TSTP Solution File: LCL084-10 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : LCL084-10 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n028.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 06:52:09 EDT 2023
% Result : Unsatisfiable 112.44s 113.17s
% Output : CNFRefutation 112.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 48
% Number of leaves : 12
% Syntax : Number of formulae : 134 ( 127 unt; 7 typ; 0 def)
% Number of atoms : 127 ( 126 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 7 ( 3 >; 4 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-4 aty)
% Number of variables : 457 ( 174 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
ifeq: ( $i * $i * $i * $i ) > $i ).
tff(decl_23,type,
implies: ( $i * $i ) > $i ).
tff(decl_24,type,
is_a_theorem: $i > $i ).
tff(decl_25,type,
true: $i ).
tff(decl_26,type,
a: $i ).
tff(decl_27,type,
b: $i ).
tff(decl_28,type,
c: $i ).
cnf(condensed_detachment,axiom,
ifeq(is_a_theorem(implies(X1,X2)),true,ifeq(is_a_theorem(X1),true,is_a_theorem(X2),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',condensed_detachment) ).
cnf(ic_1,axiom,
is_a_theorem(implies(X1,X1)) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ic_1) ).
cnf(ifeq_axiom,axiom,
ifeq(X1,X1,X2,X3) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
cnf(ic_JLukasiewicz,axiom,
is_a_theorem(implies(implies(implies(X1,X2),X3),implies(implies(X3,X1),implies(X4,X1)))) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ic_JLukasiewicz) ).
cnf(prove_ic_4,negated_conjecture,
is_a_theorem(implies(implies(a,b),implies(implies(b,c),implies(a,c)))) != true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_ic_4) ).
cnf(c_0_5,axiom,
ifeq(is_a_theorem(implies(X1,X2)),true,ifeq(is_a_theorem(X1),true,is_a_theorem(X2),true),true) = true,
condensed_detachment ).
cnf(c_0_6,axiom,
is_a_theorem(implies(X1,X1)) = true,
ic_1 ).
cnf(c_0_7,axiom,
ifeq(X1,X1,X2,X3) = X2,
ifeq_axiom ).
cnf(c_0_8,axiom,
is_a_theorem(implies(implies(implies(X1,X2),X3),implies(implies(X3,X1),implies(X4,X1)))) = true,
ic_JLukasiewicz ).
cnf(c_0_9,plain,
ifeq(is_a_theorem(implies(implies(X1,X1),X2)),true,is_a_theorem(X2),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_6]),c_0_7]) ).
cnf(c_0_10,plain,
ifeq(is_a_theorem(implies(implies(X1,X2),X3)),true,is_a_theorem(implies(implies(X3,X1),implies(X4,X1))),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_8]),c_0_7]) ).
cnf(c_0_11,plain,
is_a_theorem(implies(implies(implies(X1,X2),X1),implies(X3,X1))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_8]),c_0_7]) ).
cnf(c_0_12,plain,
is_a_theorem(implies(implies(implies(X1,X2),implies(X2,X3)),implies(X4,implies(X2,X3)))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_7]) ).
cnf(c_0_13,plain,
ifeq(is_a_theorem(implies(implies(implies(implies(X1,X2),X3),implies(implies(X3,X1),implies(X4,X1))),X5)),true,is_a_theorem(X5),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_8]),c_0_7]) ).
cnf(c_0_14,plain,
is_a_theorem(implies(implies(implies(X1,implies(X2,X3)),implies(X4,X2)),implies(X5,implies(X4,X2)))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_12]),c_0_7]) ).
cnf(c_0_15,plain,
is_a_theorem(implies(X1,implies(implies(implies(implies(X2,X3),X4),X3),implies(X2,X3)))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_7]) ).
cnf(c_0_16,plain,
is_a_theorem(implies(implies(implies(implies(X1,X2),X3),X2),implies(X1,X2))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_15]),c_0_7]) ).
cnf(c_0_17,plain,
ifeq(is_a_theorem(implies(implies(implies(implies(X1,X2),X1),implies(X3,X1)),X4)),true,is_a_theorem(X4),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_11]),c_0_7]) ).
cnf(c_0_18,plain,
is_a_theorem(implies(implies(implies(X1,X2),implies(implies(X1,X2),X3)),implies(X4,implies(implies(X1,X2),X3)))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_16]),c_0_7]) ).
