TSTP Solution File: LCL444-2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : LCL444-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 06:54:08 EDT 2023
% Result : Unsatisfiable 10.55s 10.63s
% Output : CNFRefutation 10.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 17
% Syntax : Number of formulae : 98 ( 63 unt; 10 typ; 0 def)
% Number of atoms : 115 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 56 ( 29 ~; 27 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 5 >; 7 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 393 ( 120 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
tc_PropLog_Opl: $i > $i ).
tff(decl_23,type,
c_insert: ( $i * $i * $i ) > $i ).
tff(decl_24,type,
c_PropLog_Othms: ( $i * $i ) > $i ).
tff(decl_25,type,
c_in: ( $i * $i * $i ) > $o ).
tff(decl_26,type,
c_PropLog_Opl_Oop_A_N_62: ( $i * $i * $i ) > $i ).
tff(decl_27,type,
c_PropLog_Opl_Ofalse: $i ).
tff(decl_28,type,
v_p: $i ).
tff(decl_29,type,
v_q: $i ).
tff(decl_30,type,
t_a: $i ).
tff(decl_31,type,
v_H: $i ).
cnf(cls_Set_OinsertCI_0,axiom,
( c_in(X1,c_insert(X4,X2,X3),X3)
| ~ c_in(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertCI_0) ).
cnf(cls_Set_OinsertCI_1,axiom,
c_in(X1,c_insert(X1,X2,X3),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertCI_1) ).
cnf(cls_PropLog_Othms_OH_0,axiom,
( c_in(X1,c_PropLog_Othms(X2,X3),tc_PropLog_Opl(X3))
| ~ c_in(X1,X2,tc_PropLog_Opl(X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PropLog_Othms_OH_0) ).
cnf(cls_PropLog_Odeduction_0,axiom,
( c_in(c_PropLog_Opl_Oop_A_N_62(X2,X1,X4),c_PropLog_Othms(X3,X4),tc_PropLog_Opl(X4))
| ~ c_in(X1,c_PropLog_Othms(c_insert(X2,X3,tc_PropLog_Opl(X4)),X4),tc_PropLog_Opl(X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PropLog_Odeduction_0) ).
cnf(cls_PropLog_Othms_OMP_0,axiom,
( c_in(X4,c_PropLog_Othms(X2,X3),tc_PropLog_Opl(X3))
| ~ c_in(X1,c_PropLog_Othms(X2,X3),tc_PropLog_Opl(X3))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(X1,X4,X3),c_PropLog_Othms(X2,X3),tc_PropLog_Opl(X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PropLog_Othms_OMP_0) ).
cnf(cls_PropLog_Othms_ODN_0,axiom,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X1,c_PropLog_Opl_Ofalse,X2),c_PropLog_Opl_Ofalse,X2),X1,X2),c_PropLog_Othms(X3,X2),tc_PropLog_Opl(X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PropLog_Othms_ODN_0) ).
cnf(cls_conjecture_0,negated_conjecture,
~ c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,c_PropLog_Opl_Ofalse,t_a),v_q,t_a),v_q,t_a),t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(c_0_7,axiom,
( c_in(X1,c_insert(X4,X2,X3),X3)
| ~ c_in(X1,X2,X3) ),
cls_Set_OinsertCI_0 ).
cnf(c_0_8,axiom,
c_in(X1,c_insert(X1,X2,X3),X3),
cls_Set_OinsertCI_1 ).
cnf(c_0_9,axiom,
( c_in(X1,c_PropLog_Othms(X2,X3),tc_PropLog_Opl(X3))
| ~ c_in(X1,X2,tc_PropLog_Opl(X3)) ),
cls_PropLog_Othms_OH_0 ).
