%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP776+1 : TPTP v9.2.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n014.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 04:27:15 PM UTC 2026
% Result : Theorem 88.64s 54.68s
% Output : CNFRefutation 89.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 19
% Syntax : Number of formulae : 182 ( 36 unt; 0 def)
% Number of atoms : 414 ( 130 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 444 ( 212 ~; 208 |; 9 &)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 229 ( 14 sgn 50 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(sos09,axiom,
! [X1,X2] :
( ( h(X2)
& h(X1) )
=> h(sum(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos09) ).
fof(sos18,axiom,
! [X1,X2] : f(product(X2,X1)) = sum(f(X2),f(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos18) ).
fof(sos10,axiom,
! [X1,X2] :
( h(X2)
=> h(opp(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos10) ).
fof(sos05,axiom,
! [X2] :
( g(X2)
=> product(eh,X2) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos05) ).
fof(sos07,axiom,
! [X2] :
( g(X2)
=> product(X2,inv(X2)) = eh ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos07) ).
fof(sos08,axiom,
! [X2] :
( g(X2)
=> product(inv(X2),X2) = eh ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos08) ).
fof(sos17,axiom,
! [X2] :
( g(X2)
=> h(f(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos17) ).
fof(sos15,axiom,
! [X2] :
( h(X2)
=> sum(X2,opp(X2)) = eg ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos15) ).
fof(sos12,axiom,
! [X3,X1,X2] :
( ( h(X2)
& h(X1)
& h(X3) )
=> sum(sum(X2,X1),X3) = sum(X2,sum(X1,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos12) ).
fof(sos11,axiom,
h(eg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos11) ).
fof(sos03,axiom,
g(eh),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos03) ).
fof(sos02,axiom,
! [X2] :
( g(X2)
=> g(inv(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos02) ).
fof(sos04,axiom,
! [X3,X1,X2] :
( ( g(X2)
& g(X1)
& g(X3) )
=> product(product(X2,X1),X3) = product(X2,product(X1,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos04) ).
fof(sos06,axiom,
! [X2] :
( g(X2)
=> product(X2,eh) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos06) ).
fof(sos01,axiom,
! [X1,X2] :
( ( g(X2)
& g(X1) )
=> g(product(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos01) ).
fof(sos14,axiom,
! [X2] :
( h(X2)
=> sum(X2,eg) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos14) ).
fof(sos16,axiom,
! [X2] :
( h(X2)
=> sum(opp(X2),X2) = eg ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos16) ).
fof(goals,conjecture,
! [X4] :
( f(eh) = eg
& ( ~ g(X4)
| f(inv(X4)) = opp(f(X4)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(sos13,axiom,
! [X2] :
( h(X2)
=> sum(eg,X2) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos13) ).
fof(c_0_19,plain,
! [X40,X41] :
( ~ h(X41)
| ~ h(X40)
| h(sum(X41,X40)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos09])]) ).
fof(c_0_20,plain,
! [X52,X53] : f(product(X53,X52)) = sum(f(X53),f(X52)),
inference(variable_rename,[status(thm)],[sos18]) ).
fof(c_0_21,plain,
! [X42,X43] :
( ~ h(X43)
| h(opp(X42)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos10])]) ).
fof(c_0_22,plain,
! [X36] :
( ~ g(X36)
| product(eh,X36) = X36 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos05])]) ).
fof(c_0_23,plain,
! [X38] :
( ~ g(X38)
| product(X38,inv(X38)) = eh ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos07])]) ).
cnf(c_0_24,plain,
( h(sum(X1,X2))
| ~ h(X1)
| ~ h(X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,plain,
f(product(X1,X2)) = sum(f(X1),f(X2)),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_26,plain,
! [X39] :
( ~ g(X39)
| product(inv(X39),X39) = eh ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos08])]) ).
fof(c_0_27,plain,
! [X51] :
( ~ g(X51)
| h(f(X51)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos17])]) ).
fof(c_0_28,plain,
! [X49] :
( ~ h(X49)
| sum(X49,opp(X49)) = eg ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos15])]) ).
fof(c_0_29,plain,
! [X44,X45,X46] :
( ~ h(X46)
| ~ h(X45)
| ~ h(X44)
| sum(sum(X46,X45),X44) = sum(X46,sum(X45,X44)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos12])]) ).
