%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET072-7 : 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 : n014.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 12:39:57 PM UTC 2026
% Result : Unsatisfiable 2.55s 1.32s
% Output : Refutation 2.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of formulae : 40 ( 16 unt; 3 def)
% Number of atoms : 70 ( 17 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 57 ( 27 ~; 27 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 27 ( 0 sgn 27 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [X2,X0,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| X0 = X1
| X0 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_member) ).
fof(f9,axiom,
! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair2) ).
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(f103,axiom,
! [X2,X3,X0,X1] :
( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| member(X0,universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',corollary_1_to_cartesian_product) ).
fof(f104,axiom,
! [X2,X3,X0,X1] :
( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| member(X1,universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',corollary_2_to_cartesian_product) ).
fof(f127,negated_conjecture,
unordered_pair(x,z) = unordered_pair(y,z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_right_cancellation_1) ).
fof(f128,negated_conjecture,
member(ordered_pair(x,y),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_right_cancellation_2) ).
fof(f129,negated_conjecture,
x != y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_right_cancellation_3) ).
fof(f130,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(f131,plain,
member(unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y))),cross_product(universal_class,universal_class)),
inference(definition_unfolding,[],[f128,f130]) ).
fof(f139,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,universal_class) ),
inference(definition_unfolding,[],[f104,f130]) ).
fof(f140,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,universal_class) ),
inference(definition_unfolding,[],[f103,f130]) ).
fof(f157,plain,
( member(y,unordered_pair(x,z))
| ~ member(y,universal_class) ),
inference(superposition,[],[f9,f127]) ).
fof(f161,definition,
( spl0_1
<=> member(y,universal_class) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f164,definition,
( spl0_2
<=> member(y,unordered_pair(x,z)) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f165,plain,
( member(y,unordered_pair(x,z))
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f164]) ).
fof(f166,plain,
( ~ spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f157,f164,f161]) ).
fof(f277,plain,
! [X0] :
( ~ member(X0,unordered_pair(x,z))
| y = X0
| z = X0 ),
inference(superposition,[],[f8,f127]) ).
fof(f368,definition,
( spl0_13
<=> member(x,universal_class) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f369,plain,
( member(x,universal_class)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f368]) ).
fof(f374,plain,
member(y,universal_class),
inference(resolution,[],[f139,f131]) ).
fof(f421,plain,
spl0_1,
inference(avatar_split_clause,[],[f374,f161]) ).
fof(f422,plain,
member(x,universal_class),
inference(resolution,[],[f140,f131]) ).
fof(f508,plain,
( x = y
| z = y
| ~ spl0_2 ),
inference(resolution,[],[f165,f8]) ).
fof(f511,plain,
( z = y
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f508,f129]) ).
fof(f657,plain,
( x = y
| x = z
| ~ member(x,universal_class) ),
inference(resolution,[],[f277,f9]) ).
fof(f666,plain,
( x = z
| ~ member(x,universal_class) ),
inference(forward_subsumption_resolution,[],[f657,f129]) ).
fof(f667,plain,
( x = z
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f666,f369]) ).
fof(f668,plain,
( x = y
| ~ spl0_2
| ~ spl0_13 ),
inference(superposition,[],[f667,f511]) ).
fof(f680,plain,
( $false
| ~ spl0_2
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f668,f129]) ).
fof(f681,plain,
( ~ spl0_2
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f680]) ).
fof(f682,plain,
spl0_13,
inference(avatar_split_clause,[],[f422,f368]) ).
cnf(s1,plain,
( ~ spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f166]) ).
cnf(s21,plain,
spl0_1,
inference(sat_conversion,[],[f421]) ).
cnf(s31,plain,
( ~ spl0_2
| ~ spl0_13 ),
inference(sat_conversion,[],[f681]) ).
cnf(s32,plain,
spl0_13,
inference(sat_conversion,[],[f682]) ).
cnf(s37,plain,
~ spl0_2,
inference(rat,[],[s31,s32]) ).
cnf(s40,plain,
$false,
inference(rat,[],[s1,s37,s21]) ).
fof(f692,plain,
$false,
inference(avatar_sat_refutation,[],[s40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET072-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n014.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 : Mon Sep 28 00:30:32 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 2.55/1.32 % (1316615)Input is clausal, will run a generic CNF schedule.
% 2.55/1.32 % (1316624)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=438354612:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.55/1.32 % (1316624)First to succeed.
% 2.55/1.32 % (1316624)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1316615"
% 2.55/1.32 % (1316623)lrs+10_1_sil=8000:sp=occurrence:random_seed=243363392:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.55/1.32 % (1316623)Also succeeded, but the first one will report.
% 2.55/1.32 % (1316620)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=4199652952:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.55/1.32 % (1316621)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2406388361:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.55/1.32 % (1316622)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2502758868:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.55/1.32 % (1316625)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=556087468:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.55/1.32 % (1316626)dis-21_1_sil=8000:lcm=predicate:random_seed=397632771: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)
% 2.55/1.32 % (1316625)Also succeeded, but the first one will report.
% 2.55/1.32 % (1316626)Instruction limit reached!
% 2.55/1.32 % (1316626)------------------------------
% 2.55/1.32 % (1316626)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.55/1.32 % (1316626)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.55/1.32 % (1316626)CaDiCaL version: 2.1.3
% 2.55/1.32 % (1316626)Termination reason: Instruction limit
% 2.55/1.32 % (1316626)Termination phase: Saturation
% 2.55/1.32 % (1316626)Time elapsed: 0.078 s
% 2.55/1.32 % (1316626)Peak memory usage: 88 MB
% 2.55/1.32 % (1316626)Instructions burned: 119 (million)
% 2.55/1.32 % (1316624)Refutation found. Thanks to Tanya!
% 2.55/1.32 % SZS status Unsatisfiable for theBenchmark
% 2.55/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 2.55/1.32 % (1316624)------------------------------
% 2.55/1.32 % (1316624)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.55/1.32 % (1316624)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.55/1.32 % (1316624)CaDiCaL version: 2.1.3
% 2.55/1.32 % (1316624)Termination reason: Refutation
% 2.55/1.32 % (1316624)Time elapsed: 0.009 s
% 2.55/1.32 % (1316624)Peak memory usage: 89 MB
% 2.55/1.32 % (1316624)Instructions burned: 22 (million)
% 2.55/1.32 % (1316624)------------------------------
% 2.55/1.32 % (1316624)------------------------------
% 2.55/1.32 % (1316615)Success in time 0.278 s
% 2.55/1.32 % Vampire exiting
%------------------------------------------------------------------------------