cnf(c_0_10,plain,
c_in(X1,c_insert(X2,c_insert(X1,X3,X4),X4),X4),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_11,axiom,
( c_in(c_PropLog_Opl_Oop_A_N_62(X2,X1,X4),c_PropLog_Othms(X3,X4),tc_PropLog_Opl(X4))
| ~ c_in(X1,c_PropLog_Othms(c_insert(X2,X3,tc_PropLog_Opl(X4)),X4),tc_PropLog_Opl(X4)) ),
cls_PropLog_Odeduction_0 ).
cnf(c_0_12,plain,
c_in(X1,c_PropLog_Othms(c_insert(X2,c_insert(X1,X3,tc_PropLog_Opl(X4)),tc_PropLog_Opl(X4)),X4),tc_PropLog_Opl(X4)),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,axiom,
( c_in(X4,c_PropLog_Othms(X2,X3),tc_PropLog_Opl(X3))
| ~ c_in(X1,c_PropLog_Othms(X2,X3),tc_PropLog_Opl(X3))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(X1,X4,X3),c_PropLog_Othms(X2,X3),tc_PropLog_Opl(X3)) ),
cls_PropLog_Othms_OMP_0 ).
cnf(c_0_14,plain,
c_in(X1,c_PropLog_Othms(c_insert(X1,X2,tc_PropLog_Opl(X3)),X3),tc_PropLog_Opl(X3)),
inference(spm,[status(thm)],[c_0_9,c_0_8]) ).
cnf(c_0_15,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(X1,X2,X3),c_PropLog_Othms(c_insert(X2,X4,tc_PropLog_Opl(X3)),X3),tc_PropLog_Opl(X3)),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_16,plain,
( c_in(X1,c_PropLog_Othms(c_insert(X2,X3,tc_PropLog_Opl(X4)),X4),tc_PropLog_Opl(X4))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(X2,X1,X4),c_PropLog_Othms(c_insert(X2,X3,tc_PropLog_Opl(X4)),X4),tc_PropLog_Opl(X4)) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,plain,
( c_in(X1,c_PropLog_Othms(c_insert(X2,X3,tc_PropLog_Opl(X4)),X4),tc_PropLog_Opl(X4))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X5,X2,X4),X1,X4),c_PropLog_Othms(c_insert(X2,X3,tc_PropLog_Opl(X4)),X4),tc_PropLog_Opl(X4)) ),
inference(spm,[status(thm)],[c_0_13,c_0_15]) ).
cnf(c_0_18,axiom,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X1,c_PropLog_Opl_Ofalse,X2),c_PropLog_Opl_Ofalse,X2),X1,X2),c_PropLog_Othms(X3,X2),tc_PropLog_Opl(X2)),
cls_PropLog_Othms_ODN_0 ).
cnf(c_0_19,plain,
c_in(X1,c_PropLog_Othms(c_insert(X2,c_insert(c_PropLog_Opl_Oop_A_N_62(X2,X1,X3),X4,tc_PropLog_Opl(X3)),tc_PropLog_Opl(X3)),X3),tc_PropLog_Opl(X3)),
inference(spm,[status(thm)],[c_0_16,c_0_12]) ).
cnf(c_0_20,plain,
c_in(X1,c_PropLog_Othms(c_insert(c_PropLog_Opl_Ofalse,X2,tc_PropLog_Opl(X3)),X3),tc_PropLog_Opl(X3)),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,plain,
( c_in(X1,c_PropLog_Othms(c_insert(X2,c_insert(c_PropLog_Opl_Oop_A_N_62(X2,X3,X4),X5,tc_PropLog_Opl(X4)),tc_PropLog_Opl(X4)),X4),tc_PropLog_Opl(X4))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(X3,X1,X4),c_PropLog_Othms(c_insert(X2,c_insert(c_PropLog_Opl_Oop_A_N_62(X2,X3,X4),X5,tc_PropLog_Opl(X4)),tc_PropLog_Opl(X4)),X4),tc_PropLog_Opl(X4)) ),
inference(spm,[status(thm)],[c_0_13,c_0_19]) ).