cnf(c_0_30,plain,
( h(opp(X2))
| ~ h(X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_31,plain,
h(eg),
inference(split_conjunct,[status(thm)],[sos11]) ).
cnf(c_0_32,plain,
( product(eh,X1) = X1
| ~ g(X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_33,plain,
( product(X1,inv(X1)) = eh
| ~ g(X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_34,plain,
g(eh),
inference(split_conjunct,[status(thm)],[sos03]) ).
fof(c_0_35,plain,
! [X32] :
( ~ g(X32)
| g(inv(X32)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos02])]) ).
cnf(c_0_36,plain,
( h(f(product(X1,X2)))
| ~ h(f(X2))
| ~ h(f(X1)) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_37,plain,
( product(inv(X1),X1) = eh
| ~ g(X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_38,plain,
( h(f(X1))
| ~ g(X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
fof(c_0_39,plain,
! [X33,X34,X35] :
( ~ g(X35)
| ~ g(X34)
| ~ g(X33)
| product(product(X35,X34),X33) = product(X35,product(X34,X33)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos04])]) ).
cnf(c_0_40,plain,
( sum(X1,opp(X1)) = eg
| ~ h(X1) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_41,plain,
( sum(sum(X1,X2),X3) = sum(X1,sum(X2,X3))
| ~ h(X1)
| ~ h(X2)
| ~ h(X3) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_42,plain,
h(opp(X1)),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_43,plain,
( inv(eh) = eh
| ~ g(inv(eh)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34])]) ).
cnf(c_0_44,plain,
( g(inv(X1))
| ~ g(X1) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_45,plain,
( h(f(eh))
| ~ h(f(inv(X1)))
| ~ g(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]) ).
cnf(c_0_46,plain,
( product(product(X1,X2),X3) = product(X1,product(X2,X3))
| ~ g(X1)
| ~ g(X2)
| ~ g(X3) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
fof(c_0_47,plain,
! [X37] :
( ~ g(X37)
| product(X37,eh) = X37 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos06])]) ).
fof(c_0_48,plain,
! [X30,X31] :
( ~ g(X31)
| ~ g(X30)
| g(product(X31,X30)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos01])]) ).
cnf(c_0_49,plain,
( sum(X1,sum(X2,opp(sum(X1,X2)))) = eg
| ~ h(X2)
| ~ h(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42])]),c_0_24]) ).
cnf(c_0_50,plain,
inv(eh) = eh,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_34])]) ).
cnf(c_0_51,plain,
( h(f(eh))
| ~ g(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_38]),c_0_44]) ).
cnf(c_0_52,plain,
( product(X1,product(inv(X1),X2)) = product(eh,X2)
| ~ g(X2)
| ~ g(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_33]),c_0_44]) ).
cnf(c_0_53,plain,
( product(X1,eh) = X1
| ~ g(X1) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_54,plain,
( g(product(X1,X2))
| ~ g(X1)
| ~ g(X2) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_55,plain,
( product(inv(X1),product(X1,X2)) = product(eh,X2)
| ~ g(X2)
| ~ g(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_37]),c_0_44]) ).
cnf(c_0_56,plain,
( sum(f(X1),sum(f(X2),opp(f(product(X1,X2))))) = eg
| ~ h(f(X2))
| ~ h(f(X1)) ),
inference(spm,[status(thm)],[c_0_49,c_0_25]) ).
cnf(c_0_57,plain,
product(eh,eh) = eh,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_50]),c_0_34])]) ).
cnf(c_0_58,plain,
h(f(eh)),
inference(spm,[status(thm)],[c_0_51,c_0_34]) ).
cnf(c_0_59,plain,
( product(eh,inv(inv(X1))) = product(X1,eh)
| ~ g(inv(inv(X1)))
| ~ g(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_33]),c_0_44]) ).
cnf(c_0_60,plain,
( product(X1,product(X2,eh)) = product(X1,X2)
| ~ g(X2)
| ~ g(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_46]),c_0_34])]),c_0_54]) ).
cnf(c_0_61,plain,
( product(inv(inv(X1)),eh) = product(eh,X1)
| ~ g(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_37]),c_0_44]) ).
fof(c_0_62,plain,
! [X48] :
( ~ h(X48)
| sum(X48,eg) = X48 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos14])]) ).
