%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL430-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 11:52:23 AM UTC 2026
% Result : Unsatisfiable 2.53s 1.03s
% Output : Refutation 2.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 29 ( 11 unt; 2 def)
% Number of atoms : 52 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 46 ( 23 ~; 21 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 5 ( 4 usr; 3 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 7 con; 0-3 aty)
% Number of variables : 61 ( 0 sgn 61 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_lessequals(X1,X4,tc_set(tc_PropLog_Opl(X3)))
| ~ c_in(X0,c_PropLog_Othms(c_minus(X1,X2,tc_set(tc_PropLog_Opl(X3))),X3),tc_PropLog_Opl(X3))
| c_in(X0,c_PropLog_Othms(c_minus(X4,X2,tc_set(tc_PropLog_Opl(X3))),X3),tc_PropLog_Opl(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PropLog_ODiff__weaken__left_0) ).
fof(f2,axiom,
! [X2,X3,X0,X1] : c_lessequals(c_PropLog_Ohyps(X0,c_insert(X1,X2,X3),X3),c_insert(c_PropLog_Opl_Ovar(X1,X3),c_minus(c_PropLog_Ohyps(X0,X2,X3),c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(X1,X3),c_PropLog_Opl_Ofalse,X3),c_emptyset,tc_PropLog_Opl(X3)),tc_set(tc_PropLog_Opl(X3))),tc_PropLog_Opl(X3)),tc_set(tc_PropLog_Opl(X3))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PropLog_Ohyps__insert_0) ).
fof(f3,axiom,
! [X2,X3,X0,X1] : c_lessequals(c_minus(X0,X1,tc_set(X2)),c_insert(X3,c_minus(X0,c_insert(X3,X1,X2),tc_set(X2)),X2),tc_set(X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PropLog_Oinsert__Diff__same_0) ).
fof(f4,axiom,
! [X2,X3,X0,X1,X4] : c_lessequals(c_minus(c_insert(X0,c_minus(X1,c_insert(X2,c_emptyset,X3),tc_set(X3)),X3),X4,tc_set(X3)),c_insert(X0,c_minus(X1,c_insert(X2,X4,X3),tc_set(X3)),X3),tc_set(X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PropLog_Oinsert__Diff__subset2_0) ).
fof(f5,axiom,
! [X2,X3,X0,X1] :
( ~ c_in(X0,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(X1,c_PropLog_Opl_Ofalse,X3),X2,tc_PropLog_Opl(X3)),X3),tc_PropLog_Opl(X3))
| ~ c_in(X0,c_PropLog_Othms(c_insert(X1,X2,tc_PropLog_Opl(X3)),X3),tc_PropLog_Opl(X3))
| c_in(X0,c_PropLog_Othms(X2,X3),tc_PropLog_Opl(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PropLog_Othms__excluded__middle__rule_0) ).
fof(f6,axiom,
! [X2,X3,X0,X1] :
( ~ c_lessequals(X1,X3,tc_set(tc_PropLog_Opl(X2)))
| ~ c_in(X0,c_PropLog_Othms(X1,X2),tc_PropLog_Opl(X2))
| c_in(X0,c_PropLog_Othms(X3,X2),tc_PropLog_Opl(X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PropLog_Oweaken__left_0) ).
fof(f7,negated_conjecture,
! [X0] : c_in(v_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p,X0,t_a),v_F,tc_set(tc_PropLog_Opl(t_a))),t_a),tc_PropLog_Opl(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f8,negated_conjecture,
~ c_in(v_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p,v_t,t_a),c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(v_v,t_a),c_PropLog_Opl_Ofalse,t_a),v_F,tc_PropLog_Opl(t_a)),tc_set(tc_PropLog_Opl(t_a))),t_a),tc_PropLog_Opl(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).
fof(f9,plain,
! [X2,X3,X0,X1,X4] :
( c_in(X0,c_PropLog_Othms(c_insert(X4,c_minus(X1,c_insert(X4,X2,tc_PropLog_Opl(X3)),tc_set(tc_PropLog_Opl(X3))),tc_PropLog_Opl(X3)),X3),tc_PropLog_Opl(X3))
| ~ c_in(X0,c_PropLog_Othms(c_minus(X1,X2,tc_set(tc_PropLog_Opl(X3))),X3),tc_PropLog_Opl(X3)) ),
inference(resolution,[],[f6,f3]) ).