cnf(c_0_22,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Ofalse,X1,X2),c_PropLog_Othms(X3,X2),tc_PropLog_Opl(X2)),
inference(spm,[status(thm)],[c_0_11,c_0_20]) ).
cnf(c_0_23,plain,
( c_in(X1,c_PropLog_Othms(c_insert(X2,c_insert(X3,X4,tc_PropLog_Opl(X5)),tc_PropLog_Opl(X5)),X5),tc_PropLog_Opl(X5))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(X3,X1,X5),c_PropLog_Othms(c_insert(X2,c_insert(X3,X4,tc_PropLog_Opl(X5)),tc_PropLog_Opl(X5)),X5),tc_PropLog_Opl(X5)) ),
inference(spm,[status(thm)],[c_0_13,c_0_12]) ).
cnf(c_0_24,plain,
c_in(X1,c_PropLog_Othms(c_insert(X2,c_insert(c_PropLog_Opl_Oop_A_N_62(X2,c_PropLog_Opl_Ofalse,X3),X4,tc_PropLog_Opl(X3)),tc_PropLog_Opl(X3)),X3),tc_PropLog_Opl(X3)),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,plain,
c_in(X1,c_PropLog_Othms(c_insert(X2,c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X3,X2,X4),X1,X4),X5,tc_PropLog_Opl(X4)),tc_PropLog_Opl(X4)),X4),tc_PropLog_Opl(X4)),
inference(spm,[status(thm)],[c_0_17,c_0_12]) ).
cnf(c_0_26,plain,
c_in(X1,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(X2,X1,X3),c_insert(X2,X4,tc_PropLog_Opl(X3)),tc_PropLog_Opl(X3)),X3),tc_PropLog_Opl(X3)),
inference(spm,[status(thm)],[c_0_23,c_0_14]) ).
cnf(c_0_27,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(X1,X2,X3),c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(X1,c_PropLog_Opl_Ofalse,X3),X4,tc_PropLog_Opl(X3)),X3),tc_PropLog_Opl(X3)),
inference(spm,[status(thm)],[c_0_11,c_0_24]) ).
cnf(c_0_28,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(X1,X2,X3),c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X4,X1,X3),X2,X3),X5,tc_PropLog_Opl(X3)),X3),tc_PropLog_Opl(X3)),
inference(spm,[status(thm)],[c_0_11,c_0_25]) ).
cnf(c_0_29,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X1,X2,X3),X2,X3),c_PropLog_Othms(c_insert(X1,X4,tc_PropLog_Opl(X3)),X3),tc_PropLog_Opl(X3)),
inference(spm,[status(thm)],[c_0_11,c_0_26]) ).
cnf(c_0_30,plain,
( c_in(X1,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(X2,c_PropLog_Opl_Ofalse,X3),X4,tc_PropLog_Opl(X3)),X3),tc_PropLog_Opl(X3))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X2,X5,X3),X1,X3),c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(X2,c_PropLog_Opl_Ofalse,X3),X4,tc_PropLog_Opl(X3)),X3),tc_PropLog_Opl(X3)) ),
inference(spm,[status(thm)],[c_0_13,c_0_27]) ).
cnf(c_0_31,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X1,X2,X3),X4,X3),c_PropLog_Opl_Oop_A_N_62(X2,X4,X3),X3),c_PropLog_Othms(X5,X3),tc_PropLog_Opl(X3)),
inference(spm,[status(thm)],[c_0_11,c_0_28]) ).
cnf(c_0_32,plain,
( c_in(X1,c_PropLog_Othms(c_insert(X2,X3,tc_PropLog_Opl(X4)),X4),tc_PropLog_Opl(X4))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X2,X5,X4),X5,X4),X1,X4),c_PropLog_Othms(c_insert(X2,X3,tc_PropLog_Opl(X4)),X4),tc_PropLog_Opl(X4)) ),
inference(spm,[status(thm)],[c_0_13,c_0_29]) ).