cnf(c_0_63,plain,
sum(f(eh),sum(f(eh),opp(f(eh)))) = eg,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_58])]) ).
cnf(c_0_64,plain,
( inv(inv(X1)) = product(X1,eh)
| ~ g(inv(inv(X1)))
| ~ g(X1) ),
inference(spm,[status(thm)],[c_0_32,c_0_59]) ).
cnf(c_0_65,plain,
( product(eh,X1) = product(X1,eh)
| ~ g(product(X1,eh))
| ~ g(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_60]),c_0_34])]) ).
cnf(c_0_66,plain,
( inv(inv(X1)) = product(eh,X1)
| ~ g(inv(inv(X1)))
| ~ g(X1) ),
inference(spm,[status(thm)],[c_0_53,c_0_61]) ).
fof(c_0_67,plain,
! [X50] :
( ~ h(X50)
| sum(opp(X50),X50) = eg ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos16])]) ).
cnf(c_0_68,plain,
( sum(X1,eg) = X1
| ~ h(X1) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_69,plain,
sum(f(eh),eg) = eg,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_40]),c_0_58])]) ).
cnf(c_0_70,plain,
( inv(inv(X1)) = product(X1,eh)
| ~ g(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_44]),c_0_44]) ).
cnf(c_0_71,plain,
( g(product(X1,product(X2,X3)))
| ~ g(X3)
| ~ g(X2)
| ~ g(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_46]),c_0_54]) ).
cnf(c_0_72,plain,
( product(eh,X1) = product(X1,eh)
| ~ g(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_54]),c_0_34])]) ).
cnf(c_0_73,plain,
( product(X1,product(X2,inv(product(X1,X2)))) = eh
| ~ g(inv(product(X1,X2)))
| ~ g(X2)
| ~ g(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_46]),c_0_54]) ).
cnf(c_0_74,plain,
( inv(inv(X1)) = product(eh,X1)
| ~ g(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_44]),c_0_44]) ).
cnf(c_0_75,plain,
( sum(sum(X1,sum(X2,X3)),X4) = sum(sum(X1,X2),sum(X3,X4))
| ~ h(X4)
| ~ h(X3)
| ~ h(X2)
| ~ h(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_41]),c_0_24]) ).
cnf(c_0_76,plain,
( h(sum(X1,sum(X2,X3)))
| ~ h(X3)
| ~ h(X2)
| ~ h(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_41]),c_0_24]) ).
cnf(c_0_77,plain,
( sum(opp(X1),X1) = eg
| ~ h(X1) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_78,plain,
f(eh) = eg,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_58])]) ).
cnf(c_0_79,plain,
( inv(product(X1,eh)) = product(inv(X1),eh)
| ~ g(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_70]),c_0_44]) ).
cnf(c_0_80,plain,
( g(product(X1,product(eh,X2)))
| ~ g(X2)
| ~ g(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_34])]) ).
cnf(c_0_81,plain,
( product(eh,product(X1,inv(product(X2,X1)))) = product(inv(X2),eh)
| ~ g(inv(product(X2,X1)))
| ~ g(X2)
| ~ g(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_73]),c_0_54]) ).
cnf(c_0_82,plain,
( inv(product(eh,X1)) = product(eh,inv(X1))
| ~ g(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_74]),c_0_44]) ).
cnf(c_0_83,plain,
( g(product(X1,eh))
| ~ g(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_72]),c_0_34])]) ).
cnf(c_0_84,plain,
( h(sum(sum(X1,X2),sum(X3,X4)))
| ~ h(X4)
| ~ h(X3)
| ~ h(X2)
| ~ h(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_75]),c_0_76]) ).
cnf(c_0_85,plain,
( sum(sum(X1,opp(X2)),sum(X2,X3)) = sum(sum(X1,eg),X3)
| ~ h(X3)
| ~ h(X2)
| ~ h(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_77]),c_0_42])]) ).
cnf(c_0_86,plain,
f(product(X1,eh)) = sum(f(X1),eg),
inference(spm,[status(thm)],[c_0_25,c_0_78]) ).
cnf(c_0_87,plain,
( product(inv(X1),eh) = inv(X1)
| ~ g(X1) ),
inference(spm,[status(thm)],[c_0_79,c_0_53]) ).
cnf(c_0_88,plain,
( g(product(inv(X1),eh))
| ~ g(inv(product(X1,eh)))
| ~ g(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_34])]) ).
