%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET020-6 : 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 : n006.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 12:39:37 PM UTC 2026
% Result : Unsatisfiable 0.14s 1.51s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 14
% Syntax : Number of formulae : 49 ( 15 unt; 3 def)
% Number of atoms : 96 ( 11 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 95 ( 48 ~; 44 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 46 ( 0 sgn 46 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_members) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',class_elements_are_sets) ).
fof(f8,axiom,
! [X2,X0,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| X0 = X1
| X0 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_member) ).
fof(f9,axiom,
! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair2) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_set) ).
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(f15,axiom,
! [X2,X3,X0,X1] :
( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| member(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartesian_product2) ).
fof(f16,axiom,
! [X2,X3,X0,X1] :
( member(ordered_pair(X0,X2),cross_product(X1,X3))
| ~ member(X2,X3)
| ~ member(X0,X1) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',cartesian_product4) ).
fof(f101,negated_conjecture,
member(ordered_pair(u,v),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_unique_1st_and_2nd_in_pair_of_sets1_1) ).
fof(f102,negated_conjecture,
first(ordered_pair(u,v)) != u,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_unique_1st_and_2nd_in_pair_of_sets1_2) ).
fof(f103,plain,
u != first(ordered_pair(u,v)),
inference(reorient_equations,[],[f102]) ).
fof(f111,plain,
! [X0] :
( member(X0,singleton(X0))
| ~ member(X0,universal_class) ),
inference(superposition,[],[f9,f12]) ).
fof(f276,plain,
! [X0,X1] :
( ~ member(X1,singleton(X0))
| X0 = X1
| X0 = X1 ),
inference(superposition,[],[f8,f12]) ).
fof(f277,plain,
! [X0,X1] :
( ~ member(X1,singleton(X0))
| X0 = X1 ),
inference(duplicate_literal_removal,[],[f276]) ).
fof(f302,plain,
ordered_pair(u,v) = ordered_pair(first(ordered_pair(u,v)),second(ordered_pair(u,v))),
inference(resolution,[],[f17,f101]) ).
fof(f315,plain,
! [X0,X1] :
( ~ member(ordered_pair(u,v),cross_product(X0,X1))
| member(second(ordered_pair(u,v)),X1) ),
inference(superposition,[],[f15,f302]) ).
fof(f316,plain,
! [X0,X1] :
( ~ member(ordered_pair(u,v),cross_product(X0,X1))
| member(first(ordered_pair(u,v)),X0) ),
inference(superposition,[],[f14,f302]) ).
fof(f341,plain,
! [X0,X1] :
( member(ordered_pair(u,v),cross_product(X0,X1))
| ~ member(second(ordered_pair(u,v)),X1)
| ~ member(first(ordered_pair(u,v)),X0) ),
inference(superposition,[],[f16,f302]) ).
fof(f1350,definition,
( spl0_94
<=> member(first(ordered_pair(u,v)),universal_class) ),
introduced(definition,[new_symbols(definition,[spl0_94])],[avatar_definition]) ).
fof(f1351,plain,
( member(first(ordered_pair(u,v)),universal_class)
| ~ spl0_94 ),
inference(avatar_component_clause,[],[f1350]) ).
fof(f1352,plain,
( ~ member(first(ordered_pair(u,v)),universal_class)
| spl0_94 ),
inference(avatar_component_clause,[],[f1350]) ).
fof(f1370,plain,
( ! [X0] :
( ~ member(first(ordered_pair(u,v)),X0)
| ~ subclass(X0,universal_class) )
| spl0_94 ),
inference(resolution,[],[f1352,f1]) ).
fof(f1371,plain,
( ! [X0] : ~ member(first(ordered_pair(u,v)),X0)
| spl0_94 ),
inference(forward_subsumption_resolution,[],[f1370,f4]) ).
fof(f1577,plain,
member(second(ordered_pair(u,v)),universal_class),
inference(resolution,[],[f315,f101]) ).
fof(f1607,plain,
( ! [X0,X1] : ~ member(ordered_pair(u,v),cross_product(X0,X1))
| spl0_94 ),
inference(forward_subsumption_resolution,[],[f316,f1371]) ).
fof(f1608,plain,
( $false
| spl0_94 ),
inference(resolution,[],[f1607,f101]) ).
fof(f1612,plain,
spl0_94,
inference(avatar_contradiction_clause,[],[f1608]) ).