cnf(c_0_33,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(X1,X2,X3),c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X4,X1,X3),c_PropLog_Opl_Ofalse,X3),X5,tc_PropLog_Opl(X3)),X3),tc_PropLog_Opl(X3)),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_34,plain,
c_in(X1,c_PropLog_Othms(c_insert(X2,c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X2,X3,X4),X3,X4),X1,X4),X5,tc_PropLog_Opl(X4)),tc_PropLog_Opl(X4)),X4),tc_PropLog_Opl(X4)),
inference(spm,[status(thm)],[c_0_32,c_0_12]) ).
cnf(c_0_35,plain,
( c_in(X1,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X2,X3,X4),c_PropLog_Opl_Ofalse,X4),X5,tc_PropLog_Opl(X4)),X4),tc_PropLog_Opl(X4))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X3,X6,X4),X1,X4),c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X2,X3,X4),c_PropLog_Opl_Ofalse,X4),X5,tc_PropLog_Opl(X4)),X4),tc_PropLog_Opl(X4)) ),
inference(spm,[status(thm)],[c_0_13,c_0_33]) ).
cnf(c_0_36,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(X1,X2,X3),c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X1,X4,X3),X4,X3),X2,X3),X5,tc_PropLog_Opl(X3)),X3),tc_PropLog_Opl(X3)),
inference(spm,[status(thm)],[c_0_11,c_0_34]) ).
cnf(c_0_37,plain,
c_in(c_PropLog_Opl_Ofalse,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X1,X2,X3),X1,X3),X1,X3),c_PropLog_Opl_Ofalse,X3),X4,tc_PropLog_Opl(X3)),X3),tc_PropLog_Opl(X3)),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_38,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X1,X2,X3),X1,X3),X1,X3),c_PropLog_Opl_Ofalse,X3),c_PropLog_Opl_Ofalse,X3),c_PropLog_Othms(X4,X3),tc_PropLog_Opl(X3)),
inference(spm,[status(thm)],[c_0_11,c_0_37]) ).
cnf(c_0_39,plain,
( c_in(X1,c_PropLog_Othms(X2,X3),tc_PropLog_Opl(X3))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X4,X5,X3),X4,X3),X4,X3),c_PropLog_Opl_Ofalse,X3),c_PropLog_Opl_Ofalse,X3),X1,X3),c_PropLog_Othms(X2,X3),tc_PropLog_Opl(X3)) ),
inference(spm,[status(thm)],[c_0_13,c_0_38]) ).
cnf(c_0_40,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X1,X2,X3),X1,X3),X1,X3),c_PropLog_Othms(X4,X3),tc_PropLog_Opl(X3)),
inference(spm,[status(thm)],[c_0_39,c_0_18]) ).
cnf(c_0_41,plain,
c_in(X1,c_insert(X2,c_insert(X3,c_insert(X1,X4,X5),X5),X5),X5),
inference(spm,[status(thm)],[c_0_7,c_0_10]) ).
cnf(c_0_42,plain,
c_in(X1,c_PropLog_Othms(c_insert(X2,c_insert(c_PropLog_Opl_Oop_A_N_62(X2,c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X1,X3,X4),X1,X4),X4),X5,tc_PropLog_Opl(X4)),tc_PropLog_Opl(X4)),X4),tc_PropLog_Opl(X4)),
inference(spm,[status(thm)],[c_0_21,c_0_40]) ).
cnf(c_0_43,plain,
c_in(X1,c_PropLog_Othms(c_insert(X2,c_insert(X3,c_insert(X1,X4,tc_PropLog_Opl(X5)),tc_PropLog_Opl(X5)),tc_PropLog_Opl(X5)),X5),tc_PropLog_Opl(X5)),
inference(spm,[status(thm)],[c_0_9,c_0_41]) ).
cnf(c_0_44,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X1,X2,X3),X2,X3),X4,X3),c_PropLog_Opl_Oop_A_N_62(X1,X4,X3),X3),c_PropLog_Othms(X5,X3),tc_PropLog_Opl(X3)),
inference(spm,[status(thm)],[c_0_11,c_0_36]) ).
