%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP746+1 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 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 : Tue May 5 04:27:11 PM UTC 2026
% Result : Theorem 50.26s 30.97s
% Output : CNFRefutation 50.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 9
% Syntax : Number of formulae : 153 ( 116 unt; 0 def)
% Number of atoms : 198 ( 197 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 61 ( 16 ~; 40 |; 5 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 304 ( 0 sgn 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f07,axiom,
! [X3,X1,X2] : mult(mult(mult(X2,X1),X3),X1) = mult(X2,mult(mult(X1,X3),X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f07) ).
fof(f03,axiom,
! [X1,X2] : mult(rd(X2,X1),X1) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f03) ).
fof(f01,axiom,
! [X1,X2] : mult(X2,ld(X2,X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f01) ).
fof(f06,axiom,
! [X2] : mult(unit,X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f06) ).
fof(f04,axiom,
! [X1,X2] : rd(mult(X2,X1),X1) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f04) ).
fof(f02,axiom,
! [X1,X2] : ld(X2,mult(X2,X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f02) ).
fof(f08,axiom,
! [X4,X5,X6] :
( ( mult(mult(X4,X5),X6) = mult(X4,mult(X5,X6))
& mult(mult(X4,X6),X5) = mult(X4,mult(X6,X5)) )
| ( mult(mult(X4,X5),X6) = mult(mult(X4,X6),X5)
& mult(X4,mult(X5,X6)) = mult(X4,mult(X6,X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f08) ).
fof(f05,axiom,
! [X2] : mult(X2,unit) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f05) ).
fof(goals,conjecture,
mult(mult(a,b),c) = mult(a,mult(b,c)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(c_0_9,plain,
! [X33,X34,X35] : mult(mult(mult(X35,X34),X33),X34) = mult(X35,mult(mult(X34,X33),X34)),
inference(variable_rename,[status(thm)],[f07]) ).
fof(c_0_10,plain,
! [X27,X28] : mult(rd(X28,X27),X27) = X28,
inference(variable_rename,[status(thm)],[f03]) ).
cnf(c_0_11,plain,
mult(mult(mult(X1,X2),X3),X2) = mult(X1,mult(mult(X2,X3),X2)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_12,plain,
mult(rd(X1,X2),X2) = X1,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_13,plain,
! [X23,X24] : mult(X24,ld(X24,X23)) = X23,
inference(variable_rename,[status(thm)],[f01]) ).
cnf(c_0_14,plain,
mult(rd(X1,X2),mult(mult(X2,X3),X2)) = mult(mult(X1,X3),X2),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,plain,
mult(X1,ld(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_16,plain,
! [X32] : mult(unit,X32) = X32,
inference(variable_rename,[status(thm)],[f06]) ).
fof(c_0_17,plain,
! [X29,X30] : rd(mult(X30,X29),X29) = X30,
inference(variable_rename,[status(thm)],[f04]) ).
cnf(c_0_18,plain,
mult(mult(X1,ld(X2,X3)),X2) = mult(rd(X1,X2),mult(X3,X2)),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,plain,
mult(unit,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_20,plain,
rd(mult(X1,X2),X2) = X1,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_21,plain,
mult(rd(unit,X1),mult(X2,X1)) = mult(ld(X1,X2),X1),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,plain,
rd(mult(X1,mult(mult(X2,X3),X2)),X2) = mult(mult(X1,X2),X3),
inference(spm,[status(thm)],[c_0_20,c_0_11]) ).
cnf(c_0_23,plain,
mult(ld(X1,unit),X1) = unit,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_19]),c_0_12]) ).
cnf(c_0_24,plain,
mult(mult(X1,X2),ld(X2,X3)) = rd(mult(X1,mult(X3,X2)),X2),
inference(spm,[status(thm)],[c_0_22,c_0_15]) ).
cnf(c_0_25,plain,
ld(X1,unit) = rd(unit,X1),
inference(spm,[status(thm)],[c_0_20,c_0_23]) ).
cnf(c_0_26,plain,
mult(mult(X1,X2),rd(unit,X2)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_19]),c_0_20]) ).
fof(c_0_27,plain,
! [X25,X26] : ld(X26,mult(X26,X25)) = X25,
inference(variable_rename,[status(thm)],[f02]) ).