cnf(c_0_19,plain,
is_a_theorem(implies(X1,implies(implies(implies(X2,X3),X2),X2))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_7]) ).
cnf(c_0_20,plain,
is_a_theorem(implies(implies(implies(X1,X2),X1),X1)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_19]),c_0_7]) ).
cnf(c_0_21,plain,
is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X3,implies(X1,X2)))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_20]),c_0_7]) ).
cnf(c_0_22,plain,
is_a_theorem(implies(X1,implies(X2,X1))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_16]),c_0_7]) ).
cnf(c_0_23,plain,
ifeq(is_a_theorem(implies(X1,implies(X1,X2))),true,is_a_theorem(implies(X3,implies(X1,X2))),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_21]),c_0_7]) ).
cnf(c_0_24,plain,
is_a_theorem(implies(implies(implies(X1,implies(X2,X3)),X2),implies(X4,X2))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_22]),c_0_7]) ).
cnf(c_0_25,plain,
is_a_theorem(implies(X1,implies(implies(X2,implies(X2,X3)),implies(X2,X3)))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_21]),c_0_7]) ).
cnf(c_0_26,plain,
is_a_theorem(implies(X1,implies(implies(implies(X2,implies(X3,X4)),X3),X3))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_7]) ).
cnf(c_0_27,plain,
is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_25]),c_0_7]) ).
cnf(c_0_28,plain,
is_a_theorem(implies(implies(implies(X1,implies(X2,X3)),X2),X2)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_26]),c_0_7]) ).
cnf(c_0_29,plain,
is_a_theorem(implies(implies(implies(X1,implies(X2,X3)),implies(X4,implies(X3,X5))),implies(X6,implies(X4,implies(X3,X5))))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_14]),c_0_7]) ).
cnf(c_0_30,plain,
ifeq(is_a_theorem(implies(X1,implies(X1,X2))),true,is_a_theorem(implies(X1,X2)),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_27]),c_0_7]) ).
cnf(c_0_31,plain,
is_a_theorem(implies(implies(X1,implies(X2,implies(X1,X3))),implies(X4,implies(X2,implies(X1,X3))))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_28]),c_0_7]) ).
cnf(c_0_32,plain,
is_a_theorem(implies(X1,implies(implies(implies(X2,X3),X4),implies(X3,X4)))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_29]),c_0_7]) ).
cnf(c_0_33,plain,
is_a_theorem(implies(implies(X1,implies(X2,implies(X1,X3))),implies(X2,implies(X1,X3)))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_7]) ).
cnf(c_0_34,plain,
is_a_theorem(implies(implies(implies(X1,X2),X3),implies(X2,X3))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_32]),c_0_7]) ).
cnf(c_0_35,plain,
is_a_theorem(implies(implies(X1,X2),implies(implies(implies(X2,X3),X1),X2))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_33]),c_0_7]) ).
cnf(c_0_36,plain,
is_a_theorem(implies(X1,implies(implies(X1,X2),implies(X3,X2)))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_34]),c_0_7]) ).
cnf(c_0_37,plain,
is_a_theorem(implies(implies(implies(implies(X1,X2),X3),implies(implies(X2,X4),X2)),implies(X1,X2))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_35]),c_0_7]) ).
cnf(c_0_38,plain,
is_a_theorem(implies(implies(implies(implies(implies(X1,X2),X3),implies(X4,X3)),X1),implies(X5,X1))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_36]),c_0_7]) ).
cnf(c_0_39,plain,
ifeq(is_a_theorem(implies(implies(implies(X1,X2),X3),implies(implies(X2,X4),X2))),true,is_a_theorem(implies(X1,X2)),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_37]),c_0_7]) ).
cnf(c_0_40,plain,
is_a_theorem(implies(implies(implies(implies(implies(X1,X2),X3),implies(X4,X3)),X1),X1)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_38]),c_0_7]) ).
cnf(c_0_41,plain,
is_a_theorem(implies(implies(implies(implies(implies(implies(X1,X2),X3),implies(X1,X2)),X4),X2),implies(X1,X2))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_7]) ).
cnf(c_0_42,plain,
is_a_theorem(implies(implies(implies(implies(implies(X1,X2),X1),X3),implies(implies(X1,X2),X1)),X1)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_41]),c_0_7]) ).
cnf(c_0_43,plain,
is_a_theorem(implies(implies(X1,implies(implies(implies(X1,X2),X1),X3)),implies(X4,implies(implies(implies(X1,X2),X1),X3)))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_42]),c_0_7]) ).