cnf(c_0_89,plain,
( product(inv(X1),product(eh,X1)) = eh
| ~ g(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_72]),c_0_57]),c_0_34])]) ).
fof(c_0_90,negated_conjecture,
~ ! [X4] :
( f(eh) = eg
& ( ~ g(X4)
| f(inv(X4)) = opp(f(X4)) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[goals])]) ).
cnf(c_0_91,plain,
( product(eh,inv(product(X1,eh))) = inv(product(eh,X1))
| ~ g(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_60]),c_0_34])]),c_0_83]) ).
cnf(c_0_92,plain,
( h(sum(sum(X1,eg),X2))
| ~ h(X2)
| ~ h(X3)
| ~ h(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_42])]) ).
cnf(c_0_93,plain,
( h(sum(f(X1),eg))
| ~ g(product(X1,eh)) ),
inference(spm,[status(thm)],[c_0_38,c_0_86]) ).
cnf(c_0_94,plain,
( sum(f(inv(X1)),eg) = f(inv(X1))
| ~ g(X1) ),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_95,plain,
( g(product(inv(X1),eh))
| ~ g(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_44]),c_0_83]) ).
cnf(c_0_96,plain,
( product(inv(X1),product(X1,eh)) = eh
| ~ g(X1) ),
inference(spm,[status(thm)],[c_0_89,c_0_72]) ).
cnf(c_0_97,plain,
( product(X1,product(X2,product(X3,eh))) = product(product(X1,X2),X3)
| ~ g(X2)
| ~ g(X1)
| ~ g(X3) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_60]),c_0_54]),c_0_83]) ).
cnf(c_0_98,plain,
( g(product(X1,product(X2,eh)))
| ~ g(X2)
| ~ g(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_34])]) ).
fof(c_0_99,negated_conjecture,
( ( g(esk1_0)
| f(eh) != eg )
& ( f(inv(esk1_0)) != opp(f(esk1_0))
| f(eh) != eg ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_90])])])]) ).
cnf(c_0_100,plain,
( g(inv(product(eh,X1)))
| ~ g(inv(product(X1,eh)))
| ~ g(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_91]),c_0_34])]) ).
cnf(c_0_101,plain,
( sum(opp(X1),sum(X1,X2)) = sum(eg,X2)
| ~ h(X2)
| ~ h(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_77]),c_0_42])]) ).
cnf(c_0_102,plain,
( h(sum(sum(X1,eg),f(X2)))
| ~ h(X3)
| ~ h(X1)
| ~ g(X2) ),
inference(spm,[status(thm)],[c_0_92,c_0_38]) ).
cnf(c_0_103,plain,
( h(f(inv(X1)))
| ~ g(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_95]) ).
fof(c_0_104,plain,
! [X47] :
( ~ h(X47)
| sum(eg,X47) = X47 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos13])]) ).
cnf(c_0_105,plain,
( sum(X1,sum(opp(X1),X2)) = sum(eg,X2)
| ~ h(X2)
| ~ h(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_40]),c_0_42])]) ).
cnf(c_0_106,plain,
( product(inv(X1),product(product(X1,eh),X2)) = product(eh,X2)
| ~ g(X2)
| ~ g(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_96]),c_0_44]),c_0_83]) ).
cnf(c_0_107,plain,
( product(inv(X1),product(product(X1,X2),X3)) = product(eh,product(X2,product(X3,eh)))
| ~ g(X1)
| ~ g(X2)
| ~ g(X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_97]),c_0_98]) ).
cnf(c_0_108,negated_conjecture,
( g(esk1_0)
| f(eh) != eg ),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
cnf(c_0_109,plain,
( g(inv(product(eh,X1)))
| ~ g(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_53]),c_0_44]) ).
cnf(c_0_110,plain,
( sum(opp(opp(X1)),eg) = sum(eg,X1)
| ~ h(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_77]),c_0_42])]) ).
cnf(c_0_111,plain,
( h(sum(sum(X1,eg),f(X2)))
| ~ h(X1)
| ~ g(X2)
| ~ g(X3) ),
inference(spm,[status(thm)],[c_0_102,c_0_103]) ).
cnf(c_0_112,plain,
( sum(eg,X1) = X1
| ~ h(X1) ),
inference(split_conjunct,[status(thm)],[c_0_104]) ).
