%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET024-4 : 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 : n002.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 2.52s 1.36s
% Output : Refutation 2.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of formulae : 8 ( 6 unt; 0 def)
% Number of atoms : 11 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 9 ( 6 ~; 3 |; 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 : 6 ( 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X2,X0,X1] :
( member(X0,non_ordered_pair(X1,X2))
| ~ little_set(X0)
| X0 != X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',non_ordered_pair3) ).
fof(f9,axiom,
! [X0] : singleton_set(X0) = non_ordered_pair(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_set) ).
fof(f162,axiom,
little_set(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_little_set) ).
fof(f163,negated_conjecture,
~ member(a,singleton_set(a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_membership_of_singleton_set) ).
fof(f166,plain,
~ member(a,non_ordered_pair(a,a)),
inference(definition_unfolding,[],[f163,f9]) ).
fof(f168,plain,
! [X2,X1] :
( member(X2,non_ordered_pair(X1,X2))
| ~ little_set(X2) ),
inference(equality_resolution,[],[f7]) ).
fof(f171,plain,
~ little_set(a),
inference(resolution,[],[f168,f166]) ).
fof(f173,plain,
$false,
inference(forward_subsumption_resolution,[],[f171,f162]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET024-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.41 % Computer : n002.cluster.edu
% 0.13/0.41 % Model : x86_64 x86_64
% 0.13/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.41 % Memory : 8046.5625MB
% 0.13/0.41 % OS : Linux 6.8.0-71-generic
% 0.13/0.42 % CPULimit : 300
% 0.13/0.42 % WCLimit : 300
% 0.13/0.42 % DateTime : Mon Sep 28 00:14:23 UTC 2026
% 0.13/0.42 % CPUTime :
% 0.13/0.42 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.45 Running first-order theorem proving
% 0.13/0.45 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
% 2.52/1.36 % (4038841)Input is clausal, will run a generic CNF schedule.
% 2.52/1.36 % (4038849)lrs+10_1_sil=8000:sp=occurrence:random_seed=1251836885:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.52/1.36 % (4038849)First to succeed.
% 2.52/1.36 % (4038849)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4038841"
% 2.52/1.36 % (4038850)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1413591131:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.52/1.36 % (4038847)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3153218747:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.52/1.36 % (4038851)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2912278048:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.52/1.36 % (4038846)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=1897688197:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.52/1.36 % (4038852)dis-21_1_sil=8000:lcm=predicate:random_seed=4100430364: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)
% 2.52/1.36 % (4038848)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1846428212:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.52/1.36 % (4038850)Also succeeded, but the first one will report.
% 2.52/1.36 % (4038852)Also succeeded, but the first one will report.
% 2.52/1.36 % (4038851)Also succeeded, but the first one will report.
% 2.52/1.36 % (4038849)Refutation found. Thanks to Tanya!
% 2.52/1.36 % SZS status Unsatisfiable for theBenchmark
% 2.52/1.36 % SZS output start Proof for theBenchmark
% See solution above
% 2.52/1.36 % (4038849)------------------------------
% 2.52/1.36 % (4038849)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.52/1.36 % (4038849)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.52/1.36 % (4038849)CaDiCaL version: 2.1.3
% 2.52/1.36 % (4038849)Termination reason: Refutation
% 2.52/1.36 % (4038849)Time elapsed: 0.001 s
% 2.52/1.36 % (4038849)Peak memory usage: 88 MB
% 2.52/1.36 % (4038849)Instructions burned: 1 (million)
% 2.52/1.36 % (4038849)------------------------------
% 2.52/1.36 % (4038849)------------------------------
% 2.52/1.36 % (4038841)Success in time 0.273 s
% 2.52/1.36 % Vampire exiting
%------------------------------------------------------------------------------