TSTP Solution File: GRP778+1 by E---3.1
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- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1
% Problem : GRP778+1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n010.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 : 2400s
% WCLimit : 300s
% DateTime : Tue Oct 10 17:43:19 EDT 2023
% Result : Theorem 258.96s 33.21s
% Output : CNFRefutation 258.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 14
% Syntax : Number of formulae : 136 ( 128 unt; 0 def)
% Number of atoms : 148 ( 126 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 22 ( 10 ~; 8 |; 2 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 129 ( 0 sgn; 42 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(sos05,axiom,
! [X3,X4,X1,X2] : product(product(X2,X1),product(X4,X3)) = product(product(X2,X4),product(X1,X3)),
file('/export/starexec/sandbox/tmp/tmp.07gUmgRvo9/E---3.1_8945.p',sos05) ).
fof(sos06,axiom,
! [X2] : product(X2,X2) = X2,
file('/export/starexec/sandbox/tmp/tmp.07gUmgRvo9/E---3.1_8945.p',sos06) ).
fof(sos03,axiom,
! [X1,X2] : quotient(product(X2,X1),X1) = X2,
file('/export/starexec/sandbox/tmp/tmp.07gUmgRvo9/E---3.1_8945.p',sos03) ).
fof(sos04,axiom,
! [X1,X2] : product(quotient(X2,X1),X1) = X2,
file('/export/starexec/sandbox/tmp/tmp.07gUmgRvo9/E---3.1_8945.p',sos04) ).
fof(sos08,axiom,
! [X5,X6,X7] :
( d(X5,X6,X7)
<=> product(X5,X6) = product(X6,X7) ),
file('/export/starexec/sandbox/tmp/tmp.07gUmgRvo9/E---3.1_8945.p',sos08) ).
fof(sos14,axiom,
d(a1,b2,c1),
file('/export/starexec/sandbox/tmp/tmp.07gUmgRvo9/E---3.1_8945.p',sos14) ).
fof(sos01,axiom,
! [X1,X2] : difference(X2,product(X2,X1)) = X1,
file('/export/starexec/sandbox/tmp/tmp.07gUmgRvo9/E---3.1_8945.p',sos01) ).
fof(sos02,axiom,
! [X1,X2] : product(X2,difference(X2,X1)) = X1,
file('/export/starexec/sandbox/tmp/tmp.07gUmgRvo9/E---3.1_8945.p',sos02) ).
fof(sos12,axiom,
d(a,b,c1),
file('/export/starexec/sandbox/tmp/tmp.07gUmgRvo9/E---3.1_8945.p',sos12) ).
fof(sos07,axiom,
! [X1,X2] : product(product(product(X2,X1),X1),product(X1,product(X1,X2))) = X1,
file('/export/starexec/sandbox/tmp/tmp.07gUmgRvo9/E---3.1_8945.p',sos07) ).
fof(sos10,axiom,
d(a1,b,c),
file('/export/starexec/sandbox/tmp/tmp.07gUmgRvo9/E---3.1_8945.p',sos10) ).
fof(sos11,axiom,
d(a,b1,c),
file('/export/starexec/sandbox/tmp/tmp.07gUmgRvo9/E---3.1_8945.p',sos11) ).
fof(sos09,axiom,
! [X8,X9,X10] :
( m(X8,X9,X10)
<=> product(product(X8,X9),product(X9,X10)) = product(X8,X10) ),
file('/export/starexec/sandbox/tmp/tmp.07gUmgRvo9/E---3.1_8945.p',sos09) ).
fof(goals,conjecture,
m(b1,b,b2),
file('/export/starexec/sandbox/tmp/tmp.07gUmgRvo9/E---3.1_8945.p',goals) ).
fof(c_0_14,plain,
! [X19,X20,X21,X22] : product(product(X22,X21),product(X20,X19)) = product(product(X22,X20),product(X21,X19)),
inference(variable_rename,[status(thm)],[sos05]) ).