cnf(c_0_45,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(X1,X2,X3),c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(X1,c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X2,X4,X3),X2,X3),X3),X5,tc_PropLog_Opl(X3)),X3),tc_PropLog_Opl(X3)),
inference(spm,[status(thm)],[c_0_11,c_0_42]) ).
cnf(c_0_46,plain,
c_in(X1,c_PropLog_Othms(c_insert(X2,c_insert(X3,c_insert(c_PropLog_Opl_Oop_A_N_62(X3,X1,X4),X5,tc_PropLog_Opl(X4)),tc_PropLog_Opl(X4)),tc_PropLog_Opl(X4)),X4),tc_PropLog_Opl(X4)),
inference(spm,[status(thm)],[c_0_23,c_0_43]) ).
cnf(c_0_47,plain,
c_in(X1,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X1,c_PropLog_Opl_Ofalse,X2),c_PropLog_Opl_Ofalse,X2),X3,tc_PropLog_Opl(X2)),X2),tc_PropLog_Opl(X2)),
inference(spm,[status(thm)],[c_0_16,c_0_18]) ).
cnf(c_0_48,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(X1,c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X1,X2,X3),X2,X3),X3),c_PropLog_Othms(X4,X3),tc_PropLog_Opl(X3)),
inference(spm,[status(thm)],[c_0_11,c_0_29]) ).
cnf(c_0_49,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X1,c_PropLog_Opl_Ofalse,X2),c_PropLog_Opl_Oop_A_N_62(X1,X3,X2),X2),c_PropLog_Othms(X4,X2),tc_PropLog_Opl(X2)),
inference(spm,[status(thm)],[c_0_11,c_0_27]) ).
cnf(c_0_50,plain,
( c_in(X1,c_PropLog_Othms(X2,X3),tc_PropLog_Opl(X3))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X4,X5,X3),X5,X3),X6,X3),c_PropLog_Opl_Oop_A_N_62(X4,X6,X3),X3),X1,X3),c_PropLog_Othms(X2,X3),tc_PropLog_Opl(X3)) ),
inference(spm,[status(thm)],[c_0_13,c_0_44]) ).
cnf(c_0_51,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X1,c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X2,X3,X4),X2,X4),X4),c_PropLog_Opl_Oop_A_N_62(X1,X2,X4),X4),c_PropLog_Othms(X5,X4),tc_PropLog_Opl(X4)),
inference(spm,[status(thm)],[c_0_11,c_0_45]) ).
cnf(c_0_52,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(X1,X2,X3),c_PropLog_Othms(c_insert(X4,c_insert(c_PropLog_Opl_Oop_A_N_62(X4,X2,X3),X5,tc_PropLog_Opl(X3)),tc_PropLog_Opl(X3)),X3),tc_PropLog_Opl(X3)),
inference(spm,[status(thm)],[c_0_11,c_0_46]) ).
cnf(c_0_53,plain,
c_in(X1,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X2,X1,X3),c_PropLog_Opl_Ofalse,X3),c_PropLog_Opl_Ofalse,X3),c_insert(X2,X4,tc_PropLog_Opl(X3)),tc_PropLog_Opl(X3)),X3),tc_PropLog_Opl(X3)),
inference(spm,[status(thm)],[c_0_23,c_0_47]) ).
cnf(c_0_54,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X1,X2,X3),X2,X3),c_PropLog_Othms(c_insert(X4,c_insert(c_PropLog_Opl_Oop_A_N_62(X4,X1,X3),X5,tc_PropLog_Opl(X3)),tc_PropLog_Opl(X3)),X3),tc_PropLog_Opl(X3)),
inference(spm,[status(thm)],[c_0_21,c_0_48]) ).