cnf(c_0_28,plain,
mult(X1,rd(unit,X2)) = rd(X1,X2),
inference(spm,[status(thm)],[c_0_26,c_0_12]) ).
cnf(c_0_29,plain,
ld(X1,mult(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_30,plain,
mult(rd(mult(X1,X2),X3),X2) = mult(X1,mult(rd(X2,X3),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_28]),c_0_28]) ).
cnf(c_0_31,plain,
rd(X1,X1) = unit,
inference(spm,[status(thm)],[c_0_20,c_0_19]) ).
cnf(c_0_32,plain,
ld(mult(X1,X2),X1) = rd(unit,X2),
inference(spm,[status(thm)],[c_0_29,c_0_26]) ).
cnf(c_0_33,plain,
mult(X1,mult(rd(X2,mult(X1,X2)),X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_19]) ).
cnf(c_0_34,plain,
mult(ld(X1,rd(X2,X1)),X1) = mult(rd(unit,X1),X2),
inference(spm,[status(thm)],[c_0_21,c_0_12]) ).
cnf(c_0_35,plain,
rd(X1,rd(unit,X2)) = mult(X1,X2),
inference(spm,[status(thm)],[c_0_20,c_0_26]) ).
cnf(c_0_36,plain,
rd(unit,ld(X1,X2)) = ld(X2,X1),
inference(spm,[status(thm)],[c_0_32,c_0_15]) ).
cnf(c_0_37,plain,
mult(rd(X1,mult(X2,X1)),X1) = ld(X2,X1),
inference(spm,[status(thm)],[c_0_29,c_0_33]) ).
cnf(c_0_38,plain,
mult(X1,mult(mult(ld(X1,X2),X3),ld(X1,X2))) = mult(mult(X2,X3),ld(X1,X2)),
inference(spm,[status(thm)],[c_0_11,c_0_15]) ).
cnf(c_0_39,plain,
ld(X1,rd(X1,X2)) = rd(unit,X2),
inference(spm,[status(thm)],[c_0_32,c_0_12]) ).
cnf(c_0_40,plain,
rd(mult(rd(unit,X1),X2),X1) = ld(X1,rd(X2,X1)),
inference(spm,[status(thm)],[c_0_20,c_0_34]) ).
cnf(c_0_41,plain,
rd(X1,ld(X2,X3)) = mult(X1,ld(X3,X2)),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_42,plain,
ld(rd(X1,X2),X2) = mult(rd(X2,X1),X2),
inference(spm,[status(thm)],[c_0_37,c_0_12]) ).
cnf(c_0_43,plain,
mult(X1,ld(X2,rd(X3,X2))) = rd(mult(rd(X1,X2),X3),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_28]),c_0_40]),c_0_28]) ).
cnf(c_0_44,plain,
rd(mult(rd(X1,X2),X3),X2) = rd(X1,mult(rd(X2,X3),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43]) ).
fof(c_0_45,plain,
! [X36,X37,X38] :
( ( mult(mult(X36,X37),X38) = mult(mult(X36,X38),X37)
| mult(mult(X36,X37),X38) = mult(X36,mult(X37,X38)) )
& ( mult(X36,mult(X37,X38)) = mult(X36,mult(X38,X37))
| mult(mult(X36,X37),X38) = mult(X36,mult(X37,X38)) )
& ( mult(mult(X36,X37),X38) = mult(mult(X36,X38),X37)
| mult(mult(X36,X38),X37) = mult(X36,mult(X38,X37)) )
& ( mult(X36,mult(X37,X38)) = mult(X36,mult(X38,X37))
| mult(mult(X36,X38),X37) = mult(X36,mult(X38,X37)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[f08])]) ).
cnf(c_0_46,plain,
rd(rd(rd(X1,X2),X3),X2) = rd(X1,mult(mult(X2,X3),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_28]),c_0_35]) ).
cnf(c_0_47,plain,
( mult(mult(X1,X2),X3) = mult(mult(X1,X3),X2)
| mult(mult(X1,X3),X2) = mult(X1,mult(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_48,plain,
ld(mult(X1,X2),rd(unit,X2)) = rd(unit,mult(mult(X2,X1),X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_35]),c_0_28]),c_0_46]) ).
cnf(c_0_49,plain,
( mult(rd(X1,X2),X3) = rd(mult(X1,X3),X2)
| mult(X1,rd(X3,X2)) = rd(mult(X1,X3),X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_28]),c_0_28]),c_0_28]) ).