cnf(c_0_113,plain,
( sum(eg,opp(opp(X1))) = sum(X1,eg)
| ~ h(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_40]),c_0_42]),c_0_42])]) ).
cnf(c_0_114,plain,
( product(product(X1,product(X2,X3)),X4) = product(product(X1,X2),product(X3,X4))
| ~ g(X4)
| ~ g(X3)
| ~ g(X2)
| ~ g(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_46]),c_0_54]) ).
cnf(c_0_115,plain,
( product(eh,product(eh,product(X1,eh))) = product(eh,X1)
| ~ g(X1)
| ~ g(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_34])]) ).
cnf(c_0_116,negated_conjecture,
g(esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_108,c_0_78])]) ).
cnf(c_0_117,plain,
( g(inv(product(X1,eh)))
| ~ g(X1) ),
inference(spm,[status(thm)],[c_0_109,c_0_72]) ).
cnf(c_0_118,plain,
( opp(opp(X1)) = sum(eg,X1)
| ~ h(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_110]),c_0_42])]) ).
cnf(c_0_119,plain,
( sum(opp(X1),eg) = sum(eg,opp(X1))
| ~ h(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_40]),c_0_42])]) ).
cnf(c_0_120,plain,
( h(sum(sum(opp(X1),eg),f(X2)))
| ~ g(X2)
| ~ g(X3) ),
inference(spm,[status(thm)],[c_0_111,c_0_42]) ).
cnf(c_0_121,plain,
( opp(opp(X1)) = sum(X1,eg)
| ~ h(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_113]),c_0_42])]) ).
cnf(c_0_122,plain,
( product(product(inv(X1),X1),product(eh,X2)) = product(eh,X2)
| ~ g(X2)
| ~ g(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_96]),c_0_34])]),c_0_44]) ).
cnf(c_0_123,negated_conjecture,
( product(eh,product(eh,product(esk1_0,eh))) = product(eh,esk1_0)
| ~ g(X1) ),
inference(spm,[status(thm)],[c_0_115,c_0_116]) ).
cnf(c_0_124,plain,
( h(f(product(eh,X1)))
| ~ g(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_72]),c_0_58])]),c_0_38]) ).
cnf(c_0_125,plain,
( g(inv(inv(product(eh,X1))))
| ~ g(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_91]),c_0_117]) ).
cnf(c_0_126,plain,
( opp(sum(eg,X1)) = sum(eg,opp(X1))
| ~ h(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_118]),c_0_42])]) ).
cnf(c_0_127,plain,
( sum(eg,opp(X1)) = opp(X1)
| ~ h(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_119]),c_0_42])]) ).
cnf(c_0_128,negated_conjecture,
( h(sum(sum(opp(X1),eg),f(esk1_0)))
| ~ g(X2) ),
inference(spm,[status(thm)],[c_0_120,c_0_116]) ).
cnf(c_0_129,plain,
opp(eg) = eg,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_40]),c_0_42]),c_0_31])]) ).
cnf(c_0_130,plain,
( opp(sum(X1,eg)) = sum(opp(X1),eg)
| ~ h(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_121]),c_0_42])]) ).
cnf(c_0_131,plain,
( product(product(X1,eh),X2) = product(eh,product(X1,X2))
| ~ g(X2)
| ~ g(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_72]),c_0_34])]) ).
cnf(c_0_132,plain,
( product(product(inv(X1),X1),X2) = X2
| ~ g(X2)
| ~ g(X1) ),
inference(spm,[status(thm)],[c_0_122,c_0_32]) ).
cnf(c_0_133,plain,
( product(X1,product(X2,product(X3,eh))) = product(X1,product(X2,X3))
| ~ g(X1)
| ~ g(X3)
| ~ g(X2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_46]),c_0_34])]),c_0_54]) ).
cnf(c_0_134,negated_conjecture,
product(eh,product(eh,product(esk1_0,eh))) = product(eh,esk1_0),
inference(spm,[status(thm)],[c_0_123,c_0_116]) ).
cnf(c_0_135,plain,
( h(f(product(X1,product(X2,X3))))
| ~ h(f(product(X1,X2)))
| ~ g(X3)
| ~ g(X2)
| ~ g(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_46]),c_0_38]) ).
