TSTP Solution File: GRP667+1 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP667+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n002.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 00:22:56 EDT 2023
% Result : Theorem 4.66s 4.77s
% Output : CNFRefutation 4.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 20
% Syntax : Number of formulae : 131 ( 115 unt; 8 typ; 0 def)
% Number of atoms : 131 ( 130 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 17 ( 9 ~; 6 |; 0 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 7 ( 4 >; 3 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 228 ( 0 sgn; 44 !; 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,
unit: $i ).
tff(decl_26,type,
f: $i > $i ).
tff(decl_27,type,
a: $i ).
tff(decl_28,type,
b: $i ).
tff(decl_29,type,
c: $i ).
fof(f04,axiom,
! [X1,X2] : rd(mult(X2,X1),X1) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f04) ).
fof(f08,axiom,
! [X1,X2] : mult(mult(X2,X1),X2) = mult(X2,mult(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f08) ).
fof(f03,axiom,
! [X1,X2] : mult(rd(X2,X1),X1) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f03) ).
fof(f06,axiom,
! [X2] : mult(unit,X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f06) ).
fof(f05,axiom,
! [X2] : mult(X2,unit) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f05) ).
fof(f07,axiom,
! [X3,X1,X2] : mult(mult(X2,X1),mult(mult(X3,X1),X3)) = mult(mult(X2,mult(mult(X1,X3),X1)),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f07) ).
fof(f02,axiom,
! [X1,X2] : ld(X2,mult(X2,X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f02) ).
fof(f09,axiom,
! [X2] : mult(f(X2),f(X2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f09) ).
fof(f12,axiom,
! [X10,X11,X12] :
( mult(mult(X10,X11),mult(X12,X10)) = mult(X10,mult(mult(X11,X12),X10))
=> mult(X10,mult(X11,mult(X10,X12))) = mult(mult(mult(X10,X11),X10),X12) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f12) ).
fof(f01,axiom,
! [X1,X2] : mult(X2,ld(X2,X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f01) ).
fof(f10,axiom,
! [X4,X5,X6] :
( mult(X4,mult(X5,mult(X6,X5))) = mult(mult(mult(X4,X5),X6),X5)
=> mult(X5,mult(X4,mult(X5,X6))) = mult(mult(mult(X5,X4),X5),X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f10) ).
fof(goals,conjecture,
mult(a,mult(b,mult(a,c))) = mult(mult(mult(a,b),a),c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(c_0_12,plain,
! [X19,X20] : rd(mult(X20,X19),X19) = X20,
inference(variable_rename,[status(thm)],[f04]) ).
fof(c_0_13,plain,
! [X26,X27] : mult(mult(X27,X26),X27) = mult(X27,mult(X26,X27)),
inference(variable_rename,[status(thm)],[f08]) ).
cnf(c_0_14,plain,
rd(mult(X1,X2),X2) = X1,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_15,plain,
mult(mult(X1,X2),X1) = mult(X1,mult(X2,X1)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_16,plain,
! [X17,X18] : mult(rd(X18,X17),X17) = X18,
inference(variable_rename,[status(thm)],[f03]) ).
fof(c_0_17,plain,
! [X22] : mult(unit,X22) = X22,
inference(variable_rename,[status(thm)],[f06]) ).
cnf(c_0_18,plain,
rd(mult(X1,mult(X2,X1)),X1) = mult(X1,X2),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,plain,
mult(rd(X1,X2),X2) = X1,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_20,plain,
! [X21] : mult(X21,unit) = X21,
inference(variable_rename,[status(thm)],[f05]) ).
cnf(c_0_21,plain,
mult(unit,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_22,plain,
! [X23,X24,X25] : mult(mult(X25,X24),mult(mult(X23,X24),X23)) = mult(mult(X25,mult(mult(X24,X23),X24)),X23),
inference(variable_rename,[status(thm)],[f07]) ).
fof(c_0_23,plain,
! [X15,X16] : ld(X16,mult(X16,X15)) = X15,
inference(variable_rename,[status(thm)],[f02]) ).
cnf(c_0_24,plain,
rd(mult(X1,X2),X1) = mult(X1,rd(X2,X1)),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_25,plain,
mult(X1,unit) = X1,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_26,plain,
rd(X1,X1) = unit,
inference(spm,[status(thm)],[c_0_14,c_0_21]) ).
fof(c_0_27,plain,
! [X28] : mult(f(X28),f(X28)) = X28,
inference(variable_rename,[status(thm)],[f09]) ).