cnf(c_0_50,plain,
rd(mult(X1,X2),mult(mult(X2,X1),X2)) = rd(unit,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_48]),c_0_28]) ).
cnf(c_0_51,plain,
( mult(X1,rd(X2,X1)) = rd(mult(X1,X2),X1)
| rd(mult(X1,X2),X1) = X2 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_31]),c_0_19]) ).
cnf(c_0_52,plain,
ld(rd(X1,X2),X1) = X2,
inference(spm,[status(thm)],[c_0_29,c_0_12]) ).
cnf(c_0_53,plain,
( rd(X1,mult(X2,X1)) = rd(unit,X2)
| rd(mult(X2,X1),X2) = X1 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_12]),c_0_12]) ).
cnf(c_0_54,plain,
( rd(X1,mult(X2,X1)) = rd(unit,X2)
| ld(X1,mult(X2,X1)) = X2 ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_55,plain,
( rd(X1,mult(X2,X1)) = rd(unit,X2)
| ld(mult(X2,X1),X1) = rd(unit,X2) ),
inference(spm,[status(thm)],[c_0_39,c_0_53]) ).
cnf(c_0_56,plain,
( rd(unit,rd(X1,X2)) = rd(X2,X1)
| ld(X2,X1) = rd(X1,X2) ),
inference(spm,[status(thm)],[c_0_54,c_0_12]) ).
fof(c_0_57,plain,
! [X31] : mult(X31,unit) = X31,
inference(variable_rename,[status(thm)],[f05]) ).
cnf(c_0_58,plain,
( rd(unit,rd(X1,X2)) = ld(X1,X2)
| rd(unit,rd(X1,X2)) = rd(X2,X1) ),
inference(spm,[status(thm)],[c_0_55,c_0_12]) ).
cnf(c_0_59,plain,
( rd(unit,rd(X1,X2)) = rd(X2,X1)
| ld(X1,X2) = rd(X2,X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_56]),c_0_25]) ).
cnf(c_0_60,plain,
mult(X1,unit) = X1,
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_61,plain,
rd(mult(X1,mult(rd(X2,X3),X2)),X2) = rd(mult(X1,X2),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_28]),c_0_28]) ).
cnf(c_0_62,plain,
rd(unit,rd(X1,X2)) = rd(X2,X1),
inference(csr,[status(thm)],[inference(ef,[status(thm)],[c_0_58]),c_0_59]) ).
cnf(c_0_63,plain,
rd(X1,unit) = X1,
inference(spm,[status(thm)],[c_0_60,c_0_12]) ).
fof(c_0_64,negated_conjecture,
mult(mult(a,b),c) != mult(a,mult(b,c)),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[goals])]) ).
cnf(c_0_65,plain,
rd(X1,rd(X2,X3)) = mult(X1,rd(X3,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_60]),c_0_63]),c_0_60]) ).
cnf(c_0_66,plain,
rd(ld(X1,X2),X2) = rd(X2,mult(X1,X2)),
inference(spm,[status(thm)],[c_0_20,c_0_37]) ).
cnf(c_0_67,negated_conjecture,
mult(mult(a,b),c) != mult(a,mult(b,c)),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_68,plain,
( mult(X1,mult(X2,X3)) = mult(X1,mult(X3,X2))
| mult(mult(X1,X3),X2) = mult(X1,mult(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_69,plain,
mult(rd(X1,X2),rd(X2,X1)) = unit,
inference(spm,[status(thm)],[c_0_31,c_0_65]) ).
cnf(c_0_70,plain,
rd(mult(X1,X2),mult(X1,mult(X1,X2))) = rd(X2,mult(X1,X2)),
inference(spm,[status(thm)],[c_0_66,c_0_29]) ).
cnf(c_0_71,negated_conjecture,
mult(a,mult(c,b)) = mult(a,mult(b,c)),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_72,plain,
mult(X1,rd(X2,mult(X1,X2))) = unit,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_20]) ).
cnf(c_0_73,plain,
( mult(mult(X1,X2),X3) = mult(X1,mult(X2,X3))
| mult(mult(X1,X3),X2) != mult(X1,mult(X2,X3)) ),
inference(ef,[status(thm)],[c_0_47]) ).
