%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET121-7 : TPTP v9.3.1. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 12:40:12 PM UTC 2026
% Result : Unsatisfiable 3.59s 1.46s
% Output : Refutation 3.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 21 ( 12 unt; 1 def)
% Number of atoms : 30 ( 9 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 20 ( 11 ~; 8 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 2 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 6 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(f175,axiom,
! [X0] :
( first(X0) = X0
| member(ordered_pair(first(X0),second(X0)),cross_product(universal_class,universal_class)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_1st_and_2nd_2) ).
fof(f177,axiom,
! [X0] :
( first(X0) = X0
| ordered_pair(first(X0),second(X0)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_1st_and_2nd_4) ).
fof(f191,negated_conjecture,
~ member(y,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_1_to_OP_determines_components2_1) ).
fof(f192,negated_conjecture,
first(ordered_pair(x,y)) != ordered_pair(x,y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_1_to_OP_determines_components2_2) ).
fof(f193,plain,
ordered_pair(x,y) != first(ordered_pair(x,y)),
inference(reorient_equations,[],[f192]) ).
fof(f355,plain,
( ordered_pair(x,y) != ordered_pair(x,y)
| ordered_pair(x,y) = ordered_pair(first(ordered_pair(x,y)),second(ordered_pair(x,y))) ),
inference(superposition,[],[f193,f177]) ).
fof(f357,plain,
ordered_pair(x,y) = ordered_pair(first(ordered_pair(x,y)),second(ordered_pair(x,y))),
inference(trivial_inequality_removal,[],[f355]) ).
fof(f449,plain,
( ordered_pair(x,y) != ordered_pair(x,y)
| member(ordered_pair(first(ordered_pair(x,y)),second(ordered_pair(x,y))),cross_product(universal_class,universal_class)) ),
inference(superposition,[],[f193,f175]) ).
fof(f451,plain,
member(ordered_pair(first(ordered_pair(x,y)),second(ordered_pair(x,y))),cross_product(universal_class,universal_class)),
inference(trivial_inequality_removal,[],[f449]) ).
fof(f617,definition,
( spl0_17
<=> member(ordered_pair(x,y),cross_product(universal_class,universal_class)) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f618,plain,
( member(ordered_pair(x,y),cross_product(universal_class,universal_class))
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f617]) ).
fof(f672,plain,
member(ordered_pair(x,y),cross_product(universal_class,universal_class)),
inference(forward_demodulation,[],[f451,f357]) ).
fof(f673,plain,
spl0_17,
inference(avatar_split_clause,[],[f672,f617]) ).
fof(f923,plain,
( member(y,universal_class)
| ~ spl0_17 ),
inference(resolution,[],[f618,f15]) ).
fof(f937,plain,
( $false
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f923,f191]) ).
fof(f938,plain,
~ spl0_17,
inference(avatar_contradiction_clause,[],[f937]) ).
cnf(s21,plain,
spl0_17,
inference(sat_conversion,[],[f673]) ).
cnf(s52,plain,
~ spl0_17,
inference(sat_conversion,[],[f938]) ).
cnf(s57,plain,
$false,
inference(rat,[],[s21,s52]) ).
fof(f954,plain,
$false,
inference(avatar_sat_refutation,[],[s57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET121-7 : TPTP v9.3.1. Bugfixed v7.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n019.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % 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 00:50:19 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 3.59/1.46 % (3560090)Input is clausal, will run a generic CNF schedule.
% 3.59/1.46 % (3560099)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=122510006:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.59/1.46 % (3560099)Instruction limit reached!