fof(f10,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ c_in(X0,c_PropLog_Othms(c_minus(c_insert(X1,c_minus(X2,c_insert(X3,c_emptyset,tc_PropLog_Opl(X4)),tc_set(tc_PropLog_Opl(X4))),tc_PropLog_Opl(X4)),X5,tc_set(tc_PropLog_Opl(X4))),X4),tc_PropLog_Opl(X4))
| c_in(X0,c_PropLog_Othms(c_insert(X1,c_minus(X2,c_insert(X3,X5,tc_PropLog_Opl(X4)),tc_set(tc_PropLog_Opl(X4))),tc_PropLog_Opl(X4)),X4),tc_PropLog_Opl(X4)) ),
inference(resolution,[],[f4,f6]) ).
fof(f13,plain,
! [X2,X3,X0,X1,X4,X5] :
( c_in(X0,c_PropLog_Othms(c_minus(c_insert(c_PropLog_Opl_Ovar(X2,X4),c_minus(c_PropLog_Ohyps(X1,X3,X4),c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(X2,X4),c_PropLog_Opl_Ofalse,X4),c_emptyset,tc_PropLog_Opl(X4)),tc_set(tc_PropLog_Opl(X4))),tc_PropLog_Opl(X4)),X5,tc_set(tc_PropLog_Opl(X4))),X4),tc_PropLog_Opl(X4))
| ~ c_in(X0,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(X1,c_insert(X2,X3,X4),X4),X5,tc_set(tc_PropLog_Opl(X4))),X4),tc_PropLog_Opl(X4)) ),
inference(resolution,[],[f2,f1]) ).
fof(f15,plain,
! [X2,X3,X0,X1,X4] :
( ~ c_in(X0,c_PropLog_Othms(c_insert(X4,c_minus(X1,c_insert(c_PropLog_Opl_Oop_A_N_62(X4,c_PropLog_Opl_Ofalse,X3),X2,tc_PropLog_Opl(X3)),tc_set(tc_PropLog_Opl(X3))),tc_PropLog_Opl(X3)),X3),tc_PropLog_Opl(X3))
| ~ c_in(X0,c_PropLog_Othms(c_minus(X1,X2,tc_set(tc_PropLog_Opl(X3))),X3),tc_PropLog_Opl(X3))
| c_in(X0,c_PropLog_Othms(c_minus(X1,c_insert(c_PropLog_Opl_Oop_A_N_62(X4,c_PropLog_Opl_Ofalse,X3),X2,tc_PropLog_Opl(X3)),tc_set(tc_PropLog_Opl(X3))),X3),tc_PropLog_Opl(X3)) ),
inference(resolution,[],[f9,f5]) ).
fof(f18,plain,
! [X2,X3,X0,X1,X4,X5] :
( c_in(X0,c_PropLog_Othms(c_insert(c_PropLog_Opl_Ovar(X2,X4),c_minus(c_PropLog_Ohyps(X1,X3,X4),c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(X2,X4),c_PropLog_Opl_Ofalse,X4),X5,tc_PropLog_Opl(X4)),tc_set(tc_PropLog_Opl(X4))),tc_PropLog_Opl(X4)),X4),tc_PropLog_Opl(X4))
| ~ c_in(X0,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(X1,c_insert(X2,X3,X4),X4),X5,tc_set(tc_PropLog_Opl(X4))),X4),tc_PropLog_Opl(X4)) ),
inference(resolution,[],[f13,f10]) ).
fof(f20,plain,
! [X2,X3,X0,X1,X4,X5] :
( c_in(X0,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(X1,X2,X3),c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(X5,X3),c_PropLog_Opl_Ofalse,X3),X4,tc_PropLog_Opl(X3)),tc_set(tc_PropLog_Opl(X3))),X3),tc_PropLog_Opl(X3))
| ~ c_in(X0,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(X1,X2,X3),X4,tc_set(tc_PropLog_Opl(X3))),X3),tc_PropLog_Opl(X3))
| ~ c_in(X0,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(X1,c_insert(X5,X2,X3),X3),X4,tc_set(tc_PropLog_Opl(X3))),X3),tc_PropLog_Opl(X3)) ),
inference(resolution,[],[f15,f18]) ).
fof(f21,plain,
( ~ c_in(v_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p,v_t,t_a),v_F,tc_set(tc_PropLog_Opl(t_a))),t_a),tc_PropLog_Opl(t_a))
| ~ c_in(v_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p,c_insert(v_v,v_t,t_a),t_a),v_F,tc_set(tc_PropLog_Opl(t_a))),t_a),tc_PropLog_Opl(t_a)) ),
inference(resolution,[],[f20,f8]) ).