cnf(c_0_74,negated_conjecture,
mult(c,b) = mult(b,c),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_71]),c_0_29]) ).
cnf(c_0_75,plain,
rd(X1,mult(X2,X1)) = rd(unit,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_72]),c_0_19]),c_0_20]) ).
cnf(c_0_76,plain,
( mult(X1,rd(X2,X3)) = rd(mult(X1,X2),X3)
| mult(rd(X1,X3),X2) != mult(X1,rd(X2,X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_28]),c_0_28]),c_0_28]),c_0_28]) ).
cnf(c_0_77,negated_conjecture,
( mult(mult(b,c),X1) = mult(c,mult(b,X1))
| mult(c,mult(X1,b)) = mult(c,mult(b,X1)) ),
inference(spm,[status(thm)],[c_0_68,c_0_74]) ).
cnf(c_0_78,plain,
mult(rd(unit,X1),X2) = ld(X1,X2),
inference(rw,[status(thm)],[c_0_37,c_0_75]) ).
cnf(c_0_79,plain,
( mult(X1,rd(X2,X1)) = rd(mult(X1,X2),X1)
| mult(X1,rd(X2,X1)) != X2 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_31]),c_0_19]) ).
cnf(c_0_80,negated_conjecture,
rd(mult(b,c),b) = c,
inference(spm,[status(thm)],[c_0_20,c_0_74]) ).
cnf(c_0_81,plain,
mult(mult(X1,X2),X2) = mult(X1,mult(X2,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_60]),c_0_60]) ).
cnf(c_0_82,negated_conjecture,
( mult(c,ld(X1,b)) = mult(c,rd(b,X1))
| mult(c,rd(b,X1)) = rd(mult(b,c),X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_77]),c_0_28]),c_0_78]),c_0_28]) ).
cnf(c_0_83,negated_conjecture,
rd(mult(b,mult(b,c)),b) = mult(b,c),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_84,negated_conjecture,
mult(mult(b,c),b) = mult(c,mult(b,b)),
inference(spm,[status(thm)],[c_0_81,c_0_74]) ).
cnf(c_0_85,plain,
rd(X1,mult(rd(X1,X2),X1)) = rd(X2,X1),
inference(spm,[status(thm)],[c_0_66,c_0_52]) ).
cnf(c_0_86,plain,
ld(X1,rd(unit,X2)) = rd(unit,mult(X2,X1)),
inference(spm,[status(thm)],[c_0_39,c_0_75]) ).
cnf(c_0_87,plain,
ld(rd(X1,X2),mult(mult(X1,X3),X2)) = mult(mult(X2,X3),X2),
inference(spm,[status(thm)],[c_0_29,c_0_14]) ).
cnf(c_0_88,negated_conjecture,
( mult(c,rd(b,X1)) = rd(mult(b,c),X1)
| ld(X1,b) = rd(b,X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_82]),c_0_29]) ).
cnf(c_0_89,plain,
ld(rd(X1,X2),X3) = mult(rd(X2,X1),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_65]),c_0_19]) ).
cnf(c_0_90,negated_conjecture,
mult(c,mult(b,b)) = mult(b,mult(b,c)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_83]),c_0_84]) ).
cnf(c_0_91,plain,
( mult(mult(X1,X2),mult(X2,X3)) = mult(mult(X1,X2),mult(X3,X2))
| mult(mult(X1,X2),mult(X3,X2)) = mult(X1,mult(mult(X2,X3),X2)) ),
inference(spm,[status(thm)],[c_0_11,c_0_68]) ).
cnf(c_0_92,plain,
rd(unit,mult(rd(X1,X2),X1)) = ld(X1,rd(X2,X1)),
inference(spm,[status(thm)],[c_0_39,c_0_85]) ).
cnf(c_0_93,plain,
rd(rd(unit,X1),X2) = rd(unit,mult(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_78]),c_0_86]) ).
cnf(c_0_94,plain,
ld(rd(X1,X2),mult(X3,X2)) = mult(mult(X2,ld(X1,X3)),X2),
inference(spm,[status(thm)],[c_0_87,c_0_15]) ).
cnf(c_0_95,plain,
ld(unit,X1) = X1,
inference(spm,[status(thm)],[c_0_29,c_0_19]) ).