cnf(c_0_44,plain,
is_a_theorem(implies(implies(implies(X1,implies(implies(implies(X2,X3),X2),X4)),X2),implies(X5,X2))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_43]),c_0_7]) ).
cnf(c_0_45,plain,
is_a_theorem(implies(implies(implies(X1,implies(implies(implies(X2,X3),X2),X4)),X2),X2)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_44]),c_0_7]) ).
cnf(c_0_46,plain,
ifeq(is_a_theorem(implies(X1,X2)),true,is_a_theorem(implies(implies(implies(X2,X3),X1),X2)),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_35]),c_0_7]) ).
cnf(c_0_47,plain,
ifeq(is_a_theorem(implies(implies(implies(implies(X1,implies(implies(implies(X2,X3),X2),X4)),X2),X2),X5)),true,is_a_theorem(X5),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_45]),c_0_7]) ).
cnf(c_0_48,plain,
is_a_theorem(implies(implies(implies(implies(implies(X1,X2),implies(X3,X2)),X4),X1),implies(implies(X1,X2),implies(X3,X2)))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_36]),c_0_7]) ).
cnf(c_0_49,plain,
ifeq(is_a_theorem(implies(implies(X1,implies(implies(X1,X2),implies(X3,X2))),X4)),true,is_a_theorem(X4),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_36]),c_0_7]) ).
cnf(c_0_50,plain,
is_a_theorem(implies(implies(X1,X2),implies(implies(implies(X1,X3),X1),X2))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_7]) ).
cnf(c_0_51,plain,
ifeq(is_a_theorem(implies(implies(implies(implies(X1,X2),implies(X2,X3)),implies(X4,implies(X2,X3))),X5)),true,is_a_theorem(X5),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_12]),c_0_7]) ).
cnf(c_0_52,plain,
is_a_theorem(implies(implies(implies(X1,X2),X1),implies(implies(X1,X3),implies(X4,X3)))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_7]) ).
cnf(c_0_53,plain,
is_a_theorem(implies(X1,implies(implies(implies(X2,X3),implies(X3,X4)),implies(X3,X4)))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_21]),c_0_7]) ).
cnf(c_0_54,plain,
ifeq(is_a_theorem(implies(implies(implies(X1,implies(X1,X2)),implies(X3,implies(X1,X2))),X4)),true,is_a_theorem(X4),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_21]),c_0_7]) ).
cnf(c_0_55,plain,
is_a_theorem(implies(implies(implies(implies(X1,X2),implies(X3,X2)),implies(X1,X4)),implies(X5,implies(X1,X4)))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_52]),c_0_7]) ).
cnf(c_0_56,plain,
is_a_theorem(implies(implies(implies(X1,X2),implies(X2,X3)),implies(X2,X3))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_53]),c_0_7]) ).
cnf(c_0_57,plain,
is_a_theorem(implies(X1,implies(X2,implies(implies(X2,X3),X3)))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_7]) ).
cnf(c_0_58,plain,
ifeq(is_a_theorem(implies(implies(implies(X1,X2),X3),X2)),true,is_a_theorem(implies(X1,X2)),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_16]),c_0_7]) ).
cnf(c_0_59,plain,
is_a_theorem(implies(implies(implies(X1,X2),implies(X3,X1)),implies(X4,implies(X3,X1)))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_56]),c_0_7]) ).
cnf(c_0_60,plain,
ifeq(is_a_theorem(implies(X1,X2)),true,is_a_theorem(implies(implies(implies(X1,X3),X1),X2)),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_50]),c_0_7]) ).
cnf(c_0_61,plain,
is_a_theorem(implies(X1,implies(implies(X1,X2),X2))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_57]),c_0_7]) ).
cnf(c_0_62,plain,
is_a_theorem(implies(X1,implies(X2,implies(X3,X1)))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_7]) ).
cnf(c_0_63,plain,
is_a_theorem(implies(implies(implies(X1,X2),X1),implies(implies(X1,X3),X3))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_7]) ).
cnf(c_0_64,plain,
ifeq(is_a_theorem(implies(implies(X1,implies(X2,implies(X3,X1))),X4)),true,is_a_theorem(X4),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_62]),c_0_7]) ).
cnf(c_0_65,plain,
is_a_theorem(implies(implies(implies(implies(X1,X2),X2),implies(X1,X3)),implies(X4,implies(X1,X3)))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_63]),c_0_7]) ).
