%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET216-6 : 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 : n011.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 6.10s 1.87s
% Output : Refutation 6.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 26 ( 12 unt; 0 def)
% Number of atoms : 43 ( 6 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 37 ( 20 ~; 17 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-2 aty)
% Number of variables : 49 ( 49 !; 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(x,intersection(y,z)),cross_product(x,y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_7_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] :
( ~ 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,f127]) ).
fof(f189,plain,
member(not_subclass_element(cross_product(x,intersection(y,z)),cross_product(x,y)),cross_product(x,intersection(y,z))),
inference(unit_resulting_resolution,[],[f2,f122]) ).
fof(f190,plain,
~ member(not_subclass_element(cross_product(x,intersection(y,z)),cross_product(x,y)),cross_product(x,y)),
inference(unit_resulting_resolution,[],[f3,f122]) ).
fof(f194,plain,
not_subclass_element(cross_product(x,intersection(y,z)),cross_product(x,y)) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(x,intersection(y,z)),cross_product(x,y))),first(not_subclass_element(cross_product(x,intersection(y,z)),cross_product(x,y)))),unordered_pair(first(not_subclass_element(cross_product(x,intersection(y,z)),cross_product(x,y))),unordered_pair(second(not_subclass_element(cross_product(x,intersection(y,z)),cross_product(x,y))),second(not_subclass_element(cross_product(x,intersection(y,z)),cross_product(x,y)))))),
inference(unit_resulting_resolution,[],[f139,f189]) ).
fof(f197,plain,
! [X0,X1] :
( ~ member(not_subclass_element(cross_product(x,intersection(y,z)),cross_product(x,y)),cross_product(X0,X1))
| member(first(not_subclass_element(cross_product(x,intersection(y,z)),cross_product(x,y))),X0) ),
inference(superposition,[],[f136,f194]) ).
fof(f198,plain,
! [X0,X1] :
( member(not_subclass_element(cross_product(x,intersection(y,z)),cross_product(x,y)),cross_product(X0,X1))
| ~ member(second(not_subclass_element(cross_product(x,intersection(y,z)),cross_product(x,y))),X1)
| ~ member(first(not_subclass_element(cross_product(x,intersection(y,z)),cross_product(x,y))),X0) ),
inference(superposition,[],[f138,f194]) ).
fof(f199,plain,
member(first(not_subclass_element(cross_product(x,intersection(y,z)),cross_product(x,y))),x),
inference(unit_resulting_resolution,[],[f197,f189]) ).
fof(f204,plain,
~ member(second(not_subclass_element(cross_product(x,intersection(y,z)),cross_product(x,y))),y),
inference(unit_resulting_resolution,[],[f198,f199,f190]) ).
fof(f207,plain,
! [X0] : ~ member(second(not_subclass_element(cross_product(x,intersection(y,z)),cross_product(x,y))),intersection(y,X0)),
inference(unit_resulting_resolution,[],[f21,f204]) ).
fof(f210,plain,
! [X0,X1] :
( ~ member(not_subclass_element(cross_product(x,intersection(y,z)),cross_product(x,y)),cross_product(X0,X1))
| member(second(not_subclass_element(cross_product(x,intersection(y,z)),cross_product(x,y))),X1) ),
inference(superposition,[],[f137,f194]) ).
fof(f212,plain,
member(second(not_subclass_element(cross_product(x,intersection(y,z)),cross_product(x,y))),intersection(y,z)),
inference(unit_resulting_resolution,[],[f210,f189]) ).
fof(f213,plain,
$false,
inference(forward_subsumption_resolution,[],[f212,f207]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET216-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 % Computer : n011.cluster.edu
% 0.11/0.41 % Model : x86_64 x86_64
% 0.11/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.41 % Memory : 8046.5625MB
% 0.11/0.41 % OS : Linux 6.8.0-71-generic
% 0.11/0.41 % CPULimit : 300
% 0.11/0.41 % WCLimit : 300
% 0.11/0.41 % DateTime : Mon Sep 28 01:08:16 UTC 2026
% 0.11/0.41 % CPUTime :
% 0.11/0.41 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.45 Running first-order theorem proving
% 0.11/0.45 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
% 5.01/1.68 % (2925425)Input is clausal, will run a generic CNF schedule.