cnf(c_0_136,plain,
( h(f(product(X1,eh)))
| ~ g(X1) ),
inference(spm,[status(thm)],[c_0_124,c_0_72]) ).
cnf(c_0_137,plain,
( inv(product(X1,eh)) = product(eh,inv(X1))
| ~ g(X1) ),
inference(spm,[status(thm)],[c_0_82,c_0_72]) ).
cnf(c_0_138,plain,
( g(inv(inv(X1)))
| ~ g(X1) ),
inference(spm,[status(thm)],[c_0_125,c_0_32]) ).
cnf(c_0_139,plain,
( g(inv(inv(inv(product(eh,X1)))))
| ~ g(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_91]),c_0_117]) ).
cnf(c_0_140,plain,
( sum(eg,opp(opp(X1))) = opp(opp(X1))
| ~ h(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_127]),c_0_42])]) ).
cnf(c_0_141,negated_conjecture,
h(sum(sum(opp(X1),eg),f(esk1_0))),
inference(spm,[status(thm)],[c_0_128,c_0_116]) ).
cnf(c_0_142,plain,
sum(eg,eg) = eg,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_129]),c_0_31])]) ).
cnf(c_0_143,plain,
f(product(eh,X1)) = sum(eg,f(X1)),
inference(spm,[status(thm)],[c_0_25,c_0_78]) ).
cnf(c_0_144,plain,
( sum(opp(X1),eg) = opp(X1)
| ~ h(X1) ),
inference(spm,[status(thm)],[c_0_130,c_0_68]) ).
cnf(c_0_145,plain,
( product(eh,product(eh,X1)) = X1
| ~ g(X1) ),
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_131,c_0_132]),c_0_50]),c_0_50]),c_0_34]),c_0_34])]) ).
cnf(c_0_146,negated_conjecture,
product(eh,product(eh,esk1_0)) = product(eh,esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_134]),c_0_34]),c_0_116])]) ).
cnf(c_0_147,plain,
( h(f(product(X1,X2)))
| ~ g(X2)
| ~ g(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_32]),c_0_34])]),c_0_136]) ).
cnf(c_0_148,plain,
( product(eh,inv(inv(inv(X1)))) = inv(product(eh,X1))
| ~ g(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_61]),c_0_138]) ).
cnf(c_0_149,plain,
( g(inv(inv(inv(X1))))
| ~ g(X1) ),
inference(spm,[status(thm)],[c_0_139,c_0_32]) ).
cnf(c_0_150,plain,
( sum(eg,opp(opp(opp(X1)))) = opp(opp(opp(X1)))
| ~ h(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_140]),c_0_42])]) ).
cnf(c_0_151,plain,
( sum(X1,sum(X2,eg)) = sum(X1,X2)
| ~ h(X2)
| ~ h(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_41]),c_0_31])]),c_0_24]) ).
cnf(c_0_152,plain,
( sum(f(X1),sum(f(X2),X3)) = sum(f(product(X1,X2)),X3)
| ~ h(f(X2))
| ~ h(f(X1))
| ~ h(X3) ),
inference(spm,[status(thm)],[c_0_41,c_0_25]) ).
cnf(c_0_153,negated_conjecture,
h(sum(eg,f(esk1_0))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_129]),c_0_142]) ).
cnf(c_0_154,plain,
( sum(eg,f(X1)) = f(X1)
| ~ g(X1) ),
inference(spm,[status(thm)],[c_0_143,c_0_32]) ).
cnf(c_0_155,plain,
( sum(opp(opp(X1)),eg) = opp(opp(X1))
| ~ h(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_144]),c_0_42])]) ).
cnf(c_0_156,negated_conjecture,
product(eh,esk1_0) = esk1_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_146]),c_0_116])]) ).
cnf(c_0_157,plain,
( h(f(inv(product(eh,X1))))
| ~ g(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_148]),c_0_34])]),c_0_149]) ).
cnf(c_0_158,plain,
( sum(eg,opp(opp(opp(opp(X1))))) = opp(opp(opp(opp(X1))))
| ~ h(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_150]),c_0_42])]) ).
cnf(c_0_159,plain,
( opp(opp(opp(X1))) = sum(opp(X1),eg)
| ~ h(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_113]),c_0_42])]) ).