cnf(c_0_66,plain,
is_a_theorem(implies(implies(implies(implies(X1,implies(X2,X3)),X4),X3),implies(X1,implies(X2,X3)))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_35]),c_0_7]) ).
cnf(c_0_67,plain,
is_a_theorem(implies(implies(implies(implies(X1,X2),X2),implies(X1,X3)),implies(X1,X3))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_65]),c_0_7]) ).
cnf(c_0_68,plain,
ifeq(is_a_theorem(implies(implies(implies(X1,implies(X2,X3)),X4),X3)),true,is_a_theorem(implies(X1,implies(X2,X3))),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_66]),c_0_7]) ).
cnf(c_0_69,plain,
ifeq(is_a_theorem(implies(implies(implies(X1,X2),X2),implies(X1,X3))),true,is_a_theorem(implies(X1,X3)),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_67]),c_0_7]) ).
cnf(c_0_70,plain,
is_a_theorem(implies(X1,implies(X2,implies(implies(X1,X3),implies(X4,X3))))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_52]),c_0_7]) ).
cnf(c_0_71,plain,
ifeq(is_a_theorem(implies(X1,implies(X2,implies(X1,X3)))),true,is_a_theorem(implies(X2,implies(X1,X3))),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_33]),c_0_7]) ).
cnf(c_0_72,plain,
is_a_theorem(implies(X1,implies(implies(implies(implies(X1,X2),X2),X3),implies(X4,X3)))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_7]) ).
cnf(c_0_73,plain,
ifeq(is_a_theorem(implies(implies(X1,implies(X2,implies(implies(X1,X3),implies(X4,X3)))),X5)),true,is_a_theorem(X5),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_70]),c_0_7]) ).
cnf(c_0_74,plain,
is_a_theorem(implies(implies(implies(implies(X1,X2),implies(X3,X2)),implies(X1,X4)),implies(X1,X4))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_55]),c_0_7]) ).
cnf(c_0_75,plain,
is_a_theorem(implies(X1,implies(X2,implies(implies(X1,X3),X3)))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_63]),c_0_7]) ).
cnf(c_0_76,plain,
is_a_theorem(implies(implies(implies(implies(X1,X2),X3),implies(implies(X4,X1),X2)),implies(X1,X2))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_34]),c_0_7]) ).
cnf(c_0_77,plain,
is_a_theorem(implies(implies(implies(implies(X1,X2),X2),X3),implies(X1,X3))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_7]) ).
cnf(c_0_78,plain,
is_a_theorem(implies(X1,implies(implies(implies(implies(X1,X2),implies(X3,X2)),X4),implies(X5,X4)))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_7]) ).
cnf(c_0_79,plain,
ifeq(is_a_theorem(implies(implies(X1,X2),X3)),true,is_a_theorem(implies(X2,X3)),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_34]),c_0_7]) ).
cnf(c_0_80,plain,
is_a_theorem(implies(implies(X1,implies(implies(implies(X1,X2),X3),implies(X4,X3))),implies(X5,implies(implies(implies(X1,X2),X3),implies(X4,X3))))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_40]),c_0_7]) ).
cnf(c_0_81,plain,
ifeq(is_a_theorem(implies(implies(X1,implies(X2,implies(implies(X1,X3),X3))),X4)),true,is_a_theorem(X4),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_75]),c_0_7]) ).
cnf(c_0_82,plain,
ifeq(is_a_theorem(implies(implies(implies(X1,X2),X3),implies(implies(X4,X1),X2))),true,is_a_theorem(implies(X1,X2)),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_76]),c_0_7]) ).
cnf(c_0_83,plain,
ifeq(is_a_theorem(implies(implies(implies(X1,X2),X2),X3)),true,is_a_theorem(implies(X1,X3)),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_77]),c_0_7]) ).
cnf(c_0_84,plain,
is_a_theorem(implies(implies(implies(implies(X1,X2),implies(X3,X2)),X4),implies(X1,X4))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_78]),c_0_7]) ).
cnf(c_0_85,plain,
is_a_theorem(implies(X1,implies(implies(implies(X2,X1),X3),implies(X4,X3)))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_36]),c_0_7]) ).
cnf(c_0_86,plain,
is_a_theorem(implies(X1,implies(implies(implies(X2,X3),implies(X4,X5)),implies(implies(X2,X5),implies(X4,X5))))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_80]),c_0_7]) ).