cnf(c_0_96,negated_conjecture,
( mult(rd(X1,mult(b,c)),c) = rd(X1,b)
| ld(X1,b) = rd(b,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_88]),c_0_89]),c_0_65]),c_0_19]) ).
cnf(c_0_97,negated_conjecture,
mult(mult(b,c),b) = mult(b,mult(b,c)),
inference(rw,[status(thm)],[c_0_84,c_0_90]) ).
cnf(c_0_98,plain,
mult(rd(X1,X2),mult(X2,X2)) = mult(X1,X2),
inference(spm,[status(thm)],[c_0_81,c_0_12]) ).
cnf(c_0_99,plain,
( mult(mult(X1,X2),mult(X3,X2)) = mult(X1,mult(mult(X2,X3),X2))
| mult(mult(X1,X2),mult(X2,X3)) != mult(X1,mult(mult(X2,X3),X2)) ),
inference(ef,[status(thm)],[c_0_91]) ).
cnf(c_0_100,plain,
mult(mult(X1,X2),X1) = mult(X1,mult(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(spm,[status(thm)],[c_0_92,c_0_93]),c_0_28]),c_0_93]),c_0_65]),c_0_63]),c_0_19]),c_0_35]),c_0_94]),c_0_95]) ).
cnf(c_0_101,plain,
rd(ld(X1,X2),X1) = ld(X1,rd(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_78]),c_0_92]) ).
cnf(c_0_102,plain,
mult(rd(X1,mult(X2,X3)),mult(X2,mult(X2,X3))) = mult(rd(X1,X3),mult(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_32]),c_0_28]) ).
cnf(c_0_103,negated_conjecture,
( rd(mult(X1,c),mult(b,c)) = rd(X1,b)
| ld(X1,b) = rd(b,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_96]),c_0_75]),c_0_28])]) ).
cnf(c_0_104,negated_conjecture,
mult(rd(X1,b),mult(b,mult(b,c))) = mult(mult(X1,c),b),
inference(spm,[status(thm)],[c_0_14,c_0_97]) ).
cnf(c_0_105,plain,
rd(mult(X1,X2),mult(rd(X2,X3),X2)) = rd(mult(X1,X3),X2),
inference(spm,[status(thm)],[c_0_44,c_0_20]) ).
cnf(c_0_106,plain,
rd(mult(X1,X1),mult(X2,X1)) = rd(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_98]),c_0_62]) ).
cnf(c_0_107,plain,
( mult(mult(X1,X2),X3) = mult(X1,mult(X2,X3))
| mult(mult(X1,X2),X3) != mult(X1,mult(X3,X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_12]),c_0_14]),c_0_14]) ).
cnf(c_0_108,plain,
mult(X1,ld(X2,X1)) = mult(rd(X1,X2),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_28]),c_0_78]) ).
cnf(c_0_109,plain,
( mult(mult(rd(X1,X2),X3),X2) = mult(rd(X1,X2),mult(X3,X2))
| mult(mult(rd(X1,X2),X3),X2) = mult(X1,X3) ),
inference(spm,[status(thm)],[c_0_47,c_0_12]) ).
cnf(c_0_110,plain,
ld(X1,rd(mult(X1,X2),X1)) = rd(X2,X1),
inference(spm,[status(thm)],[c_0_101,c_0_29]) ).
cnf(c_0_111,negated_conjecture,
( mult(mult(X1,c),b) = mult(X1,mult(b,c))
| ld(X1,b) = rd(b,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_104]),c_0_20]) ).
cnf(c_0_112,plain,
mult(X1,rd(X2,X1)) = rd(mult(X1,X2),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_65]) ).
cnf(c_0_113,plain,
( mult(X1,mult(ld(X1,X2),X3)) = mult(X2,X3)
| mult(X1,mult(X3,ld(X1,X2))) != mult(X2,X3) ),
inference(spm,[status(thm)],[c_0_107,c_0_15]) ).
cnf(c_0_114,plain,
mult(X1,rd(ld(X2,X3),X4)) = rd(X1,mult(X4,ld(X3,X2))),
inference(spm,[status(thm)],[c_0_65,c_0_41]) ).
cnf(c_0_115,plain,
mult(X1,rd(rd(X2,X3),X4)) = rd(X1,mult(X4,rd(X3,X2))),
inference(spm,[status(thm)],[c_0_65,c_0_65]) ).
