%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL430-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 : Sun Sep 27 07:58:53 AM UTC 2026
% Result : Unsatisfiable 0.08s 0.38s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 8
% Syntax : Number of formulae : 25 ( 14 unt; 0 def)
% Number of atoms : 42 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 39 ( 22 ~; 17 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 8 ( 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 : 76 ( 3 sgn 27 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_PropLog_Ohyps__insert_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : c_lessequals(c_PropLog_Ohyps(VAR_0,c_insert(VAR_1,VAR_2,VAR_3),VAR_3),c_insert(c_PropLog_Opl_Ovar(VAR_1,VAR_3),c_minus(c_PropLog_Ohyps(VAR_0,VAR_2,VAR_3),c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(VAR_1,VAR_3),c_PropLog_Opl_Ofalse,VAR_3),c_emptyset,tc_PropLog_Opl(VAR_3)),tc_set(tc_PropLog_Opl(VAR_3))),tc_PropLog_Opl(VAR_3)),tc_set(tc_PropLog_Opl(VAR_3))),
file('theBenchmark.p',cls_PropLog_Ohyps__insert_0) ).
cnf(c_1,plain,
c_lessequals(c_PropLog_Ohyps(A,c_insert(B,C,D),D),c_insert(c_PropLog_Opl_Ovar(B,D),c_minus(c_PropLog_Ohyps(A,C,D),c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(B,D),c_PropLog_Opl_Ofalse,D),c_emptyset,tc_PropLog_Opl(D)),tc_set(tc_PropLog_Opl(D))),tc_PropLog_Opl(D)),tc_set(tc_PropLog_Opl(D))),
inference(clausify,[status(thm)],[cls_PropLog_Ohyps__insert_0]) ).
fof(cls_PropLog_ODiff__weaken__left_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( c_in(VAR_0,c_PropLog_Othms(c_minus(VAR_4,VAR_2,tc_set(tc_PropLog_Opl(VAR_3))),VAR_3),tc_PropLog_Opl(VAR_3))
| ~ c_lessequals(VAR_1,VAR_4,tc_set(tc_PropLog_Opl(VAR_3)))
| ~ c_in(VAR_0,c_PropLog_Othms(c_minus(VAR_1,VAR_2,tc_set(tc_PropLog_Opl(VAR_3))),VAR_3),tc_PropLog_Opl(VAR_3)) ),
file('theBenchmark.p',cls_PropLog_ODiff__weaken__left_0) ).
cnf(c_2,plain,
( c_in(A,c_PropLog_Othms(c_minus(E,C,tc_set(tc_PropLog_Opl(D))),D),tc_PropLog_Opl(D))
| ~ c_lessequals(B,E,tc_set(tc_PropLog_Opl(D)))
| ~ c_in(A,c_PropLog_Othms(c_minus(B,C,tc_set(tc_PropLog_Opl(D))),D),tc_PropLog_Opl(D)) ),
inference(clausify,[status(thm)],[cls_PropLog_ODiff__weaken__left_0]) ).
fof(cls_PropLog_Oinsert__Diff__same_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : c_lessequals(c_minus(VAR_0,VAR_1,tc_set(VAR_2)),c_insert(VAR_3,c_minus(VAR_0,c_insert(VAR_3,VAR_1,VAR_2),tc_set(VAR_2)),VAR_2),tc_set(VAR_2)),
file('theBenchmark.p',cls_PropLog_Oinsert__Diff__same_0) ).
cnf(c_3,plain,
c_lessequals(c_minus(A,B,tc_set(C)),c_insert(D,c_minus(A,c_insert(D,B,C),tc_set(C)),C),tc_set(C)),
inference(clausify,[status(thm)],[cls_PropLog_Oinsert__Diff__same_0]) ).
fof(cls_PropLog_Oinsert__Diff__subset2_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] : c_lessequals(c_minus(c_insert(VAR_0,c_minus(VAR_1,c_insert(VAR_2,c_emptyset,VAR_3),tc_set(VAR_3)),VAR_3),VAR_4,tc_set(VAR_3)),c_insert(VAR_0,c_minus(VAR_1,c_insert(VAR_2,VAR_4,VAR_3),tc_set(VAR_3)),VAR_3),tc_set(VAR_3)),
file('theBenchmark.p',cls_PropLog_Oinsert__Diff__subset2_0) ).