cnf(c_0_55,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(X1,X2,X3),c_PropLog_Othms(c_insert(X4,c_insert(c_PropLog_Opl_Oop_A_N_62(X4,c_PropLog_Opl_Oop_A_N_62(X1,c_PropLog_Opl_Ofalse,X3),X3),X5,tc_PropLog_Opl(X3)),tc_PropLog_Opl(X3)),X3),tc_PropLog_Opl(X3)),
inference(spm,[status(thm)],[c_0_21,c_0_49]) ).
cnf(c_0_56,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X1,X2,X3),X4,X3),X4,X3),X1,X3),X1,X3),c_PropLog_Othms(X5,X3),tc_PropLog_Opl(X3)),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_57,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(X1,c_PropLog_Opl_Oop_A_N_62(X2,X3,X4),X4),c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(X1,X3,X4),X5,tc_PropLog_Opl(X4)),X4),tc_PropLog_Opl(X4)),
inference(spm,[status(thm)],[c_0_11,c_0_52]) ).
cnf(c_0_58,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X1,X2,X3),c_PropLog_Opl_Ofalse,X3),c_PropLog_Opl_Ofalse,X3),X2,X3),c_PropLog_Othms(c_insert(X1,X4,tc_PropLog_Opl(X3)),X3),tc_PropLog_Opl(X3)),
inference(spm,[status(thm)],[c_0_11,c_0_53]) ).
cnf(c_0_59,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(X1,c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X2,X3,X4),X3,X4),X4),c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(X1,X2,X4),X5,tc_PropLog_Opl(X4)),X4),tc_PropLog_Opl(X4)),
inference(spm,[status(thm)],[c_0_11,c_0_54]) ).
cnf(c_0_60,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(X1,c_PropLog_Opl_Oop_A_N_62(X2,X3,X4),X4),c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(X1,c_PropLog_Opl_Oop_A_N_62(X2,c_PropLog_Opl_Ofalse,X4),X4),X5,tc_PropLog_Opl(X4)),X4),tc_PropLog_Opl(X4)),
inference(spm,[status(thm)],[c_0_11,c_0_55]) ).
cnf(c_0_61,plain,
( c_in(X1,c_PropLog_Othms(X2,X3),tc_PropLog_Opl(X3))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X4,X5,X3),X6,X3),X6,X3),X4,X3),X4,X3),X1,X3),c_PropLog_Othms(X2,X3),tc_PropLog_Opl(X3)) ),
inference(spm,[status(thm)],[c_0_13,c_0_56]) ).
cnf(c_0_62,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X1,X2,X3),c_PropLog_Opl_Oop_A_N_62(X1,c_PropLog_Opl_Oop_A_N_62(X4,X2,X3),X3),X3),c_PropLog_Othms(X5,X3),tc_PropLog_Opl(X3)),
inference(spm,[status(thm)],[c_0_11,c_0_57]) ).
cnf(c_0_63,plain,
( c_in(X1,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(X2,X3,X4),X5,tc_PropLog_Opl(X4)),X4),tc_PropLog_Opl(X4))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X2,c_PropLog_Opl_Oop_A_N_62(X6,X3,X4),X4),X1,X4),c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(X2,X3,X4),X5,tc_PropLog_Opl(X4)),X4),tc_PropLog_Opl(X4)) ),
inference(spm,[status(thm)],[c_0_13,c_0_57]) ).
cnf(c_0_64,plain,
c_in(X1,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X1,X2,X3),X1,X3),X4,tc_PropLog_Opl(X3)),X3),tc_PropLog_Opl(X3)),
inference(spm,[status(thm)],[c_0_39,c_0_58]) ).
cnf(c_0_65,plain,
( c_in(X1,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(X2,X3,X4),X5,tc_PropLog_Opl(X4)),X4),tc_PropLog_Opl(X4))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X2,c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X3,X6,X4),X6,X4),X4),X1,X4),c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(X2,X3,X4),X5,tc_PropLog_Opl(X4)),X4),tc_PropLog_Opl(X4)) ),
inference(spm,[status(thm)],[c_0_13,c_0_59]) ).