% 5.01/1.68 % (2925431)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2081734706:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 5.01/1.68 % (2925430)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=796798073:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 5.01/1.68 % (2925435)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1631311323:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 5.01/1.68 % (2925434)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3762761908:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 5.01/1.68 % (2925432)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=290184890:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 5.01/1.68 % (2925436)dis-21_1_sil=8000:lcm=predicate:random_seed=34747613: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)
% 5.01/1.68 % (2925433)lrs+10_1_sil=8000:sp=occurrence:random_seed=597887013:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 5.01/1.68 % (2925433)Refutation not found, incomplete strategy
% 5.01/1.68 % (2925433)------------------------------
% 5.01/1.68 % (2925433)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.01/1.68 % (2925433)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.01/1.68 % (2925433)CaDiCaL version: 2.1.3
% 5.01/1.68 % (2925433)Termination reason: Refutation not found, incomplete strategy
% 5.01/1.68 % (2925433)Time elapsed: 0.002 s
% 5.01/1.68 % (2925433)Peak memory usage: 88 MB
% 5.01/1.68 % (2925433)Instructions burned: 1 (million)
% 5.01/1.68 % (2925434)Refutation not found, incomplete strategy
% 5.01/1.68 % (2925434)------------------------------
% 5.01/1.68 % (2925434)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.01/1.68 % (2925434)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.01/1.68 % (2925434)CaDiCaL version: 2.1.3
% 5.01/1.68 % (2925434)Termination reason: Refutation not found, incomplete strategy
% 5.01/1.68 % (2925434)Time elapsed: 0.004 s
% 5.01/1.68 % (2925434)Peak memory usage: 88 MB
% 5.01/1.68 % (2925434)Instructions burned: 4 (million)
% 5.01/1.68 % (2925436)Instruction limit reached!
% 5.01/1.68 % (2925436)------------------------------
% 5.01/1.68 % (2925436)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.01/1.68 % (2925436)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.01/1.68 % (2925436)CaDiCaL version: 2.1.3
% 5.01/1.68 % (2925436)Termination reason: Instruction limit
% 5.01/1.68 % (2925436)Termination phase: Saturation
% 5.01/1.68 % (2925436)Time elapsed: 0.071 s
% 5.01/1.68 % (2925436)Peak memory usage: 89 MB
% 5.01/1.68 % (2925436)Instructions burned: 117 (million)
% 5.01/1.68 % (2925435)Instruction limit reached!
% 5.01/1.68 % (2925435)------------------------------
% 5.01/1.68 % (2925435)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.01/1.68 % (2925435)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.01/1.68 % (2925435)CaDiCaL version: 2.1.3
% 5.01/1.68 % (2925435)Termination reason: Instruction limit
% 5.01/1.68 % (2925435)Termination phase: Saturation
% 5.01/1.68 % (2925435)Time elapsed: 0.128 s
% 5.01/1.68 % (2925435)Peak memory usage: 90 MB
% 5.01/1.68 % (2925435)Instructions burned: 181 (million)
% 5.01/1.68 % (2925444)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=730400627:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 5.01/1.68 % (2925444)Refutation not found, incomplete strategy
% 5.01/1.68 % (2925444)------------------------------
% 5.01/1.68 % (2925444)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.01/1.68 % (2925444)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.01/1.68 % (2925444)CaDiCaL version: 2.1.3
% 5.01/1.68 % (2925444)Termination reason: Refutation not found, incomplete strategy
% 5.01/1.68 % (2925444)Time elapsed: 0.003 s
% 5.01/1.68 % (2925444)Peak memory usage: 88 MB
% 5.01/1.68 % (2925444)Instructions burned: 3 (million)
% 5.01/1.68 % (2925434)------------------------------
% 6.10/1.87 % (2925434)------------------------------
% 6.10/1.87 % (2925433)------------------------------
% 6.10/1.87 % (2925433)------------------------------
% 6.10/1.87 % (2925445)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=478176362:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 6.10/1.87 % (2925445)Refutation not found, incomplete strategy
% 6.10/1.87 % (2925445)------------------------------
% 6.10/1.87 % (2925445)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.10/1.87 % (2925445)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.10/1.87 % (2925445)CaDiCaL version: 2.1.3
% 6.10/1.87 % (2925445)Termination reason: Refutation not found, incomplete strategy
% 6.10/1.87 % (2925445)Time elapsed: 0.011 s
% 6.10/1.87 % (2925445)Peak memory usage: 88 MB
% 6.10/1.87 % (2925445)Instructions burned: 20 (million)
% 6.10/1.87 % (2925448)lrs+10_64_to=lpo:sil=8000:random_seed=1761445000:i=126:bd=preordered_2995 on theBenchmark for (2995ds/126Mi)
% 6.10/1.87 % (2925431)First to succeed.