fof(c_0_15,plain,
! [X23] : product(X23,X23) = X23,
inference(variable_rename,[status(thm)],[sos06]) ).
cnf(c_0_16,plain,
product(product(X1,X2),product(X3,X4)) = product(product(X1,X3),product(X2,X4)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_17,plain,
product(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_18,plain,
! [X15,X16] : quotient(product(X16,X15),X15) = X16,
inference(variable_rename,[status(thm)],[sos03]) ).
cnf(c_0_19,plain,
product(product(X1,X2),product(X3,X2)) = product(product(X1,X3),X2),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,plain,
quotient(product(X1,X2),X2) = X1,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_21,plain,
product(product(X1,X2),X1) = product(X1,product(X2,X1)),
inference(spm,[status(thm)],[c_0_19,c_0_17]) ).
fof(c_0_22,plain,
! [X17,X18] : product(quotient(X18,X17),X17) = X18,
inference(variable_rename,[status(thm)],[sos04]) ).
fof(c_0_23,plain,
! [X26,X27,X28] :
( ( ~ d(X26,X27,X28)
| product(X26,X27) = product(X27,X28) )
& ( product(X26,X27) != product(X27,X28)
| d(X26,X27,X28) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos08])]) ).
cnf(c_0_24,plain,
quotient(product(X1,product(X2,X1)),X1) = product(X1,X2),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,plain,
product(quotient(X1,X2),X2) = X1,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_26,plain,
( product(X1,X2) = product(X2,X3)
| ~ d(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_27,plain,
d(a1,b2,c1),
inference(split_conjunct,[status(thm)],[sos14]) ).
fof(c_0_28,plain,
! [X11,X12] : difference(X12,product(X12,X11)) = X11,
inference(variable_rename,[status(thm)],[sos01]) ).
cnf(c_0_29,plain,
quotient(product(X1,X2),X1) = product(X1,quotient(X2,X1)),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_30,plain,
product(b2,c1) = product(a1,b2),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
fof(c_0_31,plain,
! [X13,X14] : product(X14,difference(X14,X13)) = X13,
inference(variable_rename,[status(thm)],[sos02]) ).
cnf(c_0_32,plain,
difference(X1,product(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_33,plain,
product(b2,quotient(c1,b2)) = a1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_20]) ).
cnf(c_0_34,plain,
product(X1,difference(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_35,plain,
quotient(c1,b2) = difference(b2,a1),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_36,plain,
d(a,b,c1),
inference(split_conjunct,[status(thm)],[sos12]) ).
cnf(c_0_37,plain,
product(product(X1,X2),product(difference(X1,X3),X4)) = product(X3,product(X2,X4)),
inference(spm,[status(thm)],[c_0_16,c_0_34]) ).
cnf(c_0_38,plain,
product(difference(b2,a1),b2) = c1,
inference(spm,[status(thm)],[c_0_25,c_0_35]) ).
cnf(c_0_39,plain,
product(a,b) = product(b,c1),
inference(spm,[status(thm)],[c_0_26,c_0_36]) ).
cnf(c_0_40,plain,
product(product(b2,X1),c1) = product(a1,product(X1,b2)),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_41,plain,
quotient(product(b,c1),b) = a,
inference(spm,[status(thm)],[c_0_20,c_0_39]) ).
fof(c_0_42,plain,
! [X24,X25] : product(product(product(X25,X24),X24),product(X24,product(X24,X25))) = X24,
inference(variable_rename,[status(thm)],[sos07]) ).
cnf(c_0_43,plain,
product(a1,product(difference(b2,X1),b2)) = product(X1,c1),
inference(spm,[status(thm)],[c_0_40,c_0_34]) ).
cnf(c_0_44,plain,
product(X1,quotient(difference(X1,X2),X1)) = quotient(X2,X1),
inference(spm,[status(thm)],[c_0_29,c_0_34]) ).