fof(f23,definition,
( spl0_1
<=> c_in(v_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p,c_insert(v_v,v_t,t_a),t_a),v_F,tc_set(tc_PropLog_Opl(t_a))),t_a),tc_PropLog_Opl(t_a)) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f24,plain,
( ~ c_in(v_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p,c_insert(v_v,v_t,t_a),t_a),v_F,tc_set(tc_PropLog_Opl(t_a))),t_a),tc_PropLog_Opl(t_a))
| spl0_1 ),
inference(avatar_component_clause,[],[f23]) ).
fof(f26,definition,
( spl0_2
<=> c_in(v_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p,v_t,t_a),v_F,tc_set(tc_PropLog_Opl(t_a))),t_a),tc_PropLog_Opl(t_a)) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f27,plain,
( ~ c_in(v_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p,v_t,t_a),v_F,tc_set(tc_PropLog_Opl(t_a))),t_a),tc_PropLog_Opl(t_a))
| spl0_2 ),
inference(avatar_component_clause,[],[f26]) ).
fof(f28,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f21,f26,f23]) ).
fof(f29,plain,
( $false
| spl0_1 ),
inference(resolution,[],[f24,f7]) ).
fof(f30,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f29]) ).
fof(f31,plain,
( $false
| spl0_2 ),
inference(resolution,[],[f27,f7]) ).
fof(f32,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f31]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f28]) ).
cnf(s2,plain,
spl0_1,
inference(sat_conversion,[],[f30]) ).
cnf(s3,plain,
spl0_2,
inference(sat_conversion,[],[f32]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s3,s2]) ).
fof(f33,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL430-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.04/0.31 % Computer : n012.cluster.edu
% 0.04/0.31 % Model : x86_64 x86_64
% 0.04/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.31 % Memory : 8046.5625MB
% 0.04/0.31 % OS : Linux 6.8.0-71-generic
% 0.04/0.31 % CPULimit : 300
% 0.04/0.31 % WCLimit : 300
% 0.04/0.31 % DateTime : Sun Sep 27 15:42:20 UTC 2026
% 0.04/0.31 % CPUTime :
% 0.04/0.31 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.04/0.33 Running first-order theorem proving
% 0.04/0.33 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
% 2.53/1.03 % (2537638)Input is clausal, will run a generic CNF schedule.
% 2.53/1.03 % (2537677)dis-21_1_sil=8000:lcm=predicate:random_seed=1328995714:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_3000 on theBenchmark for (3000ds/117Mi)
% 2.53/1.03 % (2537677)First to succeed.
% 2.53/1.03 % (2537677)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2537638"
% 2.53/1.03 % (2537670)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=726570391:i=140167_3000 on theBenchmark for (3000ds/140167Mi)
% 2.53/1.03 % (2537674)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2800652118:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_3000 on theBenchmark for (3000ds/114Mi)
% 2.53/1.03 % (2537673)lrs+10_1_sil=8000:sp=occurrence:random_seed=3452066741:i=107:sd=3:ss=axioms:sgt=8_3000 on theBenchmark for (3000ds/107Mi)
% 2.53/1.03 % (2537675)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1409810443:s2a=on:i=180:gtg=position_3000 on theBenchmark for (3000ds/180Mi)
% 2.53/1.03 % (2537671)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3126018347:i=132376:av=off_3000 on theBenchmark for (3000ds/132376Mi)
% 2.53/1.03 % (2537672)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1967661654:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_3000 on theBenchmark for (3000ds/137899Mi)
% 2.53/1.03 % (2537673)Also succeeded, but the first one will report.
% 2.53/1.03 % (2537675)Also succeeded, but the first one will report.
% 2.53/1.03 % (2537674)Also succeeded, but the first one will report.
% 2.53/1.03 % (2537677)Refutation found. Thanks to Tanya!
% 2.53/1.03 % SZS status Unsatisfiable for theBenchmark
% 2.53/1.03 % SZS output start Proof for theBenchmark
% See solution above
% 2.53/1.03 % (2537677)------------------------------
% 2.53/1.03 % (2537677)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.53/1.03 % (2537677)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.53/1.03 % (2537677)CaDiCaL version: 2.1.3
% 2.53/1.03 % (2537677)Termination reason: Refutation
% 2.53/1.03 % (2537677)Time elapsed: 0.003 s
% 2.53/1.03 % (2537677)Peak memory usage: 89 MB
% 2.53/1.03 % (2537677)Instructions burned: 3 (million)
% 2.53/1.03 % (2537677)------------------------------
% 2.53/1.03 % (2537677)------------------------------
% 2.53/1.03 % (2537638)Success in time 0.312 s
% 2.53/1.03 % Vampire exiting
%------------------------------------------------------------------------------