fof(f1666,plain,
! [X0,X1] :
( ~ member(second(ordered_pair(u,v)),X0)
| ~ member(first(ordered_pair(u,v)),X1)
| member(u,X1) ),
inference(resolution,[],[f341,f14]) ).
fof(f1669,definition,
( spl0_114
<=> ! [X1] :
( ~ member(first(ordered_pair(u,v)),X1)
| member(u,X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_114])],[avatar_definition]) ).
fof(f1670,plain,
( ! [X1] :
( ~ member(first(ordered_pair(u,v)),X1)
| member(u,X1) )
| ~ spl0_114 ),
inference(avatar_component_clause,[],[f1669]) ).
fof(f1672,definition,
( spl0_115
<=> ! [X0] : ~ member(second(ordered_pair(u,v)),X0) ),
introduced(definition,[new_symbols(definition,[spl0_115])],[avatar_definition]) ).
fof(f1673,plain,
( ! [X0] : ~ member(second(ordered_pair(u,v)),X0)
| ~ spl0_115 ),
inference(avatar_component_clause,[],[f1672]) ).
fof(f1674,plain,
( spl0_114
| spl0_115 ),
inference(avatar_split_clause,[],[f1666,f1672,f1669]) ).
fof(f2555,plain,
( member(u,singleton(first(ordered_pair(u,v))))
| ~ member(first(ordered_pair(u,v)),universal_class)
| ~ spl0_114 ),
inference(resolution,[],[f1670,f111]) ).
fof(f2585,plain,
( member(u,singleton(first(ordered_pair(u,v))))
| ~ spl0_94
| ~ spl0_114 ),
inference(forward_subsumption_resolution,[],[f2555,f1351]) ).
fof(f2618,plain,
( u = first(ordered_pair(u,v))
| ~ spl0_94
| ~ spl0_114 ),
inference(resolution,[],[f2585,f277]) ).
fof(f2619,plain,
( $false
| ~ spl0_94
| ~ spl0_114 ),
inference(forward_subsumption_resolution,[],[f2618,f103]) ).
fof(f2620,plain,
( ~ spl0_94
| ~ spl0_114 ),
inference(avatar_contradiction_clause,[],[f2619]) ).
fof(f2625,plain,
( $false
| ~ spl0_115 ),
inference(resolution,[],[f1673,f1577]) ).
fof(f2648,plain,
~ spl0_115,
inference(avatar_contradiction_clause,[],[f2625]) ).
cnf(s68,plain,
spl0_94,
inference(sat_conversion,[],[f1612]) ).
cnf(s73,plain,
( spl0_114
| spl0_115 ),
inference(sat_conversion,[],[f1674]) ).
cnf(s124,plain,
( ~ spl0_94
| ~ spl0_114 ),
inference(sat_conversion,[],[f2620]) ).
cnf(s125,plain,
~ spl0_115,
inference(sat_conversion,[],[f2648]) ).
cnf(s127,plain,
spl0_114,
inference(rat,[],[s73,s125]) ).
cnf(s128,plain,
~ spl0_94,
inference(rat,[],[s124,s127]) ).
cnf(s131,plain,
$false,
inference(rat,[],[s68,s128]) ).
fof(f2650,plain,
$false,
inference(avatar_sat_refutation,[],[s131]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET020-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n006.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 28 00:09:26 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 Running first-order theorem proving
% 0.12/0.40 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
% 2.77/1.31 % (3472961)Input is clausal, will run a generic CNF schedule.
% 2.77/1.31 % (3472966)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=3576304824:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.77/1.31 % (3472970)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2281466000:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.77/1.31 % (3472967)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=228932813:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.77/1.31 % (3472971)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3185872217:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.77/1.31 % (3472969)lrs+10_1_sil=8000:sp=occurrence:random_seed=2025084680:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.77/1.31 % (3472968)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=750481255:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.77/1.31 % (3472972)dis-21_1_sil=8000:lcm=predicate:random_seed=3178645710: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)
% 2.77/1.31 % (3472969)Instruction limit reached!
% 2.77/1.31 % (3472969)------------------------------
% 2.77/1.31 % (3472969)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.77/1.31 % (3472969)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/1.31 % (3472969)CaDiCaL version: 2.1.3
% 2.77/1.31 % (3472969)Termination reason: Instruction limit
% 2.77/1.31 % (3472969)Termination phase: Saturation
% 2.77/1.31 % (3472969)Time elapsed: 0.075 s
% 2.77/1.31 % (3472969)Peak memory usage: 89 MB
% 2.77/1.31 % (3472969)Instructions burned: 108 (million)
% 2.77/1.31 % (3472972)Instruction limit reached!