cnf(c_0_116,plain,
mult(rd(X1,X2),mult(rd(X2,X3),X2)) = mult(rd(X1,X3),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_28]),c_0_28]) ).
cnf(c_0_117,plain,
mult(rd(X1,mult(X1,X2)),X1) = rd(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_32]),c_0_28]) ).
cnf(c_0_118,plain,
rd(rd(unit,X1),rd(X2,X1)) = mult(ld(X2,rd(unit,X1)),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_66]),c_0_28]) ).
cnf(c_0_119,plain,
( mult(mult(rd(X1,X2),X3),X2) = mult(X1,X3)
| mult(rd(X1,X2),mult(X3,X2)) != mult(X1,X3) ),
inference(ef,[status(thm)],[c_0_109]) ).
cnf(c_0_120,plain,
mult(mult(X1,X2),rd(X3,X2)) = rd(mult(X1,mult(X2,X3)),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_110]),c_0_12]) ).
cnf(c_0_121,negated_conjecture,
( mult(mult(X1,c),b) = mult(X1,mult(b,c))
| rd(mult(X1,b),X1) = b ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_111]),c_0_112]) ).
cnf(c_0_122,plain,
( rd(X1,mult(X2,ld(X3,X1))) = rd(X3,X2)
| mult(X1,ld(X2,ld(X1,X3))) != rd(X3,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_78]),c_0_28]),c_0_28]),c_0_28]),c_0_114]) ).
cnf(c_0_123,plain,
ld(rd(unit,X1),X2) = mult(X1,X2),
inference(spm,[status(thm)],[c_0_52,c_0_75]) ).
cnf(c_0_124,plain,
rd(unit,mult(X1,rd(X2,X3))) = rd(rd(X3,X2),X1),
inference(spm,[status(thm)],[c_0_19,c_0_115]) ).
cnf(c_0_125,plain,
mult(rd(X1,X2),rd(X2,X3)) = mult(rd(X1,mult(X2,X3)),X2),
inference(spm,[status(thm)],[c_0_116,c_0_117]) ).
cnf(c_0_126,plain,
rd(unit,mult(rd(X1,X2),X3)) = ld(X3,rd(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_65]),c_0_19]) ).
cnf(c_0_127,plain,
rd(rd(X1,X2),rd(X3,X2)) = mult(mult(X1,ld(X3,rd(unit,X2))),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_118]),c_0_28]),c_0_20]),c_0_35]),c_0_28]) ).
cnf(c_0_128,plain,
( rd(mult(mult(X1,X2),X3),X2) = mult(X1,X3)
| rd(mult(X1,mult(X2,X3)),X2) != mult(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_119,c_0_28]),c_0_65]),c_0_63]),c_0_28]),c_0_65]),c_0_63]),c_0_120]) ).
cnf(c_0_129,negated_conjecture,
( mult(mult(X1,c),b) = mult(X1,mult(b,c))
| mult(b,X1) = mult(X1,b) ),
inference(spm,[status(thm)],[c_0_12,c_0_121]) ).
cnf(c_0_130,plain,
( ld(X1,rd(mult(X1,X2),X3)) = rd(X2,X3)
| ld(X1,ld(X3,mult(X1,X2))) != rd(X2,X3) ),
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_122,c_0_78]),c_0_86]),c_0_28]),c_0_65]),c_0_78]),c_0_123]) ).
cnf(c_0_131,plain,
ld(X1,rd(mult(X1,X2),X3)) = mult(rd(X2,mult(X1,X3)),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_125]),c_0_126]),c_0_127]),c_0_86]),c_0_28]) ).
cnf(c_0_132,plain,
ld(ld(X1,X2),X3) = mult(ld(X2,X1),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_41]),c_0_19]) ).
cnf(c_0_133,plain,
( mult(rd(X1,X2),X3) = rd(mult(X1,X3),X2)
| mult(rd(X1,X2),X3) != mult(X1,rd(X3,X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_44]),c_0_12]),c_0_117]),c_0_65]) ).
cnf(c_0_134,negated_conjecture,
mult(rd(X1,c),mult(b,mult(c,c))) = mult(mult(X1,b),c),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_74]),c_0_81]) ).
cnf(c_0_135,negated_conjecture,
rd(mult(X1,mult(b,mult(c,c))),c) = mult(mult(X1,c),b),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_74]),c_0_81]) ).