cnf(c_4,plain,
c_lessequals(c_minus(c_insert(A,c_minus(B,c_insert(C,c_emptyset,D),tc_set(D)),D),E,tc_set(D)),c_insert(A,c_minus(B,c_insert(C,E,D),tc_set(D)),D),tc_set(D)),
inference(clausify,[status(thm)],[cls_PropLog_Oinsert__Diff__subset2_0]) ).
fof(cls_PropLog_Oweaken__left_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_in(VAR_0,c_PropLog_Othms(VAR_3,VAR_2),tc_PropLog_Opl(VAR_2))
| ~ c_lessequals(VAR_1,VAR_3,tc_set(tc_PropLog_Opl(VAR_2)))
| ~ c_in(VAR_0,c_PropLog_Othms(VAR_1,VAR_2),tc_PropLog_Opl(VAR_2)) ),
file('theBenchmark.p',cls_PropLog_Oweaken__left_0) ).
cnf(c_5,plain,
( c_in(A,c_PropLog_Othms(D,C),tc_PropLog_Opl(C))
| ~ c_lessequals(B,D,tc_set(tc_PropLog_Opl(C)))
| ~ c_in(A,c_PropLog_Othms(B,C),tc_PropLog_Opl(C)) ),
inference(clausify,[status(thm)],[cls_PropLog_Oweaken__left_0]) ).
cnf(c_7,plain,
( c_in(A,c_PropLog_Othms(c_insert(E,c_minus(B,c_insert(E,C,tc_PropLog_Opl(D)),tc_set(tc_PropLog_Opl(D))),tc_PropLog_Opl(D)),D),tc_PropLog_Opl(D))
| ~ c_in(A,c_PropLog_Othms(c_minus(B,C,tc_set(tc_PropLog_Opl(D))),D),tc_PropLog_Opl(D)) ),
inference(resolve,[status(thm)],[c_5,c_3]) ).
cnf(c_8,plain,
( c_in(A,c_PropLog_Othms(c_insert(B,c_minus(C,c_insert(D,F,tc_PropLog_Opl(E)),tc_set(tc_PropLog_Opl(E))),tc_PropLog_Opl(E)),E),tc_PropLog_Opl(E))
| ~ c_in(A,c_PropLog_Othms(c_minus(c_insert(B,c_minus(C,c_insert(D,c_emptyset,tc_PropLog_Opl(E)),tc_set(tc_PropLog_Opl(E))),tc_PropLog_Opl(E)),F,tc_set(tc_PropLog_Opl(E))),E),tc_PropLog_Opl(E)) ),
inference(resolve,[status(thm)],[c_5,c_4]) ).
cnf(c_11,plain,
( c_in(A,c_PropLog_Othms(c_minus(c_insert(c_PropLog_Opl_Ovar(C,E),c_minus(c_PropLog_Ohyps(B,D,E),c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(C,E),c_PropLog_Opl_Ofalse,E),c_emptyset,tc_PropLog_Opl(E)),tc_set(tc_PropLog_Opl(E))),tc_PropLog_Opl(E)),F,tc_set(tc_PropLog_Opl(E))),E),tc_PropLog_Opl(E))
| ~ c_in(A,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(B,c_insert(C,D,E),E),F,tc_set(tc_PropLog_Opl(E))),E),tc_PropLog_Opl(E)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
fof(cls_conjecture_5,axiom,
~ 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('theBenchmark.p',cls_conjecture_5) ).
cnf(c_12,plain,
~ 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)),
inference(clausify,[status(thm)],[cls_conjecture_5]) ).
fof(cls_conjecture_3,axiom,
! [VAR_0] : c_in(v_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p,VAR_0,t_a),v_F,tc_set(tc_PropLog_Opl(t_a))),t_a),tc_PropLog_Opl(t_a)),
file('theBenchmark.p',cls_conjecture_3) ).
