%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET021-7 : 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 12:39:38 PM UTC 2026
% Result : Unsatisfiable 3.80s 1.41s
% Output : Refutation 3.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 29 ( 11 unt; 3 def)
% Number of atoms : 55 ( 15 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 54 ( 28 ~; 23 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 19 ( 0 sgn 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(f173,axiom,
! [X2,X3,X0,X1] :
( ordered_pair(X0,X1) != ordered_pair(X2,X3)
| ~ member(X1,universal_class)
| X1 = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pair_determines_components2) ).
fof(f179,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_sets2_1) ).
fof(f180,negated_conjecture,
second(ordered_pair(u,v)) != v,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_unique_1st_and_2nd_in_pair_of_sets2_2) ).
fof(f181,plain,
v != second(ordered_pair(u,v)),
inference(reorient_equations,[],[f180]) ).
fof(f310,definition,
( spl0_3
<=> ordered_pair(u,v) = ordered_pair(first(ordered_pair(u,v)),second(ordered_pair(u,v))) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f312,plain,
( ordered_pair(u,v) = ordered_pair(first(ordered_pair(u,v)),second(ordered_pair(u,v)))
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f310]) ).
fof(f318,plain,
ordered_pair(u,v) = ordered_pair(first(ordered_pair(u,v)),second(ordered_pair(u,v))),
inference(resolution,[],[f17,f179]) ).
fof(f321,plain,
spl0_3,
inference(avatar_split_clause,[],[f318,f310]) ).
fof(f325,plain,
( ! [X0,X1] :
( ~ member(ordered_pair(u,v),cross_product(X0,X1))
| member(second(ordered_pair(u,v)),X1) )
| ~ spl0_3 ),
inference(superposition,[],[f15,f312]) ).
fof(f419,plain,
( ! [X0,X1] :
( ordered_pair(X0,X1) != ordered_pair(u,v)
| ~ member(second(ordered_pair(u,v)),universal_class)
| second(ordered_pair(u,v)) = X1 )
| ~ spl0_3 ),
inference(superposition,[],[f173,f312]) ).
fof(f423,definition,
( spl0_17
<=> member(second(ordered_pair(u,v)),universal_class) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f427,definition,
( spl0_18
<=> ! [X0,X1] :
( ordered_pair(X0,X1) != ordered_pair(u,v)
| second(ordered_pair(u,v)) = X1 ) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f428,plain,
( ! [X0,X1] :
( ordered_pair(X0,X1) != ordered_pair(u,v)
| second(ordered_pair(u,v)) = X1 )
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f427]) ).
fof(f429,plain,
( ~ spl0_17
| spl0_18
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f419,f310,f427,f423]) ).
fof(f1899,plain,
( member(second(ordered_pair(u,v)),universal_class)
| ~ spl0_3 ),
inference(resolution,[],[f325,f179]) ).
fof(f1968,plain,
( v = second(ordered_pair(u,v))
| ~ spl0_18 ),
inference(equality_resolution,[],[f428]) ).
fof(f1969,plain,
( $false
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f1968,f181]) ).
fof(f1970,plain,
~ spl0_18,
inference(avatar_contradiction_clause,[],[f1969]) ).
fof(f1997,plain,
( spl0_17
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f1899,f310,f423]) ).
cnf(s3,plain,
spl0_3,
inference(sat_conversion,[],[f321]) ).
cnf(s12,plain,
( ~ spl0_3
| ~ spl0_17
| spl0_18 ),
inference(sat_conversion,[],[f429]) ).
cnf(s72,plain,
~ spl0_18,
inference(sat_conversion,[],[f1970]) ).
cnf(s77,plain,
( ~ spl0_3
| spl0_17 ),
inference(sat_conversion,[],[f1997]) ).
cnf(s82,plain,
( ~ spl0_3
| ~ spl0_17 ),
inference(rat,[],[s12,s72]) ).
cnf(s87,plain,
spl0_17,
inference(rat,[],[s77,s3]) ).
cnf(s90,plain,
$false,
inference(rat,[],[s82,s87,s3]) ).
fof(f1998,plain,
$false,
inference(avatar_sat_refutation,[],[s90]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET021-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n006.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 28 00:09:56 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 3.80/1.41 % (3473788)Input is clausal, will run a generic CNF schedule.
% 3.80/1.41 % (3473799)dis-21_1_sil=8000:lcm=predicate:random_seed=3443646076: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)
% 3.80/1.41 % (3473796)lrs+10_1_sil=8000:sp=occurrence:random_seed=2970414893:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.80/1.41 % (3473793)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=1570476288:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.80/1.41 % (3473794)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=887422966:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.80/1.41 % (3473797)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3994019488:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.80/1.41 % (3473798)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=816591896:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.80/1.41 % (3473795)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=881010799:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.80/1.41 % (3473799)Instruction limit reached!
