TSTP Solution File: GRP654+3 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP654+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n016.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 00:22:46 EDT 2023
% Result : Theorem 21.07s 21.16s
% Output : CNFRefutation 21.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 11
% Syntax : Number of formulae : 134 ( 125 unt; 5 typ; 0 def)
% Number of atoms : 133 ( 132 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 6 ~; 2 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 6 ( 3 >; 3 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 310 ( 0 sgn; 26 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
ld: ( $i * $i ) > $i ).
tff(decl_23,type,
mult: ( $i * $i ) > $i ).
tff(decl_24,type,
rd: ( $i * $i ) > $i ).
tff(decl_25,type,
esk1_0: $i ).
tff(decl_26,type,
esk2_0: $i ).
fof(f04,axiom,
! [X1,X2] : rd(mult(X2,X1),X1) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f04) ).
fof(f05,axiom,
! [X3,X1,X2] : mult(X2,mult(X1,mult(X2,X3))) = mult(mult(mult(X2,X1),X2),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f05) ).
fof(f03,axiom,
! [X1,X2] : mult(rd(X2,X1),X1) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f03) ).
fof(f01,axiom,
! [X1,X2] : mult(X2,ld(X2,X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f01) ).
fof(f02,axiom,
! [X1,X2] : ld(X2,mult(X2,X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f02) ).
fof(goals,conjecture,
! [X4,X5] :
( mult(X4,ld(X5,X5)) = X4
& mult(ld(X5,X5),X4) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(c_0_6,plain,
! [X12,X13] : rd(mult(X13,X12),X12) = X13,
inference(variable_rename,[status(thm)],[f04]) ).
fof(c_0_7,plain,
! [X14,X15,X16] : mult(X16,mult(X15,mult(X16,X14))) = mult(mult(mult(X16,X15),X16),X14),
inference(variable_rename,[status(thm)],[f05]) ).
cnf(c_0_8,plain,
rd(mult(X1,X2),X2) = X1,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,plain,
mult(X1,mult(X2,mult(X1,X3))) = mult(mult(mult(X1,X2),X1),X3),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_10,plain,
! [X10,X11] : mult(rd(X11,X10),X10) = X11,
inference(variable_rename,[status(thm)],[f03]) ).
cnf(c_0_11,plain,
rd(mult(X1,mult(X2,mult(X1,X3))),X3) = mult(mult(X1,X2),X1),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_12,plain,
mult(rd(X1,X2),X2) = X1,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_13,plain,
mult(mult(X1,rd(X2,mult(X1,X3))),X1) = rd(mult(X1,X2),X3),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
fof(c_0_14,plain,
! [X6,X7] : mult(X7,ld(X7,X6)) = X6,
inference(variable_rename,[status(thm)],[f01]) ).
fof(c_0_15,plain,
! [X8,X9] : ld(X9,mult(X9,X8)) = X8,
inference(variable_rename,[status(thm)],[f02]) ).
cnf(c_0_16,plain,
rd(rd(mult(X1,X2),X3),X1) = mult(X1,rd(X2,mult(X1,X3))),
inference(spm,[status(thm)],[c_0_8,c_0_13]) ).
cnf(c_0_17,plain,
mult(X1,ld(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_18,plain,
ld(X1,mult(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_19,plain,
mult(X1,rd(X2,mult(X1,X2))) = rd(X1,X1),
inference(spm,[status(thm)],[c_0_16,c_0_8]) ).
cnf(c_0_20,plain,
rd(mult(X1,mult(X2,X3)),ld(X1,X3)) = mult(mult(X1,X2),X1),
inference(spm,[status(thm)],[c_0_11,c_0_17]) ).
cnf(c_0_21,plain,
ld(rd(X1,X2),X1) = X2,
inference(spm,[status(thm)],[c_0_18,c_0_12]) ).
cnf(c_0_22,plain,
ld(X1,rd(X1,X1)) = rd(X2,mult(X1,X2)),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,plain,
rd(mult(X1,X2),ld(X1,X3)) = mult(mult(X1,rd(X2,X3)),X1),
inference(spm,[status(thm)],[c_0_20,c_0_12]) ).
cnf(c_0_24,plain,
ld(ld(X1,rd(X1,X1)),X2) = mult(X1,X2),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,plain,
mult(mult(X1,rd(ld(X1,X2),X2)),X1) = X1,
inference(spm,[status(thm)],[c_0_8,c_0_23]) ).
