%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET855-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 12:42:09 PM UTC 2026
% Result : Unsatisfiable 2.72s 1.35s
% Output : Refutation 2.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 8 ( 5 unt; 0 def)
% Number of atoms : 13 ( 5 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 11 ( 6 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 6 ( 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_set(X2))
| ~ c_lessequals(X1,X0,tc_set(X2))
| X1 = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
fof(f2,plain,
! [X2,X0,X1] :
( ~ c_lessequals(X1,X0,tc_set(X2))
| ~ c_lessequals(X0,X1,tc_set(X2))
| X0 = X1 ),
inference(reorient_equations,[],[f1]) ).
fof(f3,negated_conjecture,
c_lessequals(v_n,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f4,negated_conjecture,
c_lessequals(c_Union(v_Y,tc_set(t_a)),v_n,tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f5,negated_conjecture,
v_n != c_Union(v_Y,tc_set(t_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f7,plain,
( ~ c_lessequals(v_n,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| v_n = c_Union(v_Y,tc_set(t_a)) ),
inference(resolution,[],[f2,f4]) ).
fof(f8,plain,
v_n = c_Union(v_Y,tc_set(t_a)),
inference(forward_subsumption_resolution,[],[f7,f3]) ).
fof(f10,plain,
$false,
inference(forward_subsumption_resolution,[],[f8,f5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET855-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n008.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 28 03:02:39 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 2.72/1.35 % (1824367)Input is clausal, will run a generic CNF schedule.
% 2.72/1.35 % (1824375)lrs+10_1_sil=8000:sp=occurrence:random_seed=4181082895:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.72/1.35 % (1824375)First to succeed.
% 2.72/1.35 % (1824375)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1824367"
% 2.72/1.35 % (1824374)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2766806351:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.72/1.35 % (1824378)dis-21_1_sil=8000:lcm=predicate:random_seed=1384954452: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)
% 2.72/1.35 % (1824372)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=213349584:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.72/1.35 % (1824373)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1902226003:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.72/1.35 % (1824376)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=375174924:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.72/1.35 % (1824377)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4104919031:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.72/1.35 % (1824378)Also succeeded, but the first one will report.
% 2.72/1.35 % (1824376)Also succeeded, but the first one will report.
% 2.72/1.35 % (1824377)Also succeeded, but the first one will report.
% 2.72/1.35 % (1824375)Refutation found. Thanks to Tanya!
% 2.72/1.35 % SZS status Unsatisfiable for theBenchmark
% 2.72/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 2.72/1.35 % (1824375)------------------------------
% 2.72/1.35 % (1824375)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.72/1.35 % (1824375)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.72/1.35 % (1824375)CaDiCaL version: 2.1.3
% 2.72/1.35 % (1824375)Termination reason: Refutation
% 2.72/1.35 % (1824375)Time elapsed: 0.001 s
% 2.72/1.35 % (1824375)Peak memory usage: 88 MB
% 2.72/1.35 % (1824375)------------------------------
% 2.72/1.35 % (1824375)------------------------------
% 2.72/1.35 % (1824367)Success in time 0.305 s
% 2.72/1.35 % Vampire exiting
%------------------------------------------------------------------------------