%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET025-3 : TPTP v9.3.1. Released v1.0.0.
% 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 12:39:39 PM UTC 2026
% Result : Unsatisfiable 3.53s 1.44s
% Output : Refutation 3.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 3
% Syntax : Number of formulae : 5 ( 5 unt; 0 def)
% Number of atoms : 5 ( 1 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 1 ( 1 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 6 ( 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [X0,X1] : little_set(non_ordered_pair(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',non_ordered_pair4) ).
fof(f10,axiom,
! [X0,X1] : ordered_pair(X0,X1) = non_ordered_pair(singleton_set(X0),non_ordered_pair(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pair) ).
fof(f172,negated_conjecture,
~ little_set(ordered_pair(a,b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_ordered_pairs_are_small) ).
fof(f212,plain,
! [X0,X1] : little_set(ordered_pair(X0,X1)),
inference(superposition,[],[f8,f10]) ).
fof(f216,plain,
$false,
inference(resolution,[],[f212,f172]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET025-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.35 % Computer : n006.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Mon Sep 28 00:10:41 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.39 Running first-order theorem proving
% 0.14/0.39 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
% 3.53/1.44 % (3474744)Input is clausal, will run a generic CNF schedule.
% 3.53/1.44 % (3474749)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=3894933761:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.53/1.44 % (3474754)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3664201159:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.53/1.44 % (3474752)lrs+10_1_sil=8000:sp=occurrence:random_seed=4010176158:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.53/1.44 % (3474750)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1741342272:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.53/1.44 % (3474751)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2748992850:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.53/1.44 % (3474753)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2554009894:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.53/1.44 % (3474752)Refutation not found, incomplete strategy
% 3.53/1.44 % (3474752)------------------------------
% 3.53/1.44 % (3474752)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.53/1.44 % (3474752)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/1.44 % (3474752)CaDiCaL version: 2.1.3
% 3.53/1.44 % (3474752)Termination reason: Refutation not found, incomplete strategy
% 3.53/1.44 % (3474752)Time elapsed: 0.001 s
% 3.53/1.44 % (3474752)Peak memory usage: 86 MB
% 3.53/1.44 % (3474753)Refutation not found, incomplete strategy
% 3.53/1.44 % (3474753)------------------------------
% 3.53/1.44 % (3474753)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.53/1.44 % (3474753)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/1.44 % (3474753)CaDiCaL version: 2.1.3
% 3.53/1.44 % (3474753)Termination reason: Refutation not found, incomplete strategy
% 3.53/1.44 % (3474753)Time elapsed: 0.002 s
% 3.53/1.44 % (3474753)Peak memory usage: 88 MB
% 3.53/1.44 % (3474753)Instructions burned: 1 (million)
% 3.53/1.44 % (3474754)First to succeed.
% 3.53/1.44 % (3474754)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3474744"
% 3.53/1.44 % (3474755)dis-21_1_sil=8000:lcm=predicate:random_seed=1613348596: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)
% 3.53/1.44 % (3474755)Also succeeded, but the first one will report.
% 3.53/1.44 % (3474752)------------------------------
% 3.53/1.44 % (3474752)------------------------------
% 3.53/1.44 % (3474753)------------------------------
% 3.53/1.44 % (3474753)------------------------------
% 3.53/1.44 % (3474754)Refutation found. Thanks to Tanya!
% 3.53/1.44 % SZS status Unsatisfiable for theBenchmark
% 3.53/1.44 % SZS output start Proof for theBenchmark
% See solution above
% 3.53/1.44 % (3474754)------------------------------
% 3.53/1.44 % (3474754)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.53/1.44 % (3474754)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/1.44 % (3474754)CaDiCaL version: 2.1.3
% 3.53/1.44 % (3474754)Termination reason: Refutation
% 3.53/1.44 % (3474754)Time elapsed: 0.006 s
% 3.53/1.44 % (3474754)Peak memory usage: 88 MB
% 3.53/1.44 % (3474754)Instructions burned: 8 (million)
% 3.53/1.44 % (3474754)------------------------------
% 3.53/1.44 % (3474754)------------------------------
% 3.53/1.44 % (3474744)Success in time 0.416 s
% 3.53/1.44 % Vampire exiting
%------------------------------------------------------------------------------