cnf(c_0_26,plain,
ld(rd(X1,mult(X2,X1)),X3) = mult(X2,X3),
inference(spm,[status(thm)],[c_0_24,c_0_22]) ).
cnf(c_0_27,plain,
mult(X1,rd(ld(X1,X2),mult(X1,X3))) = rd(rd(X2,X3),X1),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_28,plain,
mult(X1,rd(ld(X1,X2),X2)) = rd(X1,X1),
inference(spm,[status(thm)],[c_0_8,c_0_25]) ).
cnf(c_0_29,plain,
ld(rd(X1,X2),X3) = mult(rd(X2,X1),X3),
inference(spm,[status(thm)],[c_0_26,c_0_12]) ).
cnf(c_0_30,plain,
rd(X1,ld(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_8,c_0_17]) ).
cnf(c_0_31,plain,
ld(X1,rd(rd(X2,X3),X1)) = rd(ld(X1,X2),mult(X1,X3)),
inference(spm,[status(thm)],[c_0_18,c_0_27]) ).
cnf(c_0_32,plain,
rd(rd(X1,X1),rd(ld(X1,X2),X2)) = X1,
inference(spm,[status(thm)],[c_0_8,c_0_28]) ).
cnf(c_0_33,plain,
mult(rd(ld(X1,X2),X2),X3) = ld(X1,X3),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_34,plain,
mult(mult(X1,rd(X1,X1)),X1) = mult(X1,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_29]),c_0_30]),c_0_29]),c_0_30]),c_0_33]),c_0_23]) ).
cnf(c_0_35,plain,
mult(X1,mult(ld(X1,X2),mult(X1,X3))) = mult(mult(X2,X1),X3),
inference(spm,[status(thm)],[c_0_9,c_0_17]) ).
cnf(c_0_36,plain,
mult(X1,rd(X1,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_34]),c_0_8]) ).
cnf(c_0_37,plain,
ld(X1,mult(mult(X2,X1),X3)) = mult(ld(X1,X2),mult(X1,X3)),
inference(spm,[status(thm)],[c_0_18,c_0_35]) ).
cnf(c_0_38,plain,
mult(mult(X1,X2),ld(X2,X3)) = mult(X2,mult(ld(X2,X1),X3)),
inference(spm,[status(thm)],[c_0_35,c_0_17]) ).
cnf(c_0_39,plain,
rd(X1,X1) = ld(X1,X1),
inference(spm,[status(thm)],[c_0_18,c_0_36]) ).
cnf(c_0_40,plain,
mult(ld(X1,X2),mult(X1,ld(mult(X2,X1),X3))) = ld(X1,X3),
inference(spm,[status(thm)],[c_0_37,c_0_17]) ).
cnf(c_0_41,plain,
ld(mult(X1,X2),mult(X2,mult(ld(X2,X1),X3))) = ld(X2,X3),
inference(spm,[status(thm)],[c_0_18,c_0_38]) ).
cnf(c_0_42,plain,
mult(ld(ld(X1,X2),X1),mult(ld(X1,X2),X3)) = ld(ld(X1,X2),mult(X2,X3)),
inference(spm,[status(thm)],[c_0_37,c_0_17]) ).
cnf(c_0_43,plain,
ld(ld(X1,X1),X2) = mult(ld(X1,X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_39]),c_0_39]) ).
cnf(c_0_44,plain,
mult(ld(X1,X1),X1) = X1,
inference(spm,[status(thm)],[c_0_12,c_0_39]) ).
cnf(c_0_45,plain,
ld(ld(X1,X2),ld(X1,X3)) = mult(X1,ld(mult(X2,X1),X3)),
inference(spm,[status(thm)],[c_0_18,c_0_40]) ).
cnf(c_0_46,plain,
ld(X1,ld(ld(X1,X2),X3)) = ld(mult(X2,X1),mult(X1,X3)),
inference(spm,[status(thm)],[c_0_41,c_0_17]) ).
cnf(c_0_47,plain,
mult(ld(X1,X1),mult(X1,X2)) = mult(X1,mult(ld(X1,X1),X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44]),c_0_43]) ).
cnf(c_0_48,plain,
mult(ld(X1,X1),ld(X1,X2)) = mult(X1,ld(mult(X1,X1),X2)),
inference(spm,[status(thm)],[c_0_45,c_0_43]) ).
