
! [X0] :
( ~ member(X0,sF1)
| member(second(X0),z)
| ~ member(X0,sF1) ),
inference(superposition,[],[f212,f192]) ).
fof(f223,plain,
! [X0] :
( member(second(X0),z)
| ~ member(X0,sF1) ),
inference(duplicate_literal_removal,[],[f222]) ).
fof(f241,plain,
! [X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),sF2)
| ~ member(X1,z)
| ~ member(X0,x) ),
inference(superposition,[],[f138,f194]) ).
fof(f243,plain,
! [X2,X0,X1] :
( ~ member(X0,cross_product(X1,X2))
| ~ member(second(X0),z)
| ~ member(first(X0),x)
| member(X0,sF2) ),
inference(superposition,[],[f241,f139]) ).
fof(f262,plain,
! [X0] :
( ~ member(X0,sF1)
| ~ member(second(X0),z)
| ~ member(first(X0),x)
| member(X0,sF2) ),
inference(superposition,[],[f243,f192]) ).
fof(f263,plain,
! [X0] :
( ~ member(first(X0),x)
| ~ member(X0,sF1)
| member(X0,sF2) ),
inference(forward_subsumption_resolution,[],[f262,f223]) ).
fof(f266,plain,
! [X0] :
( ~ member(X0,sF1)
| member(X0,sF2)
| ~ member(first(X0),sF0) ),
inference(resolution,[],[f263,f201]) ).
fof(f268,plain,
! [X0] :
( member(X0,sF2)
| ~ member(X0,sF1) ),
inference(forward_subsumption_resolution,[],[f266,f219]) ).
fof(f269,plain,
! [X0] :
( ~ member(not_subclass_element(X0,sF2),sF1)
| subclass(X0,sF2) ),
inference(resolution,[],[f268,f3]) ).
fof(f270,plain,
( subclass(sF1,sF2)
| subclass(sF1,sF2) ),
inference(resolution,[],[f269,f2]) ).
fof(f271,plain,
subclass(sF1,sF2),
inference(duplicate_literal_removal,[],[f270]) ).
fof(f272,plain,
$false,
inference(forward_subsumption_resolution,[],[f271,f195]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET214-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 % Computer : n004.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Mon Sep 28 01:07:22 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.43 Running first-order theorem proving
% 0.13/0.43 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
% 3.76/1.59 % (4051052)Input is clausal, will run a generic CNF schedule.
% 3.76/1.59 % (4051059)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3329464379:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.76/1.59 % (4051062)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1410651528:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.76/1.59 % (4051063)dis-21_1_sil=8000:lcm=predicate:random_seed=1554567254: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)
% 3.76/1.59 % (4051061)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3431009437:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.76/1.59 % (4051058)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3132882385:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.76/1.59 % (4051057)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=3966896476:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.76/1.59 % (4051060)lrs+10_1_sil=8000:sp=occurrence:random_seed=2690264800:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.76/1.59 % (4051060)Refutation not found, incomplete strategy
% 3.76/1.59 % (4051060)------------------------------
% 3.76/1.59 % (4051060)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.76/1.59 % (4051060)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.76/1.59 % (4051060)CaDiCaL version: 2.1.3
% 3.76/1.59 % (4051060)Termination reason: Refutation not found, incomplete strategy
% 3.76/1.59 % (4051060)Time elapsed: 0.002 s
% 3.76/1.59 % (4051060)Peak memory usage: 87 MB
% 3.76/1.59 % (4051060)Instructions burned: 1 (million)
% 3.76/1.59 % (4051061)Refutation not found, incomplete strategy
% 3.76/1.59 % (4051061)------------------------------
% 3.76/1.59 % (4051061)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.76/1.59 % (4051061)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.76/1.59 % (4051061)CaDiCaL version: 2.1.3
% 3.76/1.59 % (4051061)Termination reason: Refutation not found, incomplete strategy
% 3.76/1.59 % (4051061)Time elapsed: 0.004 s
% 3.76/1.59 % (4051061)Peak memory usage: 88 MB
% 3.76/1.59 % (4051061)Instructions burned: 4 (million)
% 3.76/1.59 % (4051063)Instruction limit reached!
% 3.76/1.59 % (4051063)------------------------------
% 3.76/1.59 % (4051063)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.76/1.59 % (4051063)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.76/1.59 % (4051063)CaDiCaL version: 2.1.3
% 3.76/1.59 % (4051063)Termination reason: Instruction limit
% 3.76/1.59 % (4051063)Termination phase: Saturation
% 3.76/1.59 % (4051063)Time elapsed: 0.071 s
% 3.76/1.59 % (4051063)Peak memory usage: 89 MB
% 3.76/1.59 % (4051063)Instructions burned: 119 (million)
% 3.76/1.59 % (4051062)Instruction limit reached!