cnf(c_13,plain,
c_in(v_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p,A,t_a),v_F,tc_set(tc_PropLog_Opl(t_a))),t_a),tc_PropLog_Opl(t_a)),
inference(clausify,[status(thm)],[cls_conjecture_3]) ).
fof(cls_PropLog_Othms__excluded__middle__rule_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_in(VAR_0,c_PropLog_Othms(VAR_2,VAR_3),tc_PropLog_Opl(VAR_3))
| ~ c_in(VAR_0,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(VAR_1,c_PropLog_Opl_Ofalse,VAR_3),VAR_2,tc_PropLog_Opl(VAR_3)),VAR_3),tc_PropLog_Opl(VAR_3))
| ~ c_in(VAR_0,c_PropLog_Othms(c_insert(VAR_1,VAR_2,tc_PropLog_Opl(VAR_3)),VAR_3),tc_PropLog_Opl(VAR_3)) ),
file('theBenchmark.p',cls_PropLog_Othms__excluded__middle__rule_0) ).
cnf(c_14,plain,
( c_in(A,c_PropLog_Othms(C,D),tc_PropLog_Opl(D))
| ~ c_in(A,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(B,c_PropLog_Opl_Ofalse,D),C,tc_PropLog_Opl(D)),D),tc_PropLog_Opl(D))
| ~ c_in(A,c_PropLog_Othms(c_insert(B,C,tc_PropLog_Opl(D)),D),tc_PropLog_Opl(D)) ),
inference(clausify,[status(thm)],[cls_PropLog_Othms__excluded__middle__rule_0]) ).
cnf(c_15,plain,
c_in(v_p,c_PropLog_Othms(c_minus(c_insert(c_PropLog_Opl_Ovar(A,t_a),c_minus(c_PropLog_Ohyps(v_p,B,t_a),c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(A,t_a),c_PropLog_Opl_Ofalse,t_a),c_emptyset,tc_PropLog_Opl(t_a)),tc_set(tc_PropLog_Opl(t_a))),tc_PropLog_Opl(t_a)),v_F,tc_set(tc_PropLog_Opl(t_a))),t_a),tc_PropLog_Opl(t_a)),
inference(resolve,[status(thm)],[c_11,c_13]) ).
cnf(c_17,plain,
( ~ c_in(v_p,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(A,c_PropLog_Opl_Ofalse,t_a),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))),tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a))
| ~ c_in(v_p,c_PropLog_Othms(c_insert(A,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))),tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) ),
inference(resolve,[status(thm)],[c_14,c_12]) ).
cnf(c_18,plain,
c_in(v_p,c_PropLog_Othms(c_insert(c_PropLog_Opl_Ovar(A,t_a),c_minus(c_PropLog_Ohyps(v_p,B,t_a),c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ovar(A,t_a),c_PropLog_Opl_Ofalse,t_a),v_F,tc_PropLog_Opl(t_a)),tc_set(tc_PropLog_Opl(t_a))),tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),
inference(resolve,[status(thm)],[c_8,c_15]) ).
cnf(c_24,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_insert(c_PropLog_Opl_Ovar(v_v,t_a),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))),tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) ),
inference(resolve,[status(thm)],[c_17,c_7]) ).
cnf(c_28,plain,
~ c_in(v_p,c_PropLog_Othms(c_insert(c_PropLog_Opl_Ovar(v_v,t_a),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))),tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),
inference(resolve,[status(thm)],[c_24,c_13]) ).
cnf(c_29,plain,
$false,
inference(resolve,[status(thm)],[c_28,c_18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL430-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n009.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Fri Sep 25 22:31:59 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 2736309 was started by sandbox on n009,
% 0.08/0.36 % Fri Sep 25 22:31:59 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.37
% 0.08/0.37 % From the command line: assign(max_seconds, 300).
% 0.08/0.38
% 0.08/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.08/0.38
% 0.08/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.08/0.38 % Length of proof is 17.
% 0.08/0.38 % Level of proof is 4.
% 0.08/0.38 % Maximum clause weight is 59.000.
% 0.08/0.38 % Given clauses 12.
% 0.08/0.38
% 0.08/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------