cnf(c_0_49,plain,
ld(X1,mult(ld(X1,X1),X2)) = ld(mult(X1,X1),mult(X1,X2)),
inference(spm,[status(thm)],[c_0_46,c_0_43]) ).
cnf(c_0_50,plain,
ld(mult(X1,X1),mult(X1,X1)) = ld(X1,X1),
inference(spm,[status(thm)],[c_0_41,c_0_44]) ).
cnf(c_0_51,plain,
ld(mult(X1,X1),mult(X1,X2)) = mult(X1,ld(mult(X1,X1),X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_33]),c_0_29]),c_0_30]),c_0_28]),c_0_39]),c_0_48]),c_0_29]),c_0_30]),c_0_28]),c_0_39]),c_0_33]),c_0_49]) ).
cnf(c_0_52,plain,
rd(mult(rd(X1,X2),mult(X3,X1)),X2) = mult(mult(rd(X1,X2),X3),rd(X1,X2)),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_53,plain,
mult(rd(X1,mult(X2,X1)),X3) = ld(X2,X3),
inference(spm,[status(thm)],[c_0_29,c_0_8]) ).
cnf(c_0_54,plain,
mult(X1,ld(mult(X1,X1),X1)) = ld(X1,X1),
inference(rw,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_55,plain,
rd(ld(X1,mult(X2,X3)),mult(X1,X3)) = mult(ld(X1,X2),rd(X3,mult(X1,X3))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_53]) ).
cnf(c_0_56,plain,
ld(X1,ld(X1,X1)) = rd(X2,mult(X1,X2)),
inference(rw,[status(thm)],[c_0_22,c_0_39]) ).
cnf(c_0_57,plain,
ld(X1,ld(X1,X1)) = ld(mult(X1,X1),X1),
inference(spm,[status(thm)],[c_0_18,c_0_54]) ).
cnf(c_0_58,plain,
mult(ld(X1,X2),rd(X3,mult(X1,X3))) = ld(X1,rd(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_8]),c_0_55]) ).
cnf(c_0_59,plain,
ld(mult(X1,X1),X1) = rd(X2,mult(X1,X2)),
inference(rw,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_60,plain,
mult(ld(X1,X2),ld(mult(X1,X1),X1)) = ld(X1,rd(X2,X1)),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_61,plain,
mult(X1,ld(mult(X2,X1),rd(X2,X1))) = ld(mult(X1,X1),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_60]),c_0_45]) ).
cnf(c_0_62,plain,
rd(X1,mult(rd(X2,X3),X1)) = rd(X3,X2),
inference(spm,[status(thm)],[c_0_30,c_0_29]) ).
cnf(c_0_63,plain,
mult(mult(X1,X2),ld(mult(X3,X2),rd(X3,X2))) = rd(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_61]),c_0_60]),c_0_17]) ).
cnf(c_0_64,plain,
rd(X1,mult(ld(X2,X2),X1)) = ld(X2,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_39]),c_0_39]) ).
cnf(c_0_65,plain,
mult(X1,ld(mult(X2,X3),rd(X2,X3))) = rd(rd(X1,X3),X3),
inference(spm,[status(thm)],[c_0_63,c_0_12]) ).
cnf(c_0_66,plain,
mult(X1,ld(mult(mult(X2,X1),X1),X2)) = ld(mult(X1,X1),X1),
inference(spm,[status(thm)],[c_0_61,c_0_8]) ).
cnf(c_0_67,plain,
mult(mult(X1,rd(ld(mult(X1,X1),X2),X2)),X1) = ld(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_40]),c_0_23]) ).
cnf(c_0_68,plain,
rd(rd(X1,ld(X2,X3)),ld(X2,X3)) = mult(X1,ld(mult(X3,ld(X2,X3)),X2)),
inference(spm,[status(thm)],[c_0_65,c_0_30]) ).
cnf(c_0_69,plain,
mult(X1,rd(ld(mult(X1,X1),X2),X2)) = ld(mult(X1,X1),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_44]),c_0_18]) ).
cnf(c_0_70,plain,
mult(X1,ld(mult(X1,ld(X2,X1)),X2)) = rd(X2,ld(X2,X1)),
inference(spm,[status(thm)],[c_0_68,c_0_30]) ).
cnf(c_0_71,plain,
mult(ld(X1,rd(X2,X1)),mult(X1,X3)) = ld(X1,mult(X2,X3)),
inference(spm,[status(thm)],[c_0_37,c_0_12]) ).