cnf(c_0_66,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X1,c_PropLog_Opl_Oop_A_N_62(X2,c_PropLog_Opl_Ofalse,X3),X3),c_PropLog_Opl_Oop_A_N_62(X1,c_PropLog_Opl_Oop_A_N_62(X2,X4,X3),X3),X3),c_PropLog_Othms(X5,X3),tc_PropLog_Opl(X3)),
inference(spm,[status(thm)],[c_0_11,c_0_60]) ).
cnf(c_0_67,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X1,X2,X3),X4,X3),X4,X3),X1,X3),c_PropLog_Opl_Oop_A_N_62(X5,X1,X3),X3),c_PropLog_Othms(X6,X3),tc_PropLog_Opl(X3)),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_68,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(X1,X2,X3),c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X1,X2,X3),X4,X3),X2,X3),X5,tc_PropLog_Opl(X3)),X3),tc_PropLog_Opl(X3)),
inference(spm,[status(thm)],[c_0_63,c_0_40]) ).
cnf(c_0_69,plain,
( c_in(X1,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X2,X3,X4),X2,X4),X5,tc_PropLog_Opl(X4)),X4),tc_PropLog_Opl(X4))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(X2,X1,X4),c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X2,X3,X4),X2,X4),X5,tc_PropLog_Opl(X4)),X4),tc_PropLog_Opl(X4)) ),
inference(spm,[status(thm)],[c_0_13,c_0_64]) ).
cnf(c_0_70,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(X1,c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X2,c_PropLog_Opl_Ofalse,X3),X4,X3),X3),c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(X1,X2,X3),X5,tc_PropLog_Opl(X3)),X3),tc_PropLog_Opl(X3)),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_71,plain,
( c_in(X1,c_PropLog_Othms(X2,X3),tc_PropLog_Opl(X3))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X4,X5,X3),X6,X3),X6,X3),X4,X3),c_PropLog_Opl_Oop_A_N_62(X7,X4,X3),X3),X1,X3),c_PropLog_Othms(X2,X3),tc_PropLog_Opl(X3)) ),
inference(spm,[status(thm)],[c_0_13,c_0_67]) ).
cnf(c_0_72,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X1,X2,X3),X4,X3),X2,X3),c_PropLog_Opl_Oop_A_N_62(X1,X2,X3),X3),c_PropLog_Othms(X5,X3),tc_PropLog_Opl(X3)),
inference(spm,[status(thm)],[c_0_11,c_0_68]) ).
cnf(c_0_73,plain,
c_in(X1,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X2,X3,X4),X2,X4),c_insert(c_PropLog_Opl_Oop_A_N_62(X2,X1,X4),X5,tc_PropLog_Opl(X4)),tc_PropLog_Opl(X4)),X4),tc_PropLog_Opl(X4)),
inference(spm,[status(thm)],[c_0_69,c_0_12]) ).
cnf(c_0_74,plain,
( c_in(X1,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(X2,X3,X4),X5,tc_PropLog_Opl(X4)),X4),tc_PropLog_Opl(X4))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X2,c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X3,c_PropLog_Opl_Ofalse,X4),X6,X4),X4),X1,X4),c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(X2,X3,X4),X5,tc_PropLog_Opl(X4)),X4),tc_PropLog_Opl(X4)) ),
inference(spm,[status(thm)],[c_0_13,c_0_70]) ).
cnf(c_0_75,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X1,X2,X3),c_PropLog_Opl_Oop_A_N_62(X4,X1,X3),X3),c_PropLog_Opl_Oop_A_N_62(X4,X1,X3),X3),c_PropLog_Othms(X5,X3),tc_PropLog_Opl(X3)),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_76,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X1,X2,X3),X1,X3),X4,X3),c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(X1,X4,X3),X5,tc_PropLog_Opl(X3)),X3),tc_PropLog_Opl(X3)),
inference(spm,[status(thm)],[c_0_11,c_0_73]) ).