% 3.80/1.41 % (3473799)------------------------------
% 3.80/1.41 % (3473799)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.80/1.41 % (3473799)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.80/1.41 % (3473799)CaDiCaL version: 2.1.3
% 3.80/1.41 % (3473799)Termination reason: Instruction limit
% 3.80/1.41 % (3473799)Termination phase: Saturation
% 3.80/1.41 % (3473799)Time elapsed: 0.040 s
% 3.80/1.41 % (3473799)Peak memory usage: 89 MB
% 3.80/1.41 % (3473799)Instructions burned: 119 (million)
% 3.80/1.41 % (3473798)First to succeed.
% 3.80/1.41 % (3473798)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3473788"
% 3.80/1.41 % (3473797)Instruction limit reached!
% 3.80/1.41 % (3473797)------------------------------
% 3.80/1.41 % (3473797)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.80/1.41 % (3473797)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.80/1.41 % (3473797)CaDiCaL version: 2.1.3
% 3.80/1.41 % (3473797)Termination reason: Instruction limit
% 3.80/1.41 % (3473797)Termination phase: Saturation
% 3.80/1.41 % (3473797)Time elapsed: 0.065 s
% 3.80/1.41 % (3473797)Peak memory usage: 88 MB
% 3.80/1.41 % (3473797)Instructions burned: 114 (million)
% 3.80/1.41 % (3473796)Instruction limit reached!
% 3.80/1.41 % (3473796)------------------------------
% 3.80/1.41 % (3473796)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.80/1.41 % (3473796)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.80/1.41 % (3473796)CaDiCaL version: 2.1.3
% 3.80/1.41 % (3473796)Termination reason: Instruction limit
% 3.80/1.41 % (3473796)Termination phase: Saturation
% 3.80/1.41 % (3473796)Time elapsed: 0.071 s
% 3.80/1.41 % (3473796)Peak memory usage: 89 MB
% 3.80/1.41 % (3473796)Instructions burned: 107 (million)
% 3.80/1.41 % (3473807)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=1295301703:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 3.80/1.41 % (3473807)Refutation not found, incomplete strategy
% 3.80/1.41 % (3473807)------------------------------
% 3.80/1.41 % (3473807)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.80/1.41 % (3473807)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.80/1.41 % (3473807)CaDiCaL version: 2.1.3
% 3.80/1.41 % (3473807)Termination reason: Refutation not found, incomplete strategy
% 3.80/1.41 % (3473807)Time elapsed: 0.001 s
% 3.80/1.41 % (3473807)Peak memory usage: 88 MB
% 3.80/1.41 % (3473807)Instructions burned: 2 (million)
% 3.80/1.41 % (3473808)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1324084373: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)
% 3.80/1.41 % (3473809)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=19905540:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 3.80/1.41 % (3473809)Refutation not found, incomplete strategy
% 3.80/1.41 % (3473809)------------------------------
% 3.80/1.41 % (3473809)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.80/1.41 % (3473809)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.80/1.41 % (3473809)CaDiCaL version: 2.1.3
% 3.80/1.41 % (3473809)Termination reason: Refutation not found, incomplete strategy
% 3.80/1.41 % (3473809)Time elapsed: 0.005 s
% 3.80/1.41 % (3473809)Peak memory usage: 88 MB
% 3.80/1.41 % (3473809)Instructions burned: 7 (million)
% 3.80/1.41 % (3473807)------------------------------
% 3.80/1.41 % (3473807)------------------------------
% 3.80/1.41 % (3473808)Also succeeded, but the first one will report.
% 3.80/1.41 % (3473798)Refutation found. Thanks to Tanya!
% 3.80/1.41 % SZS status Unsatisfiable for theBenchmark
% 3.80/1.41 % SZS output start Proof for theBenchmark
% See solution above
% 3.80/1.41 % (3473798)------------------------------
% 3.80/1.41 % (3473798)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.80/1.41 % (3473798)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.80/1.41 % (3473798)CaDiCaL version: 2.1.3
% 3.80/1.41 % (3473798)Termination reason: Refutation
% 3.80/1.41 % (3473798)Time elapsed: 0.064 s
% 3.80/1.41 % (3473798)Peak memory usage: 90 MB
% 3.80/1.41 % (3473798)Instructions burned: 79 (million)
% 3.80/1.41 % (3473798)------------------------------
% 3.80/1.41 % (3473798)------------------------------
% 3.80/1.41 % (3473788)Success in time 0.465 s
% 3.80/1.41 % Vampire exiting
%------------------------------------------------------------------------------