% 2.77/1.31 % (3472972)------------------------------
% 2.77/1.31 % (3472972)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.77/1.31 % (3472972)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/1.31 % (3472972)CaDiCaL version: 2.1.3
% 2.77/1.31 % (3472972)Termination reason: Instruction limit
% 2.77/1.31 % (3472972)Termination phase: Saturation
% 2.77/1.31 % (3472972)Time elapsed: 0.067 s
% 2.77/1.31 % (3472972)Peak memory usage: 89 MB
% 2.77/1.31 % (3472972)Instructions burned: 119 (million)
% 2.77/1.31 % (3472970)Instruction limit reached!
% 2.77/1.31 % (3472970)------------------------------
% 2.77/1.31 % (3472970)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.77/1.31 % (3472970)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/1.31 % (3472970)CaDiCaL version: 2.1.3
% 2.77/1.31 % (3472970)Termination reason: Instruction limit
% 2.77/1.31 % (3472970)Termination phase: Saturation
% 2.77/1.31 % (3472970)Time elapsed: 0.082 s
% 2.77/1.31 % (3472970)Peak memory usage: 89 MB
% 2.77/1.31 % (3472970)Instructions burned: 114 (million)
% 2.77/1.31 % (3472971)First to succeed.
% 2.77/1.31 % (3472971)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3472961"
% 2.77/1.31 % (3472980)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=989804458:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 2.77/1.31 % (3472982)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=653697400:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 2.77/1.31 % (3472981)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2392087064: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)
% 2.77/1.31 % (3472980)Refutation not found, incomplete strategy
% 2.77/1.31 % (3472980)------------------------------
% 2.77/1.31 % (3472980)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.77/1.31 % (3472980)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/1.31 % (3472980)CaDiCaL version: 2.1.3
% 2.77/1.31 % (3472980)Termination reason: Refutation not found, incomplete strategy
% 2.77/1.31 % (3472980)Time elapsed: 0.002 s
% 2.77/1.31 % (3472980)Peak memory usage: 88 MB
% 2.77/1.31 % (3472980)Instructions burned: 1 (million)
% 2.77/1.31 % (3472982)Refutation not found, incomplete strategy
% 0.14/1.51 % (3472982)------------------------------
% 0.14/1.51 % (3472982)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.14/1.51 % (3472982)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.14/1.51 % (3472982)CaDiCaL version: 2.1.3
% 0.14/1.51 % (3472982)Termination reason: Refutation not found, incomplete strategy
% 0.14/1.51 % (3472982)Time elapsed: 0.007 s
% 0.14/1.51 % (3472982)Peak memory usage: 88 MB
% 0.14/1.51 % (3472982)Instructions burned: 9 (million)
% 0.14/1.51 % (3472981)Instruction limit reached!
% 0.14/1.51 % (3472981)------------------------------
% 0.14/1.51 % (3472981)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.14/1.51 % (3472981)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.14/1.51 % (3472981)CaDiCaL version: 2.1.3
% 0.14/1.51 % (3472981)Termination reason: Instruction limit
% 0.14/1.51 % (3472981)Termination phase: Saturation
% 0.14/1.51 % (3472981)Time elapsed: 0.088 s
% 0.14/1.51 % (3472981)Peak memory usage: 90 MB
% 0.14/1.51 % (3472981)Instructions burned: 189 (million)
% 0.14/1.51 % (3472971)Refutation found. Thanks to Tanya!
% 0.14/1.51 % SZS status Unsatisfiable for theBenchmark
% 0.14/1.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/1.51 % (3472971)------------------------------
% 0.14/1.51 % (3472971)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.14/1.51 % (3472971)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.14/1.51 % (3472971)CaDiCaL version: 2.1.3
% 0.14/1.51 % (3472971)Termination reason: Refutation
% 0.14/1.51 % (3472971)Time elapsed: 0.078 s
% 0.14/1.51 % (3472971)Peak memory usage: 90 MB
% 0.14/1.51 % (3472971)Instructions burned: 101 (million)
% 0.14/1.51 % (3472971)------------------------------
% 0.14/1.51 % (3472971)------------------------------
% 0.14/1.51 % (3472961)Success in time 0.488 s
% 0.14/1.51 % Vampire exiting
%------------------------------------------------------------------------------