%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM044-1 : 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 12:11:38 PM UTC 2026
% Result : Unsatisfiable 5.46s 1.74s
% Output : Refutation 5.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of formulae : 27 ( 18 unt; 0 def)
% Number of atoms : 38 ( 8 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 26 ( 15 ~; 11 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 29 ( 29 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( ~ member(X2,X0)
| ~ subclass(X0,X1)
| member(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_members) ).
fof(f21,axiom,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection1) ).
fof(f22,axiom,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection2) ).
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(f24,axiom,
! [X0,X1] :
( ~ member(X0,complement(X1))
| ~ member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement1) ).
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(f67,axiom,
! [X0] :
( X0 = null_class
| member(regular(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',regularity1) ).
fof(f68,plain,
! [X0] :
( member(regular(X0),X0)
| null_class = X0 ),
inference(reorient_equations,[],[f67]) ).
fof(f123,axiom,
! [X0,X1] :
( ~ irreflexive(X0,X1)
| subclass(restrict(X0,X1,X1),complement(identity_relation)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',irreflexive1) ).
fof(f176,negated_conjecture,
irreflexive(x,y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_irreflexive_class_property6_1) ).
fof(f177,negated_conjecture,
restrict(intersection(x,identity_relation),y,y) != null_class,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_irreflexive_class_property6_2) ).
fof(f178,plain,
null_class != restrict(intersection(x,identity_relation),y,y),
inference(reorient_equations,[],[f177]) ).
fof(f202,plain,
! [X2,X0,X1] : intersection(cross_product(X0,X1),X2) = intersection(X2,cross_product(X0,X1)),
inference(definition_unfolding,[],[f29,f28]) ).
fof(f245,plain,
! [X0,X1] :
( subclass(intersection(X0,cross_product(X1,X1)),complement(identity_relation))
| ~ irreflexive(X0,X1) ),
inference(definition_unfolding,[],[f123,f28]) ).
fof(f269,plain,
null_class != intersection(intersection(x,identity_relation),cross_product(y,y)),
inference(definition_unfolding,[],[f178,f28]) ).
fof(f276,plain,
subclass(intersection(x,cross_product(y,y)),complement(identity_relation)),
inference(unit_resulting_resolution,[],[f245,f176]) ).
fof(f277,plain,
member(regular(intersection(intersection(x,identity_relation),cross_product(y,y))),intersection(intersection(x,identity_relation),cross_product(y,y))),
inference(unit_resulting_resolution,[],[f68,f269]) ).
fof(f278,plain,
member(regular(intersection(cross_product(y,y),intersection(x,identity_relation))),intersection(cross_product(y,y),intersection(x,identity_relation))),
inference(forward_demodulation,[],[f277,f202]) ).
fof(f279,plain,
member(regular(intersection(cross_product(y,y),intersection(x,identity_relation))),intersection(x,identity_relation)),
inference(unit_resulting_resolution,[],[f22,f278]) ).
fof(f280,plain,
member(regular(intersection(cross_product(y,y),intersection(x,identity_relation))),cross_product(y,y)),
inference(unit_resulting_resolution,[],[f21,f278]) ).
fof(f281,plain,
member(regular(intersection(cross_product(y,y),intersection(x,identity_relation))),identity_relation),
inference(unit_resulting_resolution,[],[f22,f279]) ).
fof(f282,plain,
member(regular(intersection(cross_product(y,y),intersection(x,identity_relation))),x),
inference(unit_resulting_resolution,[],[f21,f279]) ).
fof(f298,plain,
member(regular(intersection(cross_product(y,y),intersection(x,identity_relation))),intersection(x,cross_product(y,y))),
inference(unit_resulting_resolution,[],[f23,f280,f282]) ).
fof(f589,plain,
~ member(regular(intersection(cross_product(y,y),intersection(x,identity_relation))),complement(identity_relation)),
inference(unit_resulting_resolution,[],[f24,f281]) ).
fof(f604,plain,
~ member(regular(intersection(cross_product(y,y),intersection(x,identity_relation))),intersection(x,cross_product(y,y))),
inference(unit_resulting_resolution,[],[f1,f276,f589]) ).
fof(f615,plain,
$false,
inference(forward_subsumption_resolution,[],[f604,f298]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM044-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n016.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 18:47:18 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 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
% 5.46/1.74 % (2926341)Input is clausal, will run a generic CNF schedule.
