%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET842-2 : 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 : 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 12:42:06 PM UTC 2026
% Result : Unsatisfiable 2.51s 1.31s
% Output : Refutation 2.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 15 ( 3 unt; 0 def)
% Number of atoms : 31 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 31 ( 15 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 24 ( 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
~ c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f2,negated_conjecture,
! [X0] :
( ~ c_in(X0,v_Y,tc_set(tc_set(t_a)))
| c_lessequals(X0,v_m,tc_set(tc_set(t_a))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f3,axiom,
! [X2,X0,X1] :
( c_in(c_Main_OUnionE__1(X0,X1,X2),X1,tc_set(X2))
| ~ c_in(X0,c_Union(X1,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnionE_0) ).
fof(f4,axiom,
! [X2,X0,X1] :
( c_in(X0,c_Main_OUnionE__1(X0,X1,X2),X2)
| ~ c_in(X0,c_Union(X1,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnionE_1) ).
fof(f5,axiom,
! [X2,X3,X0,X1] :
( ~ c_lessequals(X1,X3,tc_set(X2))
| ~ c_in(X0,X1,X2)
| c_in(X0,X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).
fof(f6,axiom,
! [X2,X0,X1] :
( c_in(c_Main_OsubsetI__1(X0,X1,X2),X0,X2)
| c_lessequals(X0,X1,tc_set(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).
fof(f7,axiom,
! [X2,X0,X1] :
( ~ c_in(c_Main_OsubsetI__1(X0,X1,X2),X1,X2)
| c_lessequals(X0,X1,tc_set(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).
fof(f14,plain,
! [X0] :
( c_lessequals(c_Main_OUnionE__1(X0,v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
| ~ c_in(X0,c_Union(v_Y,tc_set(t_a)),tc_set(t_a)) ),
inference(resolution,[],[f3,f2]) ).
fof(f15,plain,
! [X0,X1] :
( c_in(X1,v_m,tc_set(t_a))
| ~ c_in(X1,c_Main_OUnionE__1(X0,v_Y,tc_set(t_a)),tc_set(t_a))
| ~ c_in(X0,c_Union(v_Y,tc_set(t_a)),tc_set(t_a)) ),
inference(resolution,[],[f14,f5]) ).
fof(f16,plain,
! [X0,X1] :
( ~ c_in(c_Main_OsubsetI__1(X0,v_m,tc_set(t_a)),c_Main_OUnionE__1(X1,v_Y,tc_set(t_a)),tc_set(t_a))
| ~ c_in(X1,c_Union(v_Y,tc_set(t_a)),tc_set(t_a))
| c_lessequals(X0,v_m,tc_set(tc_set(t_a))) ),
inference(resolution,[],[f15,f7]) ).
fof(f20,plain,
! [X0] :
( ~ c_in(c_Main_OsubsetI__1(X0,v_m,tc_set(t_a)),c_Union(v_Y,tc_set(t_a)),tc_set(t_a))
| c_lessequals(X0,v_m,tc_set(tc_set(t_a)))
| ~ c_in(c_Main_OsubsetI__1(X0,v_m,tc_set(t_a)),c_Union(v_Y,tc_set(t_a)),tc_set(t_a)) ),
inference(resolution,[],[f16,f4]) ).
fof(f21,plain,
! [X0] :
( ~ c_in(c_Main_OsubsetI__1(X0,v_m,tc_set(t_a)),c_Union(v_Y,tc_set(t_a)),tc_set(t_a))
| c_lessequals(X0,v_m,tc_set(tc_set(t_a))) ),
inference(duplicate_literal_removal,[],[f20]) ).
fof(f23,plain,
( c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))) ),
inference(resolution,[],[f21,f6]) ).
fof(f24,plain,
c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
inference(duplicate_literal_removal,[],[f23]) ).
fof(f25,plain,
$false,
inference(forward_subsumption_resolution,[],[f24,f1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET842-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.38 % Computer : n010.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Mon Sep 28 02:58:48 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.42 Running first-order theorem proving
% 0.09/0.42 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
% 2.51/1.31 % (1519232)Input is clausal, will run a generic CNF schedule.
% 2.51/1.31 % (1519242)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=837862201:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.51/1.31 % (1519242)First to succeed.
% 2.51/1.31 % (1519242)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1519232"
% 2.51/1.31 % (1519238)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=4281326441:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.51/1.31 % (1519240)lrs+10_1_sil=8000:sp=occurrence:random_seed=3735163738:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.51/1.31 % (1519243)dis-21_1_sil=8000:lcm=predicate:random_seed=272916453: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)
% 2.51/1.31 % (1519239)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1054304394:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.51/1.31 % (1519237)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=1991977989:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.51/1.31 % (1519240)Also succeeded, but the first one will report.
% 2.51/1.31 % (1519243)Also succeeded, but the first one will report.
% 2.51/1.31 % (1519241)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=295627226:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.51/1.31 % (1519241)Refutation not found, incomplete strategy
% 2.51/1.31 % (1519241)------------------------------
% 2.51/1.31 % (1519241)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.51/1.31 % (1519241)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.51/1.31 % (1519241)CaDiCaL version: 2.1.3
% 2.51/1.31 % (1519241)Termination reason: Refutation not found, incomplete strategy
% 2.51/1.31 % (1519241)Time elapsed: 0.001 s
% 2.51/1.31 % (1519241)Peak memory usage: 87 MB
% 2.51/1.31 % (1519242)Refutation found. Thanks to Tanya!
% 2.51/1.31 % SZS status Unsatisfiable for theBenchmark
% 2.51/1.31 % SZS output start Proof for theBenchmark
% See solution above
% 2.51/1.31 % (1519242)------------------------------
% 2.51/1.31 % (1519242)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.51/1.31 % (1519242)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.51/1.31 % (1519242)CaDiCaL version: 2.1.3
% 2.51/1.31 % (1519242)Termination reason: Refutation
% 2.51/1.31 % (1519242)Time elapsed: 0.001 s
% 2.51/1.31 % (1519242)Peak memory usage: 88 MB
% 2.51/1.31 % (1519242)Instructions burned: 1 (million)
% 2.51/1.31 % (1519242)------------------------------
% 2.51/1.31 % (1519242)------------------------------
% 2.51/1.31 % (1519232)Success in time 0.27 s
% 2.51/1.31 % Vampire exiting
%------------------------------------------------------------------------------