% 6.10/1.87 % (2925431)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2925425"
% 6.10/1.87 % (2925448)Instruction limit reached!
% 6.10/1.87 % (2925448)------------------------------
% 6.10/1.87 % (2925448)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.10/1.87 % (2925448)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.10/1.87 % (2925448)CaDiCaL version: 2.1.3
% 6.10/1.87 % (2925448)Termination reason: Instruction limit
% 6.10/1.87 % (2925448)Termination phase: Saturation
% 6.10/1.87 % (2925448)Time elapsed: 0.042 s
% 6.10/1.87 % (2925448)Peak memory usage: 89 MB
% 6.10/1.87 % (2925448)Instructions burned: 127 (million)
% 6.10/1.87 % (2925447)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=3428704563:st=4:i=219:sd=3:ss=axioms_2995 on theBenchmark for (2995ds/219Mi)
% 6.10/1.87 % (2925447)Refutation not found, incomplete strategy
% 6.10/1.87 % (2925447)------------------------------
% 6.10/1.87 % (2925447)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.10/1.87 % (2925447)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.10/1.87 % (2925447)CaDiCaL version: 2.1.3
% 6.10/1.87 % (2925447)Termination reason: Refutation not found, incomplete strategy
% 6.10/1.87 % (2925447)Time elapsed: 0.003 s
% 6.10/1.87 % (2925447)Peak memory usage: 88 MB
% 6.10/1.87 % (2925447)Instructions burned: 3 (million)
% 6.10/1.87 % (2925444)------------------------------
% 6.10/1.87 % (2925444)------------------------------
% 6.10/1.87 % (2925451)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=85976066:avsq=on:i=194:fgj=on:bd=preordered_2994 on theBenchmark for (2994ds/194Mi)
% 6.10/1.87 % (2925445)------------------------------
% 6.10/1.87 % (2925445)------------------------------
% 6.10/1.87 % (2925451)Instruction limit reached!
% 6.10/1.87 % (2925451)------------------------------
% 6.10/1.87 % (2925451)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.10/1.87 % (2925451)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.10/1.87 % (2925451)CaDiCaL version: 2.1.3
% 6.10/1.87 % (2925451)Termination reason: Instruction limit
% 6.10/1.87 % (2925451)Termination phase: Saturation
% 6.10/1.87 % (2925451)Time elapsed: 0.069 s
% 6.10/1.87 % (2925451)Peak memory usage: 90 MB
% 6.10/1.87 % (2925451)Instructions burned: 197 (million)
% 6.10/1.87 % (2925453)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=3363422244:i=157:gtg=all_2993 on theBenchmark for (2993ds/157Mi)
% 6.10/1.87 % (2925431)Refutation found. Thanks to Tanya!
% 6.10/1.87 % SZS status Unsatisfiable for theBenchmark
% 6.10/1.87 % SZS output start Proof for theBenchmark
% See solution above
% 6.10/1.87 % (2925431)------------------------------
% 6.10/1.87 % (2925431)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.10/1.87 % (2925431)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.10/1.87 % (2925431)CaDiCaL version: 2.1.3
% 6.10/1.87 % (2925431)Termination reason: Refutation
% 6.10/1.87 % (2925431)Time elapsed: 0.413 s
% 6.10/1.87 % (2925431)Peak memory usage: 129 MB
% 6.10/1.87 % (2925431)Instructions burned: 975 (million)
% 6.10/1.87 % (2925431)------------------------------
% 6.10/1.87 % (2925431)------------------------------
% 6.10/1.87 % (2925425)Success in time 0.787 s
% 6.10/1.87 % Vampire exiting
%------------------------------------------------------------------------------