cnf(c_0_87,plain,
is_a_theorem(implies(X1,implies(implies(implies(X2,X3),X4),implies(implies(X2,X4),X4)))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_80]),c_0_7]) ).
cnf(c_0_88,plain,
is_a_theorem(implies(X1,implies(implies(implies(X2,X1),X3),X3))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_57]),c_0_7]) ).
cnf(c_0_89,plain,
is_a_theorem(implies(implies(X1,X2),implies(X1,implies(X3,X2)))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_7]) ).
cnf(c_0_90,plain,
ifeq(is_a_theorem(implies(implies(X1,implies(implies(implies(X2,X1),X3),implies(X4,X3))),X5)),true,is_a_theorem(X5),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_85]),c_0_7]) ).
cnf(c_0_91,plain,
is_a_theorem(implies(implies(implies(X1,X2),implies(X3,X4)),implies(implies(X1,X4),implies(X3,X4)))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_86]),c_0_7]) ).
cnf(c_0_92,plain,
is_a_theorem(implies(implies(implies(X1,X2),X3),implies(implies(X1,X3),X3))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_87]),c_0_7]) ).
cnf(c_0_93,plain,
ifeq(is_a_theorem(implies(implies(X1,implies(implies(implies(X2,X1),X3),X3)),X4)),true,is_a_theorem(X4),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_88]),c_0_7]) ).
cnf(c_0_94,plain,
is_a_theorem(implies(implies(implies(implies(implies(X1,X2),X2),X3),X1),implies(implies(X1,X2),X2))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_61]),c_0_7]) ).
cnf(c_0_95,plain,
ifeq(is_a_theorem(implies(implies(implies(X1,X2),implies(X1,implies(X3,X2))),X4)),true,is_a_theorem(X4),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_89]),c_0_7]) ).
cnf(c_0_96,plain,
is_a_theorem(implies(implies(X1,implies(X2,X3)),implies(implies(implies(X4,implies(X1,X5)),X3),implies(X2,X3)))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_7]) ).
cnf(c_0_97,plain,
is_a_theorem(implies(implies(implies(X1,X2),implies(implies(implies(X2,X3),X4),implies(X5,X4))),implies(X6,implies(implies(implies(X2,X3),X4),implies(X5,X4))))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_38]),c_0_7]) ).
cnf(c_0_98,plain,
ifeq(is_a_theorem(implies(implies(X1,X2),X3)),true,is_a_theorem(implies(implies(X1,X3),X3)),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_92]),c_0_7]) ).
cnf(c_0_99,plain,
is_a_theorem(implies(implies(X1,X2),implies(implies(implies(X3,implies(X1,X4)),X2),X2))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_91]),c_0_7]) ).
cnf(c_0_100,plain,
ifeq(is_a_theorem(implies(implies(implies(implies(X1,X2),X2),X3),X1)),true,is_a_theorem(implies(implies(X1,X2),X2)),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_94]),c_0_7]) ).
cnf(c_0_101,plain,
is_a_theorem(implies(implies(implies(X1,implies(implies(X2,X3),X4)),implies(X5,X3)),implies(X2,implies(X5,X3)))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_7]) ).
cnf(c_0_102,plain,
is_a_theorem(implies(X1,implies(implies(implies(X2,X3),X4),implies(implies(implies(X5,X2),X4),X4)))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_97]),c_0_7]) ).
cnf(c_0_103,plain,
is_a_theorem(implies(implies(implies(X1,X2),implies(implies(X1,X3),X3)),implies(implies(X1,X3),X3))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_63]),c_0_7]) ).
cnf(c_0_104,plain,
is_a_theorem(implies(X1,implies(implies(implies(X2,implies(implies(X1,X3),X4)),X3),X3))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_99]),c_0_7]) ).
cnf(c_0_105,plain,
is_a_theorem(implies(implies(implies(X1,implies(X2,implies(X3,X4))),X3),implies(X5,X3))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_62]),c_0_7]) ).
cnf(c_0_106,plain,
is_a_theorem(implies(implies(implies(X1,implies(X2,X3)),implies(implies(X1,X3),X4)),implies(implies(X1,X3),X4))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_7]) ).
cnf(c_0_107,plain,
is_a_theorem(implies(implies(implies(X1,X2),X3),implies(implies(implies(X4,X1),X3),X3))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_102]),c_0_7]) ).