% 5.46/1.74 % (2926347)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1312663109:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 5.46/1.74 % (2926349)lrs+10_1_sil=8000:sp=occurrence:random_seed=275746377:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 5.46/1.74 % (2926348)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3615071487:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 5.46/1.74 % (2926352)dis-21_1_sil=8000:lcm=predicate:random_seed=1777319148: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)
% 5.46/1.74 % (2926346)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=3227948508:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 5.46/1.74 % (2926350)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=4017276360:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 5.46/1.74 % (2926351)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1722530443:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 5.46/1.74 % (2926349)Instruction limit reached!
% 5.46/1.74 % (2926349)------------------------------
% 5.46/1.74 % (2926349)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.46/1.74 % (2926349)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.46/1.74 % (2926349)CaDiCaL version: 2.1.3
% 5.46/1.74 % (2926349)Termination reason: Instruction limit
% 5.46/1.74 % (2926349)Termination phase: Saturation
% 5.46/1.74 % (2926349)Time elapsed: 0.042 s
% 5.46/1.74 % (2926349)Peak memory usage: 88 MB
% 5.46/1.74 % (2926349)Instructions burned: 107 (million)
% 5.46/1.74 % (2926350)Instruction limit reached!
% 5.46/1.74 % (2926350)------------------------------
% 5.46/1.74 % (2926350)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.46/1.74 % (2926350)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.46/1.74 % (2926350)CaDiCaL version: 2.1.3
% 5.46/1.74 % (2926350)Termination reason: Instruction limit
% 5.46/1.74 % (2926350)Termination phase: Saturation
% 5.46/1.74 % (2926350)Time elapsed: 0.071 s
% 5.46/1.74 % (2926350)Peak memory usage: 89 MB
% 5.46/1.74 % (2926350)Instructions burned: 115 (million)
% 5.46/1.74 % (2926352)Instruction limit reached!
% 5.46/1.74 % (2926352)------------------------------
% 5.46/1.74 % (2926352)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.46/1.74 % (2926352)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.46/1.74 % (2926352)CaDiCaL version: 2.1.3
% 5.46/1.74 % (2926352)Termination reason: Instruction limit
% 5.46/1.74 % (2926352)Termination phase: Saturation
% 5.46/1.74 % (2926352)Time elapsed: 0.075 s
% 5.46/1.74 % (2926352)Peak memory usage: 89 MB
% 5.46/1.74 % (2926352)Instructions burned: 119 (million)
% 5.46/1.74 % (2926351)Instruction limit reached!