cnf(c_0_72,plain,
mult(mult(X1,X2),rd(ld(mult(X2,X2),X3),X3)) = rd(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_69]),c_0_60]),c_0_17]) ).
cnf(c_0_73,plain,
ld(X1,rd(X2,ld(X2,X1))) = ld(mult(X1,ld(X2,X1)),X2),
inference(spm,[status(thm)],[c_0_18,c_0_70]) ).
cnf(c_0_74,plain,
mult(ld(X1,rd(X2,X1)),X3) = ld(X1,mult(X2,ld(X1,X3))),
inference(spm,[status(thm)],[c_0_71,c_0_17]) ).
cnf(c_0_75,plain,
ld(ld(X1,rd(X2,X1)),X3) = mult(X1,ld(X2,mult(X1,X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_71]),c_0_23]),c_0_9]),c_0_53]) ).
cnf(c_0_76,plain,
ld(mult(mult(X1,rd(X2,X3)),X1),X4) = mult(rd(ld(X1,X3),mult(X1,X2)),X4),
inference(spm,[status(thm)],[c_0_29,c_0_23]) ).
cnf(c_0_77,plain,
mult(X1,rd(ld(mult(X2,X2),X3),X3)) = rd(rd(X1,X2),X2),
inference(spm,[status(thm)],[c_0_72,c_0_12]) ).
cnf(c_0_78,plain,
rd(ld(X1,X2),mult(X1,ld(X3,X2))) = ld(X1,rd(X3,X1)),
inference(spm,[status(thm)],[c_0_31,c_0_30]) ).
cnf(c_0_79,plain,
ld(mult(X1,X2),rd(X1,X2)) = ld(mult(mult(X1,X2),X2),X1),
inference(spm,[status(thm)],[c_0_73,c_0_18]) ).
cnf(c_0_80,plain,
mult(mult(X1,rd(ld(X1,X2),X3)),X1) = rd(X2,ld(X1,X3)),
inference(spm,[status(thm)],[c_0_23,c_0_17]) ).
cnf(c_0_81,plain,
mult(mult(X1,rd(mult(ld(X1,X2),mult(X1,X3)),X4)),X1) = rd(mult(mult(X2,X1),X3),ld(X1,X4)),
inference(spm,[status(thm)],[c_0_23,c_0_35]) ).
cnf(c_0_82,plain,
mult(mult(rd(X1,X2),rd(X3,mult(X4,X3))),rd(X1,X2)) = rd(mult(rd(X1,X2),ld(X4,X1)),X2),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_83,plain,
mult(mult(rd(X1,X2),X3),mult(rd(X2,X1),X4)) = mult(rd(X1,X2),mult(mult(X3,rd(X2,X1)),X4)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_29]),c_0_29]) ).
cnf(c_0_84,plain,
rd(X1,mult(rd(X2,X3),mult(X4,mult(rd(X2,X3),X1)))) = rd(X3,mult(rd(X2,X3),mult(X4,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_52]),c_0_9]) ).
cnf(c_0_85,plain,
mult(ld(X1,ld(X1,X1)),X2) = ld(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_39]),c_0_17]) ).
cnf(c_0_86,plain,
mult(X1,ld(mult(X2,X1),mult(X1,X3))) = ld(ld(X1,X2),X3),
inference(spm,[status(thm)],[c_0_75,c_0_8]) ).
cnf(c_0_87,plain,
ld(mult(rd(rd(X1,X2),X2),X1),X3) = ld(X1,mult(mult(X2,X2),ld(X1,X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_78]),c_0_74]) ).
cnf(c_0_88,plain,
ld(X1,rd(rd(X1,X2),X2)) = ld(mult(mult(X1,X2),X2),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_12]),c_0_79]) ).
cnf(c_0_89,plain,
mult(mult(X1,mult(X1,ld(mult(X2,X1),X2))),X1) = rd(X2,ld(X1,ld(X1,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_39]),c_0_45]) ).
cnf(c_0_90,plain,
mult(rd(X1,X2),mult(rd(X2,X1),X3)) = X3,
inference(spm,[status(thm)],[c_0_18,c_0_29]) ).
cnf(c_0_91,plain,
rd(X1,mult(X2,X1)) = rd(X3,mult(X2,X3)),
inference(spm,[status(thm)],[c_0_22,c_0_22]) ).