% 3.59/1.46 % (3560099)------------------------------
% 3.59/1.46 % (3560099)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.59/1.46 % (3560099)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.59/1.46 % (3560099)CaDiCaL version: 2.1.3
% 3.59/1.46 % (3560099)Termination reason: Instruction limit
% 3.59/1.46 % (3560099)Termination phase: Saturation
% 3.59/1.46 % (3560099)Time elapsed: 0.036 s
% 3.59/1.46 % (3560099)Peak memory usage: 88 MB
% 3.59/1.46 % (3560099)Instructions burned: 116 (million)
% 3.59/1.46 % (3560100)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3946570721:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.59/1.46 % (3560098)lrs+10_1_sil=8000:sp=occurrence:random_seed=3245303854:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.59/1.46 % (3560096)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1075180124:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.59/1.46 % (3560095)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=686600920:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.59/1.46 % (3560097)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1998865174:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.59/1.46 % (3560101)dis-21_1_sil=8000:lcm=predicate:random_seed=2911480645: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)
% 3.59/1.46 % (3560098)Refutation not found, incomplete strategy
% 3.59/1.46 % (3560098)------------------------------
% 3.59/1.46 % (3560098)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.59/1.46 % (3560098)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.59/1.46 % (3560098)CaDiCaL version: 2.1.3
% 3.59/1.46 % (3560098)Termination reason: Refutation not found, incomplete strategy
% 3.59/1.46 % (3560098)Time elapsed: 0.017 s
% 3.59/1.46 % (3560098)Peak memory usage: 88 MB
% 3.59/1.46 % (3560098)Instructions burned: 29 (million)
% 3.59/1.46 % (3560100)First to succeed.
% 3.59/1.46 % (3560100)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3560090"
% 3.59/1.46 % (3560101)Instruction limit reached!
% 3.59/1.46 % (3560101)------------------------------
% 3.59/1.46 % (3560101)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.59/1.46 % (3560101)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.59/1.46 % (3560101)CaDiCaL version: 2.1.3
% 3.59/1.46 % (3560101)Termination reason: Instruction limit
% 3.59/1.46 % (3560101)Termination phase: Saturation
% 3.59/1.46 % (3560101)Time elapsed: 0.073 s
% 3.59/1.46 % (3560101)Peak memory usage: 89 MB
% 3.59/1.46 % (3560101)Instructions burned: 117 (million)
% 3.59/1.46 % (3560103)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=2888223427:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 3.59/1.46 % (3560103)Refutation not found, incomplete strategy
% 3.59/1.46 % (3560103)------------------------------
% 3.59/1.46 % (3560103)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.59/1.46 % (3560103)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.59/1.46 % (3560103)CaDiCaL version: 2.1.3
% 3.59/1.46 % (3560103)Termination reason: Refutation not found, incomplete strategy
% 3.59/1.46 % (3560103)Time elapsed: 0.001 s
% 3.59/1.46 % (3560103)Peak memory usage: 88 MB
% 3.59/1.46 % (3560103)Instructions burned: 3 (million)
% 3.59/1.46 % (3560111)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=188435736: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)
% 3.59/1.46 % (3560103)------------------------------
% 3.59/1.46 % (3560103)------------------------------
% 3.59/1.46 % (3560098)------------------------------
% 3.59/1.46 % (3560098)------------------------------
% 3.59/1.46 % (3560100)Refutation found. Thanks to Tanya!
% 3.59/1.46 % SZS status Unsatisfiable for theBenchmark
% 3.59/1.46 % SZS output start Proof for theBenchmark
% See solution above
% 3.59/1.46 % (3560100)------------------------------
% 3.59/1.46 % (3560100)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.59/1.46 % (3560100)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.59/1.46 % (3560100)CaDiCaL version: 2.1.3
% 3.59/1.46 % (3560100)Termination reason: Refutation
% 3.59/1.46 % (3560100)Time elapsed: 0.029 s
% 3.59/1.46 % (3560100)Peak memory usage: 90 MB
% 3.59/1.46 % (3560100)Instructions burned: 34 (million)
% 3.59/1.46 % (3560100)------------------------------
% 3.59/1.46 % (3560100)------------------------------
% 3.59/1.46 % (3560090)Success in time 0.43 s
% 3.59/1.46 % Vampire exiting
%------------------------------------------------------------------------------