cnf(c_0_77,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X1,c_PropLog_Opl_Ofalse,X2),X3,X2),c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X3,X4,X2),X1,X2),X5,tc_PropLog_Opl(X2)),X2),tc_PropLog_Opl(X2)),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_78,plain,
( c_in(X1,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(X2,X3,X4),X5,tc_PropLog_Opl(X4)),X4),tc_PropLog_Opl(X4))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X2,X6,X4),X2,X4),X3,X4),X1,X4),c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(X2,X3,X4),X5,tc_PropLog_Opl(X4)),X4),tc_PropLog_Opl(X4)) ),
inference(spm,[status(thm)],[c_0_13,c_0_76]) ).
cnf(c_0_79,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X1,X2,X3),X4,X3),c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X4,c_PropLog_Opl_Ofalse,X3),X1,X3),X3),c_PropLog_Othms(X5,X3),tc_PropLog_Opl(X3)),
inference(spm,[status(thm)],[c_0_11,c_0_77]) ).
cnf(c_0_80,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X1,c_PropLog_Opl_Ofalse,X2),c_PropLog_Opl_Oop_A_N_62(X3,X4,X2),X2),c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(X3,X1,X2),X5,tc_PropLog_Opl(X2)),X2),tc_PropLog_Opl(X2)),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_81,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X1,X2,X3),X2,X3),c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X2,X4,X3),X1,X3),X5,tc_PropLog_Opl(X3)),X3),tc_PropLog_Opl(X3)),
inference(spm,[status(thm)],[c_0_65,c_0_75]) ).
cnf(c_0_82,plain,
( c_in(X1,c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(X2,X3,X4),X5,tc_PropLog_Opl(X4)),X4),tc_PropLog_Opl(X4))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X3,c_PropLog_Opl_Ofalse,X4),c_PropLog_Opl_Oop_A_N_62(X2,X6,X4),X4),X1,X4),c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(X2,X3,X4),X5,tc_PropLog_Opl(X4)),X4),tc_PropLog_Opl(X4)) ),
inference(spm,[status(thm)],[c_0_13,c_0_80]) ).
cnf(c_0_83,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X1,X2,X3),X4,X3),c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X4,X1,X3),X1,X3),X3),c_PropLog_Othms(X5,X3),tc_PropLog_Opl(X3)),
inference(spm,[status(thm)],[c_0_11,c_0_81]) ).
cnf(c_0_84,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X1,X2,X3),X4,X3),X4,X3),c_PropLog_Othms(c_insert(c_PropLog_Opl_Oop_A_N_62(X1,X4,X3),X5,tc_PropLog_Opl(X3)),X3),tc_PropLog_Opl(X3)),
inference(spm,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_85,negated_conjecture,
~ c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(v_p,c_PropLog_Opl_Ofalse,t_a),v_q,t_a),v_q,t_a),t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
cls_conjecture_0 ).
cnf(c_0_86,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X1,X2,X3),c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(c_PropLog_Opl_Oop_A_N_62(X1,X4,X3),X2,X3),X2,X3),X3),c_PropLog_Othms(X5,X3),tc_PropLog_Opl(X3)),
inference(spm,[status(thm)],[c_0_11,c_0_84]) ).
cnf(c_0_87,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_85,c_0_86])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : LCL444-2 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n005.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Aug 24 23:49:08 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.19/0.55 start to proof: theBenchmark
% 10.55/10.63 % Version : CSE_E---1.5
% 10.55/10.63 % Problem : theBenchmark.p
% 10.55/10.63 % Proof found
% 10.55/10.63 % SZS status Theorem for theBenchmark.p
% 10.55/10.63 % SZS output start Proof
% See solution above
% 10.55/10.64 % Total time : 10.076000 s
% 10.55/10.64 % SZS output end Proof
% 10.55/10.64 % Total time : 10.079000 s
%------------------------------------------------------------------------------