cnf(c_0_28,plain,
mult(mult(X1,X2),mult(mult(X3,X2),X3)) = mult(mult(X1,mult(mult(X2,X3),X2)),X3),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_29,plain,
ld(X1,mult(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_30,plain,
mult(X1,rd(unit,X1)) = unit,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
cnf(c_0_31,plain,
mult(f(X1),f(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_32,plain,
mult(mult(X1,mult(X2,mult(X3,X2))),X3) = mult(mult(X1,X2),mult(X3,mult(X2,X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_15]),c_0_15]) ).
cnf(c_0_33,plain,
rd(unit,X1) = ld(X1,unit),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_34,plain,
mult(f(X1),X1) = mult(X1,f(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_31]),c_0_31]) ).
cnf(c_0_35,plain,
mult(mult(X1,X2),X2) = mult(X1,mult(X2,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_32]),c_0_25]),c_0_21]),c_0_21]) ).
cnf(c_0_36,plain,
mult(ld(X1,unit),X1) = unit,
inference(spm,[status(thm)],[c_0_19,c_0_33]) ).
cnf(c_0_37,plain,
rd(mult(X1,f(X1)),X1) = f(X1),
inference(spm,[status(thm)],[c_0_14,c_0_34]) ).
cnf(c_0_38,plain,
mult(ld(X1,unit),mult(X1,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_21]) ).
cnf(c_0_39,plain,
mult(X1,rd(f(X1),X1)) = f(X1),
inference(rw,[status(thm)],[c_0_37,c_0_24]) ).
fof(c_0_40,plain,
! [X35,X36,X37] :
( mult(mult(X35,X36),mult(X37,X35)) != mult(X35,mult(mult(X36,X37),X35))
| mult(X35,mult(X36,mult(X35,X37))) = mult(mult(mult(X35,X36),X35),X37) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[f12])]) ).
cnf(c_0_41,plain,
rd(X1,mult(X1,X1)) = ld(X1,unit),
inference(spm,[status(thm)],[c_0_14,c_0_38]) ).
cnf(c_0_42,plain,
rd(f(X1),X1) = ld(X1,f(X1)),
inference(spm,[status(thm)],[c_0_29,c_0_39]) ).
fof(c_0_43,plain,
! [X13,X14] : mult(X14,ld(X14,X13)) = X13,
inference(variable_rename,[status(thm)],[f01]) ).
fof(c_0_44,plain,
! [X29,X30,X31] :
( mult(X29,mult(X30,mult(X31,X30))) != mult(mult(mult(X29,X30),X31),X30)
| mult(X30,mult(X29,mult(X30,X31))) = mult(mult(mult(X30,X29),X30),X31) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[f10])]) ).
cnf(c_0_45,plain,
( mult(X1,mult(X2,mult(X1,X3))) = mult(mult(mult(X1,X2),X1),X3)
| mult(mult(X1,X2),mult(X3,X1)) != mult(X1,mult(mult(X2,X3),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_46,plain,
ld(X1,f(X1)) = ld(f(X1),unit),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_31]),c_0_42]) ).
cnf(c_0_47,plain,
mult(X1,ld(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_48,plain,
( mult(X2,mult(X1,mult(X2,X3))) = mult(mult(mult(X2,X1),X2),X3)
| mult(X1,mult(X2,mult(X3,X2))) != mult(mult(mult(X1,X2),X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_49,plain,
( mult(mult(X1,mult(X2,X1)),X3) = mult(X1,mult(X2,mult(X1,X3)))
| mult(mult(X1,X2),mult(X3,X1)) != mult(X1,mult(mult(X2,X3),X1)) ),
inference(rw,[status(thm)],[c_0_45,c_0_15]) ).
cnf(c_0_50,plain,
rd(mult(X1,mult(X2,X2)),X2) = mult(X1,X2),
inference(spm,[status(thm)],[c_0_14,c_0_35]) ).
cnf(c_0_51,plain,
mult(ld(X1,f(X1)),X1) = f(X1),
inference(spm,[status(thm)],[c_0_19,c_0_42]) ).
cnf(c_0_52,plain,
mult(ld(X1,f(X1)),f(X1)) = unit,
inference(spm,[status(thm)],[c_0_36,c_0_46]) ).
cnf(c_0_53,plain,
mult(X1,rd(ld(X1,X2),X1)) = rd(X2,X1),
inference(spm,[status(thm)],[c_0_24,c_0_47]) ).
