%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET042-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 12:39:45 PM UTC 2026
% Result : Unsatisfiable 3.22s 1.22s
% Output : Refutation 3.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 36 ( 13 unt; 1 def)
% Number of atoms : 75 ( 8 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 84 ( 45 ~; 38 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 2 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 23 ( 0 sgn 23 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( ~ member(X0,X1)
| little_set(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2) ).
fof(f15,axiom,
! [X2,X0,X1] :
( ordered_pair_predicate(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| X0 != ordered_pair(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pair_predicate4) ).
fof(f16,plain,
! [X2,X0,X1] :
( ordered_pair_predicate(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| ordered_pair(X1,X2) != X0 ),
inference(reorient_equations,[],[f15]) ).
fof(f49,axiom,
! [X2,X0,X1] :
( member(X0,cross_product(X1,X2))
| ~ little_set(X0)
| ~ ordered_pair_predicate(X0)
| ~ member(first(X0),X1)
| ~ member(second(X0),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cross_product4) ).
fof(f167,axiom,
! [X0,X1] :
( ~ little_set(X1)
| ~ little_set(X0)
| first(ordered_pair(X0,X1)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_of_first) ).
fof(f168,axiom,
! [X0,X1] :
( ~ little_set(X1)
| ~ little_set(X0)
| second(ordered_pair(X0,X1)) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_of_second) ).
fof(f173,axiom,
! [X0] :
( ~ ordered_pair_predicate(X0)
| little_set(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pairs_are_small2) ).
fof(f189,axiom,
member(a,set_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_set_a) ).
fof(f190,axiom,
member(b,set_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_set_b) ).
fof(f191,negated_conjecture,
~ member(ordered_pair(a,b),cross_product(set_a,set_b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_ordered_pair_is_in_cross_product) ).
fof(f193,plain,
! [X2,X1] :
( ordered_pair_predicate(ordered_pair(X1,X2))
| ~ little_set(X1)
| ~ little_set(X2) ),
inference(equality_resolution,[],[f16]) ).
fof(f198,plain,
! [X2,X0,X1] :
( member(X0,cross_product(X1,X2))
| ~ ordered_pair_predicate(X0)
| ~ member(first(X0),X1)
| ~ member(second(X0),X2) ),
inference(forward_subsumption_resolution,[],[f49,f173]) ).
fof(f199,plain,
little_set(a),
inference(resolution,[],[f1,f189]) ).
fof(f200,plain,
little_set(b),
inference(resolution,[],[f1,f190]) ).
fof(f211,plain,
! [X0] :
( ~ little_set(X0)
| first(ordered_pair(X0,b)) = X0 ),
inference(resolution,[],[f167,f200]) ).
fof(f217,plain,
! [X0] :
( ~ little_set(X0)
| b = second(ordered_pair(X0,b)) ),
inference(resolution,[],[f168,f200]) ).
fof(f235,plain,
a = first(ordered_pair(a,b)),
inference(resolution,[],[f211,f199]) ).
fof(f273,definition,
( spl0_3
<=> ordered_pair_predicate(ordered_pair(a,b)) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f274,plain,
( ordered_pair_predicate(ordered_pair(a,b))
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f273]) ).
fof(f275,plain,
( ~ ordered_pair_predicate(ordered_pair(a,b))
| spl0_3 ),
inference(avatar_component_clause,[],[f273]) ).
fof(f302,plain,
( ~ ordered_pair_predicate(ordered_pair(a,b))
| ~ member(first(ordered_pair(a,b)),set_a)
| ~ member(second(ordered_pair(a,b)),set_b) ),
inference(resolution,[],[f198,f191]) ).
fof(f328,plain,
( ~ little_set(a)
| ~ little_set(b)
| spl0_3 ),
inference(resolution,[],[f275,f193]) ).
fof(f329,plain,
( ~ little_set(b)
| spl0_3 ),
inference(forward_subsumption_resolution,[],[f328,f199]) ).
fof(f330,plain,
( $false
| spl0_3 ),
inference(forward_subsumption_resolution,[],[f329,f200]) ).