cnf(c_0_108,plain,
ifeq(is_a_theorem(implies(implies(X1,X2),implies(implies(X1,X3),X3))),true,is_a_theorem(implies(implies(X1,X3),X3)),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_103]),c_0_7]) ).
cnf(c_0_109,plain,
is_a_theorem(implies(implies(implies(X1,X2),X1),implies(implies(implies(X3,implies(implies(X1,X4),X5)),X4),X4))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_104]),c_0_7]) ).
cnf(c_0_110,plain,
is_a_theorem(implies(X1,implies(implies(implies(X2,implies(X3,implies(X4,X5))),X4),X4))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_105]),c_0_7]) ).
cnf(c_0_111,plain,
is_a_theorem(implies(implies(X1,X2),implies(implies(implies(X1,implies(X3,X2)),X4),implies(X5,X4)))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_106]),c_0_7]) ).
cnf(c_0_112,plain,
ifeq(is_a_theorem(implies(implies(X1,X2),X3)),true,is_a_theorem(implies(implies(implies(X4,X1),X3),X3)),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_107]),c_0_7]) ).
cnf(c_0_113,plain,
is_a_theorem(implies(implies(implies(X1,implies(implies(X1,X2),X3)),X2),X2)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_109]),c_0_7]) ).
cnf(c_0_114,plain,
is_a_theorem(implies(implies(implies(X1,implies(X2,implies(X3,X4))),X3),X3)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_110]),c_0_7]) ).
cnf(c_0_115,plain,
is_a_theorem(implies(implies(implies(X1,implies(X2,X3)),X4),implies(implies(X1,X3),X4))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_111]),c_0_7]) ).
cnf(c_0_116,plain,
is_a_theorem(implies(implies(implies(X1,implies(X2,implies(implies(X2,X3),X4))),X3),X3)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_113]),c_0_7]) ).
cnf(c_0_117,plain,
is_a_theorem(implies(implies(X1,implies(X2,implies(X3,implies(X1,X4)))),implies(X5,implies(X2,implies(X3,implies(X1,X4)))))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_114]),c_0_7]) ).
cnf(c_0_118,plain,
ifeq(is_a_theorem(implies(implies(X1,implies(X2,X3)),X4)),true,is_a_theorem(implies(implies(X1,X3),X4)),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_115]),c_0_7]) ).
cnf(c_0_119,plain,
is_a_theorem(implies(implies(X1,implies(X2,implies(implies(X2,X1),X3))),implies(X2,implies(implies(X2,X1),X3)))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_116]),c_0_7]) ).
cnf(c_0_120,plain,
is_a_theorem(implies(implies(X1,implies(X2,implies(X3,implies(X1,X4)))),implies(X2,implies(X3,implies(X1,X4))))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_117]),c_0_7]) ).
cnf(c_0_121,plain,
is_a_theorem(implies(implies(X1,implies(implies(X2,X1),X3)),implies(X2,implies(implies(X2,X1),X3)))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_119]),c_0_7]) ).
cnf(c_0_122,plain,
ifeq(is_a_theorem(implies(X1,implies(X2,implies(X3,implies(X1,X4))))),true,is_a_theorem(implies(X2,implies(X3,implies(X1,X4)))),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_120]),c_0_7]) ).
cnf(c_0_123,plain,
is_a_theorem(implies(X1,implies(implies(X1,X2),implies(implies(X2,X3),implies(X4,X3))))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_121]),c_0_7]) ).
cnf(c_0_124,negated_conjecture,
is_a_theorem(implies(implies(a,b),implies(implies(b,c),implies(a,c)))) != true,
prove_ic_4 ).
cnf(c_0_125,plain,
is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3)))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_123]),c_0_7]) ).
cnf(c_0_126,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_124,c_0_125])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL084-10 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34 % Computer : n028.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Aug 25 06:34:05 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.57 start to proof: theBenchmark
% 112.44/113.17 % Version : CSE_E---1.5
% 112.44/113.17 % Problem : theBenchmark.p
% 112.44/113.17 % Proof found
% 112.44/113.17 % SZS status Theorem for theBenchmark.p
% 112.44/113.17 % SZS output start Proof
% See solution above
% 112.44/113.18 % Total time : 111.904000 s
% 112.44/113.18 % SZS output end Proof
% 112.44/113.18 % Total time : 111.911000 s
%------------------------------------------------------------------------------