cnf(c_0_54,plain,
( mult(mult(X1,mult(X2,X1)),X3) = mult(X1,mult(X2,mult(X1,X3)))
| mult(mult(mult(X2,X1),X3),X1) != mult(X2,mult(X1,mult(X3,X1))) ),
inference(rw,[status(thm)],[c_0_48,c_0_15]) ).
cnf(c_0_55,plain,
mult(mult(X1,mult(X2,X2)),X2) = mult(mult(X1,X2),mult(X2,X2)),
inference(spm,[status(thm)],[c_0_35,c_0_35]) ).
cnf(c_0_56,plain,
mult(mult(X1,X1),X2) = mult(X1,mult(X1,X2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_25]),c_0_21]),c_0_21]),c_0_21])]) ).
cnf(c_0_57,plain,
mult(mult(X1,X2),mult(X1,X1)) = mult(X1,mult(X2,mult(X1,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_15]),c_0_15]),c_0_35]) ).
cnf(c_0_58,plain,
rd(mult(X1,X2),f(X2)) = mult(X1,f(X2)),
inference(spm,[status(thm)],[c_0_50,c_0_31]) ).
cnf(c_0_59,plain,
mult(mult(X1,mult(X2,f(X2))),ld(X2,f(X2))) = mult(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_51]),c_0_47]),c_0_52]),c_0_25]) ).
cnf(c_0_60,plain,
mult(ld(mult(X1,X1),unit),X1) = ld(X1,unit),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_36]),c_0_33]) ).
cnf(c_0_61,plain,
rd(ld(X1,X2),X1) = ld(X1,rd(X2,X1)),
inference(spm,[status(thm)],[c_0_29,c_0_53]) ).
cnf(c_0_62,plain,
mult(X1,mult(mult(X2,X1),mult(X1,X1))) = mult(X1,mult(X2,mult(X1,mult(X1,X1)))),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_35]),c_0_35]),c_0_56]),c_0_15])]),c_0_57]) ).
cnf(c_0_63,plain,
mult(mult(X1,f(X2)),X2) = mult(mult(X1,X2),f(X2)),
inference(spm,[status(thm)],[c_0_55,c_0_31]) ).
cnf(c_0_64,plain,
mult(rd(X1,X2),f(X2)) = rd(X1,f(X2)),
inference(spm,[status(thm)],[c_0_58,c_0_19]) ).
cnf(c_0_65,plain,
rd(mult(X1,X2),ld(X2,f(X2))) = mult(X1,mult(X2,f(X2))),
inference(spm,[status(thm)],[c_0_14,c_0_59]) ).
cnf(c_0_66,plain,
rd(X1,ld(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_14,c_0_47]) ).
cnf(c_0_67,plain,
ld(mult(X1,X1),unit) = ld(X1,ld(X1,unit)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_60]),c_0_61]),c_0_33]) ).
cnf(c_0_68,plain,
ld(rd(X1,X2),X1) = X2,
inference(spm,[status(thm)],[c_0_29,c_0_19]) ).
cnf(c_0_69,plain,
mult(rd(X1,mult(X2,X2)),X2) = rd(X1,X2),
inference(spm,[status(thm)],[c_0_50,c_0_19]) ).
cnf(c_0_70,plain,
mult(mult(X1,X2),mult(X2,X2)) = mult(X1,mult(X2,mult(X2,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_62]),c_0_29]) ).
cnf(c_0_71,plain,
mult(rd(X1,f(X2)),X2) = mult(X1,f(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_19]) ).
cnf(c_0_72,plain,
mult(rd(X1,X2),mult(X2,f(X2))) = rd(X1,ld(X2,f(X2))),
inference(spm,[status(thm)],[c_0_65,c_0_19]) ).
cnf(c_0_73,plain,
ld(ld(X1,ld(X1,unit)),unit) = mult(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_33]) ).
cnf(c_0_74,plain,
ld(ld(X1,f(X1)),unit) = f(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_46]),c_0_33]) ).
cnf(c_0_75,plain,
ld(ld(X1,f(X1)),f(X1)) = X1,
inference(spm,[status(thm)],[c_0_68,c_0_42]) ).
cnf(c_0_76,plain,
rd(rd(X1,X2),X2) = rd(X1,mult(X2,X2)),
inference(spm,[status(thm)],[c_0_14,c_0_69]) ).
cnf(c_0_77,plain,
rd(X1,ld(X2,f(X2))) = mult(X1,f(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_70,c_0_64]),c_0_31]),c_0_71]),c_0_31]),c_0_34]),c_0_72]) ).
