%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET024-3 : 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 : n018.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 2.65s 1.38s
% Output : Refutation 2.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 8 ( 5 unt; 0 def)
% Number of atoms : 12 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 10 ( 6 ~; 4 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 7 ( 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X2,X0,X1] :
( member(X0,non_ordered_pair(X1,X2))
| ~ little_set(X0)
| X0 != X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',non_ordered_pair2) ).
fof(f9,axiom,
! [X0] : singleton_set(X0) = non_ordered_pair(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_set) ).
fof(f171,axiom,
little_set(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_little_set) ).
fof(f172,negated_conjecture,
~ member(a,singleton_set(a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_membership_of_singleton_set) ).
fof(f173,plain,
! [X2,X1] :
( member(X1,non_ordered_pair(X1,X2))
| ~ little_set(X1) ),
inference(equality_resolution,[],[f6]) ).
fof(f193,plain,
! [X0] :
( member(X0,singleton_set(X0))
| ~ little_set(X0) ),
inference(superposition,[],[f173,f9]) ).
fof(f203,plain,
~ little_set(a),
inference(resolution,[],[f193,f172]) ).
fof(f206,plain,
$false,
inference(forward_subsumption_resolution,[],[f203,f171]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET024-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 % Computer : n018.cluster.edu
% 0.11/0.41 % Model : x86_64 x86_64
% 0.11/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.41 % Memory : 8046.5625MB
% 0.11/0.41 % OS : Linux 6.8.0-71-generic
% 0.11/0.41 % CPULimit : 300
% 0.11/0.41 % WCLimit : 300
% 0.11/0.41 % DateTime : Mon Sep 28 00:14:24 UTC 2026
% 0.11/0.41 % CPUTime :
% 0.11/0.41 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.44 Running first-order theorem proving
% 0.11/0.44 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
% 2.65/1.38 % (2874636)Input is clausal, will run a generic CNF schedule.
% 2.65/1.38 % (2874646)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=446441920:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.65/1.38 % (2874646)First to succeed.
% 2.65/1.38 % (2874646)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2874636"
% 2.65/1.38 % (2874642)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=725837176:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.65/1.38 % (2874645)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1250224877:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.65/1.38 % (2874644)lrs+10_1_sil=8000:sp=occurrence:random_seed=3971952039:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.65/1.38 % (2874643)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3918359573:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.65/1.38 % (2874641)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=1275405493:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.65/1.38 % (2874645)Also succeeded, but the first one will report.
% 2.65/1.38 % (2874644)Also succeeded, but the first one will report.
% 2.65/1.38 % (2874647)dis-21_1_sil=8000:lcm=predicate:random_seed=1637222877: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)
% 2.65/1.38 % (2874647)Also succeeded, but the first one will report.
% 2.65/1.38 % (2874646)Refutation found. Thanks to Tanya!
% 2.65/1.38 % SZS status Unsatisfiable for theBenchmark
% 2.65/1.38 % SZS output start Proof for theBenchmark
% See solution above
% 2.65/1.38 % (2874646)------------------------------
% 2.65/1.38 % (2874646)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.65/1.38 % (2874646)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/1.38 % (2874646)CaDiCaL version: 2.1.3
% 2.65/1.38 % (2874646)Termination reason: Refutation
% 2.65/1.38 % (2874646)Time elapsed: 0.003 s
% 2.65/1.38 % (2874646)Peak memory usage: 88 MB
% 2.65/1.38 % (2874646)Instructions burned: 6 (million)
% 2.65/1.38 % (2874646)------------------------------
% 2.65/1.38 % (2874646)------------------------------
% 2.65/1.38 % (2874636)Success in time 0.296 s
% 2.65/1.38 % Vampire exiting
%------------------------------------------------------------------------------