%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL429-2 : 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 : 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 11:52:23 AM UTC 2026
% Result : Unsatisfiable 4.19s 1.56s
% Output : Refutation 4.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 17 ( 7 unt; 0 def)
% Number of atoms : 32 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 32 ( 17 ~; 15 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 7 con; 0-3 aty)
% Number of variables : 64 ( 64 !; 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/sandbox/benchmark/theBenchmark.p',cls_PropLog_ODiff__weaken__left_0) ).
fof(f2,axiom,
! [X2,X3,X0,X1] : c_lessequals(c_PropLog_Ohyps(X0,c_minus(X1,c_insert(X2,c_emptyset,X3),tc_set(X3)),X3),c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(X2,X3),c_PropLog_Opl_Ofalse,X3),c_minus(c_PropLog_Ohyps(X0,X1,X3),c_insert(c_PropLog_Opl_Ovar(X2,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/sandbox/benchmark/theBenchmark.p',cls_PropLog_Ohyps__Diff_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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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_Ovar(v_v,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/sandbox/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_Oop_A_N_62(c_PropLog_Opl_Ovar(X3,X4),c_PropLog_Opl_Ofalse,X4),c_minus(c_PropLog_Ohyps(X1,X2,X4),c_insert(c_PropLog_Opl_Ovar(X3,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_minus(X2,c_insert(X3,c_emptyset,X4),tc_set(X4)),X4),X5,tc_set(tc_PropLog_Opl(X4))),X4),tc_PropLog_Opl(X4)) ),
inference(resolution,[],[f2,f1]) ).
fof(f19,plain,
! [X2,X3,X0,X1,X4,X5] :
( c_in(X0,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(X3,X4),c_PropLog_Opl_Ofalse,X4),c_minus(c_PropLog_Ohyps(X1,X2,X4),c_insert(c_PropLog_Opl_Ovar(X3,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_minus(X2,c_insert(X3,c_emptyset,X4),tc_set(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_insert(c_PropLog_Opl_Ovar(X3,X4),c_minus(c_PropLog_Ohyps(X1,X2,X4),c_insert(c_PropLog_Opl_Ovar(X3,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_minus(X2,c_insert(X3,c_emptyset,X4),tc_set(X4)),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,X2,X4),c_insert(c_PropLog_Opl_Ovar(X3,X4),X5,tc_PropLog_Opl(X4)),tc_set(tc_PropLog_Opl(X4))),X4),tc_PropLog_Opl(X4)) ),
inference(resolution,[],[f19,f5]) ).
fof(f24,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ c_in(X0,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(X1,c_minus(X2,c_insert(X3,c_emptyset,X4),tc_set(X4)),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,X2,X4),c_insert(c_PropLog_Opl_Ovar(X3,X4),X5,tc_PropLog_Opl(X4)),tc_set(tc_PropLog_Opl(X4))),X4),tc_PropLog_Opl(X4))
| ~ c_in(X0,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(X1,X2,X4),X5,tc_set(tc_PropLog_Opl(X4))),X4),tc_PropLog_Opl(X4)) ),
inference(resolution,[],[f20,f9]) ).
fof(f25,plain,
! [X0,X1] :
( c_in(v_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p,X0,t_a),c_insert(c_PropLog_Opl_Ovar(X1,t_a),v_F,tc_PropLog_Opl(t_a)),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,X0,t_a),v_F,tc_set(tc_PropLog_Opl(t_a))),t_a),tc_PropLog_Opl(t_a)) ),
inference(resolution,[],[f24,f7]) ).
fof(f31,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)),
inference(resolution,[],[f25,f8]) ).
fof(f37,plain,
$false,
inference(resolution,[],[f31,f7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL429-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n002.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 15:44:36 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 4.19/1.56 % (3698179)Input is clausal, will run a generic CNF schedule.
% 4.19/1.56 % (3698252)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=300712080:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 4.19/1.56 % (3698253)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1493601564:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 4.19/1.56 % (3698255)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=132778003:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 4.19/1.56 % (3698260)dis-21_1_sil=8000:lcm=predicate:random_seed=1885908837: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)
% 4.19/1.56 % (3698259)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=782832240:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 4.19/1.56 % (3698257)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=460814900:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 4.19/1.56 % (3698260)First to succeed.
% 4.19/1.56 % (3698260)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3698179"
% 4.19/1.56 % (3698259)Also succeeded, but the first one will report.
% 4.19/1.56 % (3698257)Also succeeded, but the first one will report.
% 4.19/1.56 % (3698256)lrs+10_1_sil=8000:sp=occurrence:random_seed=779046682:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 4.19/1.56 % (3698256)Also succeeded, but the first one will report.
% 4.19/1.56 % (3698260)Refutation found. Thanks to Tanya!
% 4.19/1.56 % SZS status Unsatisfiable for theBenchmark
% 4.19/1.56 % SZS output start Proof for theBenchmark
% See solution above
% 4.19/1.56 % (3698260)------------------------------
% 4.19/1.56 % (3698260)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.19/1.56 % (3698260)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.19/1.56 % (3698260)CaDiCaL version: 2.1.3
% 4.19/1.56 % (3698260)Termination reason: Refutation
% 4.19/1.56 % (3698260)Time elapsed: 0.006 s
% 4.19/1.56 % (3698260)Peak memory usage: 88 MB
% 4.19/1.56 % (3698260)Instructions burned: 5 (million)
% 4.19/1.56 % (3698260)------------------------------
% 4.19/1.56 % (3698260)------------------------------
% 4.19/1.56 % (3698179)Success in time 0.51 s
% 4.19/1.56 % Vampire exiting
%------------------------------------------------------------------------------