cnf(c_0_78,plain,
mult(ld(X1,f(X1)),ld(X1,f(X1))) = ld(X1,unit),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_75]) ).
cnf(c_0_79,plain,
rd(mult(X1,mult(X1,X2)),X2) = mult(X1,X1),
inference(spm,[status(thm)],[c_0_14,c_0_56]) ).
cnf(c_0_80,plain,
rd(X1,ld(X2,unit)) = mult(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_77]),c_0_35]),c_0_31]),c_0_78]) ).
cnf(c_0_81,plain,
mult(mult(X1,mult(X2,X1)),X2) = mult(X1,mult(X2,mult(X1,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_21]),c_0_21]) ).
cnf(c_0_82,plain,
mult(rd(X1,X2),mult(X2,rd(X1,X2))) = mult(X1,rd(X1,X2)),
inference(spm,[status(thm)],[c_0_15,c_0_19]) ).
cnf(c_0_83,plain,
rd(mult(X1,X2),ld(X1,X2)) = mult(X1,X1),
inference(spm,[status(thm)],[c_0_79,c_0_47]) ).
cnf(c_0_84,plain,
mult(X1,ld(X2,unit)) = rd(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_68]),c_0_33]) ).
cnf(c_0_85,plain,
mult(mult(X1,rd(X1,X2)),X2) = mult(rd(X1,X2),mult(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_19]) ).
cnf(c_0_86,plain,
ld(mult(X1,X1),mult(X1,X2)) = ld(X1,X2),
inference(spm,[status(thm)],[c_0_68,c_0_83]) ).
cnf(c_0_87,plain,
ld(mult(X1,X2),X1) = ld(X2,unit),
inference(spm,[status(thm)],[c_0_68,c_0_80]) ).
cnf(c_0_88,plain,
mult(rd(X1,X2),mult(X2,X1)) = mult(X1,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_84]),c_0_80]),c_0_85]) ).
cnf(c_0_89,plain,
ld(mult(X1,X1),X2) = ld(X1,ld(X1,X2)),
inference(spm,[status(thm)],[c_0_86,c_0_47]) ).
cnf(c_0_90,plain,
ld(X1,rd(X1,X2)) = ld(X2,unit),
inference(spm,[status(thm)],[c_0_29,c_0_84]) ).
cnf(c_0_91,plain,
ld(ld(X1,X2),unit) = ld(X2,X1),
inference(spm,[status(thm)],[c_0_87,c_0_47]) ).
cnf(c_0_92,plain,
ld(mult(X1,X2),unit) = ld(X2,ld(X1,unit)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_89]),c_0_90]) ).
cnf(c_0_93,plain,
ld(unit,X1) = X1,
inference(spm,[status(thm)],[c_0_29,c_0_21]) ).
cnf(c_0_94,plain,
ld(ld(X1,unit),X2) = mult(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_91]),c_0_93]) ).
cnf(c_0_95,plain,
ld(ld(X1,X2),X3) = mult(ld(X2,X1),X3),
inference(spm,[status(thm)],[c_0_94,c_0_91]) ).
cnf(c_0_96,plain,
mult(ld(X1,unit),X2) = ld(X1,X2),
inference(spm,[status(thm)],[c_0_95,c_0_93]) ).
cnf(c_0_97,plain,
mult(X1,mult(ld(X1,X2),X1)) = mult(X2,X1),
inference(spm,[status(thm)],[c_0_15,c_0_47]) ).
cnf(c_0_98,plain,
rd(ld(X1,X2),X2) = ld(X1,unit),
inference(spm,[status(thm)],[c_0_14,c_0_96]) ).
cnf(c_0_99,plain,
ld(X1,mult(X2,X1)) = mult(ld(X1,X2),X1),
inference(spm,[status(thm)],[c_0_29,c_0_97]) ).
cnf(c_0_100,plain,
mult(f(X1),mult(f(X1),X2)) = mult(X1,X2),
inference(spm,[status(thm)],[c_0_56,c_0_31]) ).
cnf(c_0_101,plain,
ld(rd(X1,X2),unit) = rd(X2,X1),
inference(spm,[status(thm)],[c_0_98,c_0_68]) ).
cnf(c_0_102,plain,
mult(ld(X1,rd(X2,X1)),X1) = ld(X1,X2),
inference(spm,[status(thm)],[c_0_99,c_0_19]) ).
cnf(c_0_103,plain,
mult(f(X1),rd(f(X1),X2)) = rd(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_84]),c_0_84]) ).