cnf(c_0_92,plain,
rd(mult(rd(X1,X2),ld(X3,X1)),X2) = rd(X1,mult(rd(X2,X1),mult(X3,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_29]),c_0_83]),c_0_29]),c_0_84]) ).
cnf(c_0_93,plain,
mult(ld(mult(X1,X1),X1),X2) = ld(X1,X2),
inference(rw,[status(thm)],[c_0_85,c_0_57]) ).
cnf(c_0_94,plain,
rd(X1,mult(X2,X1)) = rd(ld(X2,X3),X3),
inference(spm,[status(thm)],[c_0_62,c_0_30]) ).
cnf(c_0_95,plain,
ld(ld(mult(mult(X1,X2),X2),X1),X3) = mult(mult(X2,X2),X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_18]),c_0_17]),c_0_88]) ).
cnf(c_0_96,plain,
mult(ld(mult(X1,ld(X2,X2)),X1),ld(X2,X2)) = ld(X1,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_39]),c_0_39]),c_0_39]),c_0_29]),c_0_39]),c_0_18]),c_0_39]) ).
cnf(c_0_97,plain,
rd(ld(X1,rd(mult(X2,X3),X4)),mult(X1,X2)) = ld(X1,rd(mult(X2,rd(X3,mult(X2,X4))),X1)),
inference(spm,[status(thm)],[c_0_31,c_0_16]) ).
cnf(c_0_98,plain,
rd(mult(X1,X2),mult(X1,mult(ld(X1,X1),X2))) = ld(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_47]),c_0_64]) ).
cnf(c_0_99,plain,
rd(ld(X1,ld(X2,X3)),mult(X1,X3)) = rd(X3,mult(X1,mult(X2,mult(X1,X3)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_59]),c_0_93]),c_0_8]) ).
cnf(c_0_100,plain,
mult(X1,mult(X1,mult(ld(X1,X1),X2))) = mult(mult(X1,X1),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_47]),c_0_43]),c_0_44]),c_0_43]),c_0_47]),c_0_35]) ).
cnf(c_0_101,plain,
mult(X1,rd(X2,mult(mult(X1,X1),X2))) = ld(mult(X1,X1),X1),
inference(spm,[status(thm)],[c_0_69,c_0_18]) ).
cnf(c_0_102,plain,
rd(X1,mult(ld(mult(mult(X2,X3),X3),X2),X1)) = mult(X3,X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_8]) ).
cnf(c_0_103,plain,
rd(ld(X1,X1),ld(X2,X2)) = ld(mult(X1,ld(X2,X2)),X1),
inference(spm,[status(thm)],[c_0_8,c_0_96]) ).
cnf(c_0_104,plain,
ld(X1,rd(ld(mult(X2,X2),X2),X1)) = rd(X2,mult(X1,mult(X2,mult(X1,X2)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_99]),c_0_100]),c_0_101]) ).
cnf(c_0_105,plain,
mult(ld(mult(mult(X1,X2),X2),X1),X3) = ld(mult(X2,X2),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_102]),c_0_8]) ).
cnf(c_0_106,plain,
mult(X1,mult(X2,mult(X1,ld(mult(mult(X1,X2),X1),X3)))) = X3,
inference(spm,[status(thm)],[c_0_17,c_0_9]) ).
cnf(c_0_107,plain,
mult(X1,ld(mult(mult(X1,X2),X1),X3)) = ld(X2,ld(X1,X3)),
inference(spm,[status(thm)],[c_0_45,c_0_18]) ).
cnf(c_0_108,plain,
mult(ld(mult(X1,X2),mult(X2,X3)),mult(X2,ld(mult(ld(ld(X2,X1),X3),X2),X4))) = ld(X2,X4),
inference(spm,[status(thm)],[c_0_40,c_0_46]) ).
cnf(c_0_109,plain,
ld(mult(ld(X1,X1),ld(X2,X2)),ld(X1,X1)) = ld(mult(X1,ld(X2,X2)),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_43]),c_0_48]),c_0_54]),c_0_103]) ).
cnf(c_0_110,plain,
mult(ld(X1,X1),mult(ld(X1,X1),X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_39]),c_0_39]) ).
cnf(c_0_111,plain,
ld(mult(X1,ld(X2,X2)),mult(ld(X2,X2),X3)) = mult(ld(X2,X2),ld(mult(ld(X2,X2),X1),X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_43]),c_0_43]) ).