fof(f331,plain,
spl0_3,
inference(avatar_contradiction_clause,[],[f330]) ).
fof(f332,plain,
( ~ member(first(ordered_pair(a,b)),set_a)
| ~ member(second(ordered_pair(a,b)),set_b)
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f302,f274]) ).
fof(f333,plain,
( ~ member(a,set_a)
| ~ member(second(ordered_pair(a,b)),set_b)
| ~ spl0_3 ),
inference(forward_demodulation,[],[f332,f235]) ).
fof(f334,plain,
( ~ member(second(ordered_pair(a,b)),set_b)
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f333,f189]) ).
fof(f414,plain,
b = second(ordered_pair(a,b)),
inference(resolution,[],[f217,f199]) ).
fof(f417,plain,
( ~ member(b,set_b)
| ~ spl0_3 ),
inference(superposition,[],[f334,f414]) ).
fof(f420,plain,
( $false
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f417,f190]) ).
fof(f421,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[],[f420]) ).
cnf(s7,plain,
spl0_3,
inference(sat_conversion,[],[f331]) ).
cnf(s10,plain,
~ spl0_3,
inference(sat_conversion,[],[f421]) ).
cnf(s11,plain,
$false,
inference(rat,[],[s7,s10]) ).
fof(f422,plain,
$false,
inference(avatar_sat_refutation,[],[s11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET042-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.40 % Computer : n010.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Mon Sep 28 00:21:03 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.43 Running first-order theorem proving
% 0.13/0.43 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
% 3.22/1.22 % (1454637)Input is clausal, will run a generic CNF schedule.
% 3.22/1.22 % (1454648)dis-21_1_sil=8000:lcm=predicate:random_seed=3000834805: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)
% 3.22/1.22 % (1454647)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=310340236:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.22/1.22 % (1454646)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3293385752:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.22/1.22 % (1454645)lrs+10_1_sil=8000:sp=occurrence:random_seed=3957560142:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.22/1.22 % (1454642)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=1343529562:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.22/1.22 % (1454644)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1233097596:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.22/1.22 % (1454643)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2174115842:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.22/1.22 % (1454645)First to succeed.
% 3.22/1.22 % (1454645)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1454637"
% 3.22/1.22 % (1454646)Also succeeded, but the first one will report.
% 3.22/1.22 % (1454647)Also succeeded, but the first one will report.
% 3.22/1.22 % (1454648)Instruction limit reached!
% 3.22/1.22 % (1454648)------------------------------
% 3.22/1.22 % (1454648)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.22/1.22 % (1454648)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.22/1.22 % (1454648)CaDiCaL version: 2.1.3
% 3.22/1.22 % (1454648)Termination reason: Instruction limit
% 3.22/1.22 % (1454648)Termination phase: Saturation
% 3.22/1.22 % (1454648)Time elapsed: 0.074 s
% 3.22/1.22 % (1454648)Peak memory usage: 89 MB
% 3.22/1.22 % (1454648)Instructions burned: 118 (million)
% 3.22/1.22 % (1454656)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=2409326749:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.22/1.22 % (1454656)Also succeeded, but the first one will report.
% 3.22/1.22 % (1454645)Refutation found. Thanks to Tanya!
% 3.22/1.22 % SZS status Unsatisfiable for theBenchmark
% 3.22/1.22 % SZS output start Proof for theBenchmark
% See solution above
% 3.22/1.22 % (1454645)------------------------------
% 3.22/1.22 % (1454645)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.22/1.22 % (1454645)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.22/1.22 % (1454645)CaDiCaL version: 2.1.3
% 3.22/1.22 % (1454645)Termination reason: Refutation
% 3.22/1.22 % (1454645)Time elapsed: 0.008 s
% 3.22/1.22 % (1454645)Peak memory usage: 89 MB
% 3.22/1.22 % (1454645)Instructions burned: 10 (million)
% 3.22/1.22 % (1454645)------------------------------
% 3.22/1.22 % (1454645)------------------------------
% 3.22/1.22 % (1454637)Success in time 0.399 s
% 3.22/1.22 % Vampire exiting
%------------------------------------------------------------------------------