cnf(c_0_104,plain,
ld(rd(X1,X2),X3) = mult(rd(X2,X1),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_101]),c_0_93]) ).
cnf(c_0_105,plain,
ld(mult(X1,f(X2)),mult(X1,X2)) = f(X2),
inference(spm,[status(thm)],[c_0_68,c_0_58]) ).
cnf(c_0_106,plain,
mult(ld(X1,rd(X2,X1)),rd(X2,X1)) = mult(ld(X1,X2),ld(X1,rd(X2,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_102]),c_0_47]) ).
cnf(c_0_107,plain,
mult(rd(X1,f(X2)),rd(X2,X1)) = mult(X1,rd(f(X2),X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_103]),c_0_104]),c_0_68]) ).
cnf(c_0_108,plain,
rd(X1,mult(X2,X1)) = ld(X2,unit),
inference(spm,[status(thm)],[c_0_98,c_0_29]) ).
cnf(c_0_109,plain,
rd(f(X1),mult(X2,X1)) = ld(f(X1),ld(X2,unit)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_105]),c_0_92]) ).
cnf(c_0_110,plain,
mult(X1,ld(X2,ld(X3,unit))) = rd(X1,mult(X3,X2)),
inference(spm,[status(thm)],[c_0_84,c_0_92]) ).
cnf(c_0_111,plain,
mult(mult(X1,X2),mult(ld(X2,X3),ld(X2,rd(X3,X2)))) = mult(mult(X1,X3),ld(X2,rd(X3,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_102]),c_0_47]),c_0_47]),c_0_106]) ).
cnf(c_0_112,plain,
rd(mult(X1,X2),mult(X1,f(X2))) = mult(X1,rd(f(X2),X1)),
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_107,c_0_108]),c_0_58]),c_0_84]),c_0_24]),c_0_109]),c_0_110]) ).
cnf(c_0_113,plain,
ld(mult(X1,X2),mult(X1,rd(X2,X1))) = ld(X1,unit),
inference(spm,[status(thm)],[c_0_90,c_0_24]) ).
cnf(c_0_114,plain,
mult(mult(X1,mult(X2,X3)),rd(X3,X2)) = mult(mult(X1,X2),mult(X3,rd(X3,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_19]),c_0_82]) ).
fof(c_0_115,negated_conjecture,
mult(a,mult(b,mult(a,c))) != mult(mult(mult(a,b),a),c),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[goals])]) ).
cnf(c_0_116,plain,
rd(mult(mult(X1,X2),mult(X3,mult(X2,X3))),X3) = mult(X1,mult(X2,mult(X3,X2))),
inference(spm,[status(thm)],[c_0_14,c_0_32]) ).
cnf(c_0_117,plain,
rd(mult(X1,mult(X2,X3)),X2) = mult(mult(X1,X2),rd(X3,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(spm,[status(thm)],[c_0_111,c_0_112]),c_0_105]),c_0_113]),c_0_84]),c_0_114]),c_0_103]),c_0_113]),c_0_84]) ).
cnf(c_0_118,negated_conjecture,
mult(a,mult(b,mult(a,c))) != mult(mult(mult(a,b),a),c),
inference(split_conjunct,[status(thm)],[c_0_115]) ).
cnf(c_0_119,plain,
mult(mult(mult(X1,X2),X3),X2) = mult(X1,mult(X2,mult(X3,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_116,c_0_117]),c_0_14]) ).
cnf(c_0_120,negated_conjecture,
mult(mult(a,mult(b,a)),c) != mult(a,mult(b,mult(a,c))),
inference(rw,[status(thm)],[c_0_118,c_0_15]) ).
cnf(c_0_121,plain,
mult(mult(X1,mult(X2,X1)),X3) = mult(X1,mult(X2,mult(X1,X3))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_119])]) ).
cnf(c_0_122,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_120,c_0_121])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP667+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.34 % Computer : n002.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Aug 28 21:52:49 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.56 start to proof: theBenchmark
% 4.66/4.77 % Version : CSE_E---1.5
% 4.66/4.77 % Problem : theBenchmark.p
% 4.66/4.77 % Proof found
% 4.66/4.77 % SZS status Theorem for theBenchmark.p
% 4.66/4.77 % SZS output start Proof
% See solution above
% 4.66/4.78 % Total time : 4.203000 s
% 4.66/4.78 % SZS output end Proof
% 4.66/4.78 % Total time : 4.206000 s
%------------------------------------------------------------------------------