cnf(c_0_112,plain,
ld(mult(ld(X1,X1),X2),mult(ld(X1,X1),X3)) = mult(ld(X1,X1),ld(mult(X2,ld(X1,X1)),X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_43]),c_0_43]) ).
cnf(c_0_113,plain,
mult(X1,rd(X2,mult(X1,mult(X2,mult(X1,X2))))) = rd(ld(mult(X2,X2),X2),X1),
inference(spm,[status(thm)],[c_0_17,c_0_104]) ).
cnf(c_0_114,plain,
ld(mult(ld(X1,X2),ld(X1,X2)),X3) = mult(ld(mult(X2,ld(X1,X2)),X1),X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_107]),c_0_17]),c_0_107]),c_0_17]),c_0_107]),c_0_17]) ).
fof(c_0_115,negated_conjecture,
~ ! [X4,X5] :
( mult(X4,ld(X5,X5)) = X4
& mult(ld(X5,X5),X4) = X4 ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_116,plain,
ld(ld(X1,mult(mult(X1,X2),X1)),X2) = ld(mult(X1,X1),X1),
inference(spm,[status(thm)],[c_0_86,c_0_66]) ).
cnf(c_0_117,plain,
mult(ld(mult(X1,ld(X2,X2)),X1),ld(X1,X1)) = ld(mult(X1,ld(X2,X2)),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_109]),c_0_43]),c_0_110]),c_0_43]),c_0_43]),c_0_111]),c_0_110]),c_0_110]),c_0_43]),c_0_43]),c_0_112]),c_0_18]) ).
cnf(c_0_118,plain,
ld(ld(mult(X1,ld(X2,X2)),X1),X3) = mult(ld(mult(X2,ld(X1,X1)),X2),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_96]),c_0_103]) ).
cnf(c_0_119,plain,
mult(ld(mult(X1,ld(X2,X1)),X2),ld(X2,X1)) = rd(X1,mult(ld(X2,X1),X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_113]),c_0_114]),c_0_12]),c_0_17]),c_0_18]) ).
cnf(c_0_120,plain,
rd(X1,mult(ld(mult(X2,ld(X3,X3)),X2),X1)) = ld(mult(X3,ld(X2,X2)),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_96]),c_0_103]) ).
fof(c_0_121,negated_conjecture,
( mult(esk1_0,ld(esk2_0,esk2_0)) != esk1_0
| mult(ld(esk2_0,esk2_0),esk1_0) != esk1_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_115])])]) ).
cnf(c_0_122,plain,
ld(mult(X1,ld(X2,X2)),X1) = ld(X1,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_117]),c_0_18]),c_0_118]),c_0_96]),c_0_114]),c_0_119]),c_0_120]) ).
cnf(c_0_123,negated_conjecture,
( mult(esk1_0,ld(esk2_0,esk2_0)) != esk1_0
| mult(ld(esk2_0,esk2_0),esk1_0) != esk1_0 ),
inference(split_conjunct,[status(thm)],[c_0_121]) ).
cnf(c_0_124,plain,
mult(X1,ld(X2,X2)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_122]),c_0_30]) ).
cnf(c_0_125,plain,
mult(mult(X1,ld(mult(X2,X1),X2)),ld(X1,X2)) = ld(X1,X2),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_126,negated_conjecture,
mult(ld(esk2_0,esk2_0),esk1_0) != esk1_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_123,c_0_124])]) ).
cnf(c_0_127,plain,
mult(ld(X1,X1),X2) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_124]),c_0_124]),c_0_43]),c_0_110]),c_0_43]) ).
cnf(c_0_128,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_126,c_0_127])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP654+3 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35 % Computer : n016.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 29 01:05:15 EDT 2023
% 0.20/0.35 % CPUTime :
% 0.64/0.67 start to proof: theBenchmark
% 21.07/21.16 % Version : CSE_E---1.5
% 21.07/21.16 % Problem : theBenchmark.p
% 21.07/21.16 % Proof found
% 21.07/21.16 % SZS status Theorem for theBenchmark.p
% 21.07/21.16 % SZS output start Proof
% See solution above
% 21.07/21.16 % Total time : 20.411000 s
% 21.07/21.16 % SZS output end Proof
% 21.07/21.16 % Total time : 20.414000 s
%------------------------------------------------------------------------------