cnf(c_0_136,plain,
rd(mult(X1,mult(X2,X2)),X2) = mult(X1,X2),
inference(spm,[status(thm)],[c_0_20,c_0_81]) ).
cnf(c_0_137,negated_conjecture,
( mult(mult(X1,b),c) = mult(X1,mult(b,c))
| mult(b,X1) = mult(X1,b) ),
inference(spm,[status(thm)],[c_0_47,c_0_129]) ).
cnf(c_0_138,plain,
mult(ld(X1,X2),X1) = ld(X1,mult(X2,X1)),
inference(rw,[status(thm)],[c_0_21,c_0_78]) ).
cnf(c_0_139,plain,
( mult(rd(X1,mult(X2,X3)),X2) = rd(X1,X3)
| ld(X2,ld(X3,mult(X2,X1))) != rd(X1,X3) ),
inference(rw,[status(thm)],[c_0_130,c_0_131]) ).
cnf(c_0_140,plain,
rd(mult(X1,ld(X2,X3)),X3) = rd(mult(X1,X3),mult(X2,X3)),
inference(spm,[status(thm)],[c_0_61,c_0_37]) ).
cnf(c_0_141,plain,
mult(X1,ld(X2,ld(X3,X4))) = rd(X1,mult(ld(X4,X3),X2)),
inference(spm,[status(thm)],[c_0_41,c_0_132]) ).
cnf(c_0_142,negated_conjecture,
mult(mult(X1,c),b) = mult(mult(X1,b),c),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_134]),c_0_135]),c_0_136]),c_0_47]) ).
cnf(c_0_143,plain,
ld(mult(X1,X2),mult(X1,mult(X2,X1))) = X1,
inference(spm,[status(thm)],[c_0_29,c_0_100]) ).
cnf(c_0_144,negated_conjecture,
mult(b,a) = mult(a,b),
inference(spm,[status(thm)],[c_0_67,c_0_137]) ).
cnf(c_0_145,plain,
ld(mult(X1,X2),mult(X1,mult(X1,X2))) = ld(X2,mult(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_32]),c_0_21]),c_0_138]) ).
cnf(c_0_146,plain,
( rd(mult(X1,X2),mult(X3,X2)) = rd(X1,X3)
| rd(X2,mult(ld(X1,X2),X3)) != rd(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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_78]),c_0_28]),c_0_78]),c_0_41]),c_0_140]),c_0_89]),c_0_63]),c_0_141]) ).
cnf(c_0_147,negated_conjecture,
mult(ld(X1,c),b) = mult(ld(X1,b),c),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_78]),c_0_78]) ).
cnf(c_0_148,negated_conjecture,
ld(b,mult(a,b)) = a,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_144]),c_0_145]) ).
cnf(c_0_149,negated_conjecture,
( rd(mult(X1,c),mult(b,c)) = rd(X1,b)
| ld(b,X1) != rd(X1,b) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_147]),c_0_75]),c_0_41]),c_0_19]) ).
cnf(c_0_150,negated_conjecture,
ld(b,a) = rd(a,b),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_148]),c_0_20]) ).
cnf(c_0_151,negated_conjecture,
rd(mult(a,c),mult(b,c)) = rd(a,b),
inference(spm,[status(thm)],[c_0_149,c_0_150]) ).
cnf(c_0_152,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_151]),c_0_104]),c_0_142]),c_0_20]),c_0_67]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP746+1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.32 % Computer : n028.cluster.edu
% 0.16/0.32 % Model : x86_64 x86_64
% 0.16/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.32 % Memory : 8042.1875MB
% 0.16/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.32 % CPULimit : 300
% 0.16/0.32 % WCLimit : 300
% 0.16/0.32 % DateTime : Mon May 4 19:04:15 EDT 2026
% 0.16/0.32 % CPUTime :
% 0.16/0.33 % start to proof: theBenchmark
% 50.26/30.97 % Version : CSE_E---1.7
% 50.26/30.97 % Problem : theBenchmark.p
% 50.26/30.97 % SZS status Theorem for theBenchmark.p
% 50.26/30.97 % SZS output start CNFRefutation
% See solution above
% 50.49/31.16 % Total time : 24.413s
%------------------------------------------------------------------------------