% 3.76/1.59 % (4051062)------------------------------
% 3.76/1.59 % (4051062)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.76/1.59 % (4051062)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.76/1.59 % (4051062)CaDiCaL version: 2.1.3
% 3.76/1.59 % (4051062)Termination reason: Instruction limit
% 3.76/1.59 % (4051062)Termination phase: Saturation
% 3.76/1.59 % (4051062)Time elapsed: 0.129 s
% 3.76/1.59 % (4051062)Peak memory usage: 90 MB
% 3.76/1.59 % (4051062)Instructions burned: 181 (million)
% 3.76/1.59 % (4051071)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=2249348119:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.76/1.59 % (4051071)Refutation not found, incomplete strategy
% 3.76/1.59 % (4051071)------------------------------
% 3.76/1.59 % (4051071)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.76/1.59 % (4051071)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.76/1.59 % (4051071)CaDiCaL version: 2.1.3
% 3.76/1.59 % (4051071)Termination reason: Refutation not found, incomplete strategy
% 3.76/1.59 % (4051071)Time elapsed: 0.003 s
% 3.76/1.59 % (4051071)Peak memory usage: 88 MB
% 3.76/1.59 % (4051071)Instructions burned: 3 (million)
% 3.76/1.59 % (4051061)------------------------------
% 5.57/1.79 % (4051061)------------------------------
% 5.57/1.79 % (4051060)------------------------------
% 5.57/1.79 % (4051060)------------------------------
% 5.57/1.79 % (4051072)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=196604618:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2996 on theBenchmark for (2996ds/189Mi)
% 5.57/1.79 % (4051072)Refutation not found, incomplete strategy
% 5.57/1.79 % (4051072)------------------------------
% 5.57/1.79 % (4051072)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.57/1.79 % (4051072)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.57/1.79 % (4051072)CaDiCaL version: 2.1.3
% 5.57/1.79 % (4051072)Termination reason: Refutation not found, incomplete strategy
% 5.57/1.79 % (4051072)Time elapsed: 0.011 s
% 5.57/1.79 % (4051072)Peak memory usage: 88 MB
% 5.57/1.79 % (4051072)Instructions burned: 20 (million)
% 5.57/1.79 % (4051059)First to succeed.
% 5.57/1.79 % (4051059)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4051052"
% 5.57/1.79 % (4051075)lrs+10_64_to=lpo:sil=8000:random_seed=1866435788:i=126:bd=preordered_2995 on theBenchmark for (2995ds/126Mi)
% 5.57/1.79 % (4051074)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=3949353977:st=4:i=219:sd=3:ss=axioms_2995 on theBenchmark for (2995ds/219Mi)
% 5.57/1.79 % (4051074)Refutation not found, incomplete strategy
% 5.57/1.79 % (4051074)------------------------------
% 5.57/1.79 % (4051074)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.57/1.79 % (4051074)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.57/1.79 % (4051074)CaDiCaL version: 2.1.3
% 5.57/1.79 % (4051074)Termination reason: Refutation not found, incomplete strategy
% 5.57/1.79 % (4051074)Time elapsed: 0.003 s
% 5.57/1.79 % (4051074)Peak memory usage: 87 MB
% 5.57/1.79 % (4051074)Instructions burned: 3 (million)
% 5.57/1.79 % (4051071)------------------------------
% 5.57/1.79 % (4051071)------------------------------
% 5.57/1.79 % (4051075)Instruction limit reached!
% 5.57/1.79 % (4051075)------------------------------
% 5.57/1.79 % (4051075)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.57/1.79 % (4051075)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.57/1.79 % (4051075)CaDiCaL version: 2.1.3
% 5.57/1.79 % (4051075)Termination reason: Instruction limit
% 5.57/1.79 % (4051075)Termination phase: Saturation
% 5.57/1.79 % (4051075)Time elapsed: 0.090 s
% 5.57/1.79 % (4051075)Peak memory usage: 90 MB
% 5.57/1.79 % (4051075)Instructions burned: 147 (million)
% 5.57/1.79 % (4051059)Refutation found. Thanks to Tanya!
% 5.57/1.79 % SZS status Unsatisfiable for theBenchmark
% 5.57/1.79 % SZS output start Proof for theBenchmark
% See solution above
% 5.57/1.79 % (4051059)------------------------------
% 5.57/1.79 % (4051059)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.57/1.79 % (4051059)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.57/1.79 % (4051059)CaDiCaL version: 2.1.3
% 5.57/1.79 % (4051059)Termination reason: Refutation
% 5.57/1.79 % (4051059)Time elapsed: 0.418 s
% 5.57/1.79 % (4051059)Peak memory usage: 130 MB
% 5.57/1.79 % (4051059)Instructions burned: 998 (million)
% 5.57/1.79 % (4051059)------------------------------
% 5.57/1.79 % (4051059)------------------------------
% 5.57/1.79 % (4051052)Success in time 0.71 s
% 5.57/1.79 % Vampire exiting
%------------------------------------------------------------------------------