cnf(c_0_160,plain,
( sum(f(product(X1,X2)),eg) = f(product(X1,X2))
| ~ h(f(X2))
| ~ h(f(X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_152]),c_0_25]),c_0_31])]) ).
cnf(c_0_161,negated_conjecture,
h(f(esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_154]),c_0_116])]) ).
cnf(c_0_162,plain,
( sum(opp(opp(opp(X1))),eg) = opp(opp(opp(X1)))
| ~ h(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_155]),c_0_42])]) ).
cnf(c_0_163,negated_conjecture,
product(eh,inv(esk1_0)) = inv(esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_156]),c_0_116])]) ).
cnf(c_0_164,negated_conjecture,
h(f(inv(esk1_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_156]),c_0_116])]) ).
cnf(c_0_165,plain,
( opp(opp(opp(opp(X1)))) = sum(opp(opp(X1)),eg)
| ~ h(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_158,c_0_113]),c_0_42])]) ).
cnf(c_0_166,plain,
( opp(opp(sum(X1,eg))) = sum(sum(X1,eg),eg)
| ~ h(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_159,c_0_121]),c_0_42])]) ).
cnf(c_0_167,negated_conjecture,
sum(f(esk1_0),eg) = f(esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_160,c_0_156]),c_0_161]),c_0_78]),c_0_31])]) ).
cnf(c_0_168,plain,
( opp(opp(opp(X1))) = sum(eg,opp(X1))
| ~ h(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_162]),c_0_42])]) ).
cnf(c_0_169,negated_conjecture,
sum(f(inv(esk1_0)),eg) = f(inv(esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_160,c_0_163]),c_0_164]),c_0_78]),c_0_31])]) ).
cnf(c_0_170,plain,
( product(product(X1,X2),inv(X2)) = product(X1,eh)
| ~ g(X2)
| ~ g(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_52]),c_0_57]),c_0_34])]),c_0_44]) ).
cnf(c_0_171,plain,
( opp(opp(opp(sum(X1,eg)))) = sum(opp(sum(X1,eg)),eg)
| ~ h(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_121]),c_0_42])]) ).
cnf(c_0_172,negated_conjecture,
opp(opp(f(esk1_0))) = f(esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_167]),c_0_167]),c_0_161])]) ).
cnf(c_0_173,plain,
( opp(opp(sum(X1,eg))) = sum(eg,sum(X1,eg))
| ~ h(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_168,c_0_121]),c_0_42])]) ).
cnf(c_0_174,negated_conjecture,
opp(opp(f(inv(esk1_0)))) = f(inv(esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_169]),c_0_169]),c_0_164])]) ).
cnf(c_0_175,negated_conjecture,
( f(inv(esk1_0)) != opp(f(esk1_0))
| f(eh) != eg ),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
cnf(c_0_176,plain,
( sum(opp(f(X1)),f(product(X1,X2))) = sum(eg,f(X2))
| ~ h(f(X2))
| ~ h(f(X1)) ),
inference(spm,[status(thm)],[c_0_101,c_0_25]) ).
cnf(c_0_177,negated_conjecture,
product(esk1_0,inv(esk1_0)) = eh,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_170,c_0_156]),c_0_57]),c_0_116]),c_0_34])]) ).
cnf(c_0_178,negated_conjecture,
sum(opp(f(esk1_0)),eg) = opp(f(esk1_0)),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_171,c_0_167]),c_0_161])]),c_0_172]) ).
cnf(c_0_179,negated_conjecture,
sum(eg,f(inv(esk1_0))) = f(inv(esk1_0)),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_173,c_0_169]),c_0_164])]),c_0_174]) ).
cnf(c_0_180,negated_conjecture,
opp(f(esk1_0)) != f(inv(esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_175,c_0_78])]) ).
cnf(c_0_181,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_176,c_0_177]),c_0_78]),c_0_164]),c_0_161])]),c_0_178]),c_0_179]),c_0_180]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP776+1 : TPTP v9.2.1. Released v4.1.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.33 % Computer : n014.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Mon May 4 19:05:51 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 88.64/54.68 % Version : CSE_E---1.7
% 88.64/54.68 % Problem : theBenchmark.p
% 88.64/54.68 % SZS status Theorem for theBenchmark.p
% 88.64/54.68 % SZS output start CNFRefutation
% See solution above
% 89.06/55.08 % Total time : 40.214s
%------------------------------------------------------------------------------