% 5.46/1.74 % (2926351)------------------------------
% 5.46/1.74 % (2926351)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.46/1.74 % (2926351)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.46/1.74 % (2926351)CaDiCaL version: 2.1.3
% 5.46/1.74 % (2926351)Termination reason: Instruction limit
% 5.46/1.74 % (2926351)Termination phase: Saturation
% 5.46/1.74 % (2926351)Time elapsed: 0.139 s
% 5.46/1.74 % (2926351)Peak memory usage: 91 MB
% 5.46/1.74 % (2926351)Instructions burned: 180 (million)
% 5.46/1.74 % (2926360)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=1181493092:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 5.46/1.74 % (2926360)Refutation not found, incomplete strategy
% 5.46/1.74 % (2926360)------------------------------
% 5.46/1.74 % (2926360)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.46/1.74 % (2926360)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.46/1.74 % (2926360)CaDiCaL version: 2.1.3
% 5.46/1.74 % (2926360)Termination reason: Refutation not found, incomplete strategy
% 5.46/1.74 % (2926360)Time elapsed: 0.003 s
% 5.46/1.74 % (2926360)Peak memory usage: 88 MB
% 5.46/1.74 % (2926360)Instructions burned: 3 (million)
% 5.46/1.74 % (2926362)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=3773191850:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 5.46/1.74 % (2926361)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=756766240: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)
% 5.46/1.74 % (2926362)Refutation not found, incomplete strategy
% 5.46/1.74 % (2926362)------------------------------
% 5.46/1.74 % (2926362)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.46/1.74 % (2926362)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.46/1.74 % (2926362)CaDiCaL version: 2.1.3
% 5.46/1.74 % (2926362)Termination reason: Refutation not found, incomplete strategy
% 5.46/1.74 % (2926362)Time elapsed: 0.004 s
% 5.46/1.74 % (2926362)Peak memory usage: 88 MB
% 5.46/1.74 % (2926362)Instructions burned: 4 (million)
% 5.46/1.74 % (2926363)lrs+10_64_to=lpo:sil=8000:random_seed=740500285:i=126:bd=preordered_2997 on theBenchmark for (2997ds/126Mi)
% 5.46/1.74 % (2926361)Instruction limit reached!
% 5.46/1.74 % (2926361)------------------------------
% 5.46/1.74 % (2926361)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.46/1.74 % (2926361)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.46/1.74 % (2926361)CaDiCaL version: 2.1.3
% 5.46/1.74 % (2926361)Termination reason: Instruction limit
% 5.46/1.74 % (2926361)Termination phase: Saturation
% 5.46/1.74 % (2926361)Time elapsed: 0.097 s
% 5.46/1.74 % (2926361)Peak memory usage: 90 MB
% 5.46/1.74 % (2926361)Instructions burned: 189 (million)
% 5.46/1.74 % (2926363)Instruction limit reached!
% 5.46/1.74 % (2926363)------------------------------
% 5.46/1.74 % (2926363)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.46/1.74 % (2926363)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.46/1.74 % (2926363)CaDiCaL version: 2.1.3
% 5.46/1.74 % (2926363)Termination reason: Instruction limit
% 5.46/1.74 % (2926363)Termination phase: Saturation
% 5.46/1.74 % (2926363)Time elapsed: 0.082 s
% 5.46/1.74 % (2926363)Peak memory usage: 89 MB
% 5.46/1.74 % (2926363)Instructions burned: 127 (million)
% 5.46/1.74 % (2926347)First to succeed.
% 5.46/1.74 % (2926347)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2926341"
% 5.46/1.74 % (2926360)------------------------------
% 5.46/1.74 % (2926360)------------------------------
% 5.46/1.74 % (2926368)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=2935436712:avsq=on:i=194:fgj=on:bd=preordered_2995 on theBenchmark for (2995ds/194Mi)
% 5.46/1.74 % (2926362)------------------------------
% 5.46/1.74 % (2926362)------------------------------
% 5.46/1.74 % (2926369)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=2280343488:i=157:gtg=all_2995 on theBenchmark for (2995ds/157Mi)
% 5.46/1.74 % (2926347)Refutation found. Thanks to Tanya!
% 5.46/1.74 % SZS status Unsatisfiable for theBenchmark
% 5.46/1.74 % SZS output start Proof for theBenchmark
% See solution above
% 5.46/1.74 % (2926347)------------------------------
% 5.46/1.74 % (2926347)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.46/1.74 % (2926347)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.46/1.74 % (2926347)CaDiCaL version: 2.1.3
% 5.46/1.74 % (2926347)Termination reason: Refutation
% 5.46/1.74 % (2926347)Time elapsed: 0.403 s
% 5.46/1.74 % (2926347)Peak memory usage: 130 MB
% 5.46/1.74 % (2926347)Instructions burned: 1077 (million)
% 5.46/1.74 % (2926347)------------------------------
% 5.46/1.74 % (2926347)------------------------------
% 5.46/1.74 % (2926341)Success in time 0.691 s
% 5.46/1.74 % Vampire exiting
%------------------------------------------------------------------------------