%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET017-6 : 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 : n013.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 12:39:35 PM UTC 2026
% Result : Unsatisfiable 0.19s 1.51s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 13
% Syntax : Number of formulae : 47 ( 17 unt; 4 def)
% Number of atoms : 82 ( 18 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 65 ( 30 ~; 31 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 5 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(f10,axiom,
! [X0,X1] :
( member(X0,unordered_pair(X1,X0))
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair3) ).
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(f101,negated_conjecture,
unordered_pair(x,y) = unordered_pair(x,z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_left_cancellation_1) ).
fof(f102,negated_conjecture,
member(ordered_pair(y,z),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_left_cancellation_2) ).
fof(f103,negated_conjecture,
y != z,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_left_cancellation_3) ).
fof(f104,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(f105,plain,
member(unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z))),cross_product(universal_class,universal_class)),
inference(definition_unfolding,[],[f102,f104]) ).
fof(f107,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,f104]) ).
fof(f108,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,f104]) ).
fof(f111,plain,
( member(z,unordered_pair(x,y))
| ~ member(z,universal_class) ),
inference(superposition,[],[f10,f101]) ).
fof(f113,definition,
( spl0_1
<=> member(z,universal_class) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f115,plain,
( ~ member(z,universal_class)
| spl0_1 ),
inference(avatar_component_clause,[],[f113]) ).
fof(f117,definition,
( spl0_2
<=> member(z,unordered_pair(x,y)) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f119,plain,
( member(z,unordered_pair(x,y))
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f117]) ).
fof(f120,plain,
( ~ spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f111,f117,f113]) ).
fof(f123,plain,
! [X0] :
( ~ member(X0,unordered_pair(x,y))
| x = X0
| z = X0 ),
inference(superposition,[],[f8,f101]) ).
fof(f125,plain,
( x = y
| y = z
| ~ member(y,universal_class) ),
inference(resolution,[],[f123,f10]) ).
fof(f126,plain,
( x = y
| ~ member(y,universal_class) ),
inference(forward_subsumption_resolution,[],[f125,f103]) ).
fof(f128,definition,
( spl0_3
<=> member(y,universal_class) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f130,plain,
( ~ member(y,universal_class)
| spl0_3 ),
inference(avatar_component_clause,[],[f128]) ).
fof(f132,definition,
( spl0_4
<=> x = y ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f134,plain,
( x = y
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f132]) ).
fof(f135,plain,
( ~ spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f126,f132,f128]) ).
fof(f136,plain,
member(z,universal_class),
inference(resolution,[],[f107,f105]) ).
fof(f137,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f136,f115]) ).
fof(f138,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f137]) ).
fof(f139,plain,
member(y,universal_class),
inference(resolution,[],[f108,f105]) ).
fof(f140,plain,
( $false
| spl0_3 ),
inference(forward_subsumption_resolution,[],[f139,f130]) ).
fof(f141,plain,
spl0_3,
inference(avatar_contradiction_clause,[],[f140]) ).
fof(f148,plain,
( x = z
| y = z
| ~ spl0_2 ),
inference(resolution,[],[f119,f8]) ).
fof(f150,plain,
( x = z
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f148,f103]) ).
fof(f155,plain,
( x != y
| ~ spl0_2 ),
inference(superposition,[],[f103,f150]) ).
fof(f156,plain,
( $false
| ~ spl0_2
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f155,f134]) ).
fof(f157,plain,
( ~ spl0_2
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[],[f156]) ).
cnf(s1,plain,
( ~ spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f120]) ).
cnf(s2,plain,
( ~ spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f135]) ).
cnf(s3,plain,
spl0_1,
inference(sat_conversion,[],[f138]) ).
cnf(s4,plain,
spl0_3,
inference(sat_conversion,[],[f141]) ).
cnf(s5,plain,
( ~ spl0_2
| ~ spl0_4 ),
inference(sat_conversion,[],[f157]) ).
cnf(s6,plain,
spl0_4,
inference(rat,[],[s2,s4]) ).
cnf(s7,plain,
~ spl0_2,
inference(rat,[],[s5,s6]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s1,s7,s3]) ).
fof(f160,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET017-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n013.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Mon Sep 28 00:08:21 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 0.19/1.51 % (683204)Input is clausal, will run a generic CNF schedule.
% 0.19/1.51 % (683215)dis-21_1_sil=8000:lcm=predicate:random_seed=964643903: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)
% 0.19/1.51 % (683215)Instruction limit reached!
% 0.19/1.51 % (683215)------------------------------
% 0.19/1.51 % (683215)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.51 % (683215)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.51 % (683215)CaDiCaL version: 2.1.3
% 0.19/1.51 % (683215)Termination reason: Instruction limit
% 0.19/1.51 % (683215)Termination phase: Saturation
% 0.19/1.51 % (683215)Time elapsed: 0.035 s
% 0.19/1.51 % (683215)Peak memory usage: 89 MB
% 0.19/1.51 % (683215)Instructions burned: 118 (million)
% 0.19/1.51 % (683209)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=3653231538:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.19/1.51 % (683213)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3446054909:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.19/1.51 % (683210)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=480495443:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.19/1.51 % (683211)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=700529023:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.19/1.51 % (683212)lrs+10_1_sil=8000:sp=occurrence:random_seed=2249386160:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.19/1.51 % (683212)First to succeed.
% 0.19/1.51 % (683212)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-683204"
% 0.19/1.51 % (683213)Also succeeded, but the first one will report.
% 0.19/1.51 % (683214)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2691750448:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.19/1.51 % (683214)Also succeeded, but the first one will report.
% 0.19/1.51 % (683217)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=2445723449:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 0.19/1.51 % (683217)Refutation not found, incomplete strategy
% 0.19/1.51 % (683217)------------------------------
% 0.19/1.51 % (683217)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.51 % (683217)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.51 % (683217)CaDiCaL version: 2.1.3
% 0.19/1.51 % (683217)Termination reason: Refutation not found, incomplete strategy
% 0.19/1.51 % (683217)Time elapsed: 0.002 s
% 0.19/1.51 % (683217)Peak memory usage: 88 MB
% 0.19/1.51 % (683217)Instructions burned: 2 (million)
% 0.19/1.51 % (683212)Refutation found. Thanks to Tanya!
% 0.19/1.51 % SZS status Unsatisfiable for theBenchmark
% 0.19/1.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/1.51 % (683212)------------------------------
% 0.19/1.51 % (683212)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.51 % (683212)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.51 % (683212)CaDiCaL version: 2.1.3
% 0.19/1.51 % (683212)Termination reason: Refutation
% 0.19/1.51 % (683212)Time elapsed: 0.004 s
% 0.19/1.51 % (683212)Peak memory usage: 89 MB
% 0.19/1.51 % (683212)Instructions burned: 3 (million)
% 0.19/1.51 % (683212)------------------------------
% 0.19/1.51 % (683212)------------------------------
% 0.19/1.51 % (683204)Success in time 0.442 s
% 0.19/1.51 % Vampire exiting
%------------------------------------------------------------------------------