cnf(c_0_45,plain,
d(a1,b,c),
inference(split_conjunct,[status(thm)],[sos10]) ).
cnf(c_0_46,plain,
d(a,b1,c),
inference(split_conjunct,[status(thm)],[sos11]) ).
cnf(c_0_47,plain,
product(b,quotient(c1,b)) = a,
inference(rw,[status(thm)],[c_0_41,c_0_29]) ).
cnf(c_0_48,plain,
product(product(product(X1,X2),X2),product(X2,product(X2,X1))) = X2,
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_49,plain,
difference(a1,product(X1,c1)) = product(difference(b2,X1),b2),
inference(spm,[status(thm)],[c_0_32,c_0_43]) ).
cnf(c_0_50,plain,
product(quotient(X1,b2),c1) = product(a1,difference(b2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_44]),c_0_25]) ).
cnf(c_0_51,plain,
product(b,c) = product(a1,b),
inference(spm,[status(thm)],[c_0_26,c_0_45]) ).
cnf(c_0_52,plain,
product(a,b1) = product(b1,c),
inference(spm,[status(thm)],[c_0_26,c_0_46]) ).
cnf(c_0_53,plain,
quotient(c1,b) = difference(b,a),
inference(spm,[status(thm)],[c_0_32,c_0_47]) ).
cnf(c_0_54,plain,
difference(product(product(X1,X2),X2),X2) = product(X2,product(X2,X1)),
inference(spm,[status(thm)],[c_0_32,c_0_48]) ).
cnf(c_0_55,plain,
product(difference(b2,quotient(X1,b2)),b2) = difference(b2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_32]) ).
cnf(c_0_56,plain,
product(b,quotient(c,b)) = a1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_51]),c_0_20]) ).
cnf(c_0_57,plain,
quotient(product(b1,c),b1) = a,
inference(spm,[status(thm)],[c_0_20,c_0_52]) ).
cnf(c_0_58,plain,
product(difference(b,a),b) = c1,
inference(spm,[status(thm)],[c_0_25,c_0_53]) ).
cnf(c_0_59,plain,
product(X1,product(difference(X1,X2),X1)) = product(X2,X1),
inference(spm,[status(thm)],[c_0_21,c_0_34]) ).
cnf(c_0_60,plain,
difference(product(difference(b2,X1),b2),b2) = product(b2,quotient(X1,b2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_34]) ).
cnf(c_0_61,plain,
quotient(c,b) = difference(b,a1),
inference(spm,[status(thm)],[c_0_32,c_0_56]) ).
cnf(c_0_62,plain,
product(b1,quotient(c,b1)) = a,
inference(rw,[status(thm)],[c_0_57,c_0_29]) ).
cnf(c_0_63,plain,
product(product(b,X1),c1) = product(a,product(X1,b)),
inference(spm,[status(thm)],[c_0_37,c_0_58]) ).
cnf(c_0_64,plain,
product(product(difference(b2,X1),b2),X1) = product(X1,b2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_37]),c_0_25]),c_0_17]),c_0_59]) ).
cnf(c_0_65,plain,
product(difference(b,a1),b) = c,
inference(spm,[status(thm)],[c_0_25,c_0_61]) ).
cnf(c_0_66,plain,
quotient(c,b1) = difference(b1,a),
inference(spm,[status(thm)],[c_0_32,c_0_62]) ).
cnf(c_0_67,plain,
product(a,product(difference(b,X1),b)) = product(X1,c1),
inference(spm,[status(thm)],[c_0_63,c_0_34]) ).
cnf(c_0_68,plain,
product(X1,quotient(b2,X1)) = product(difference(b2,X1),b2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_64]),c_0_29]) ).
cnf(c_0_69,plain,
product(product(b,X1),c) = product(a1,product(X1,b)),
inference(spm,[status(thm)],[c_0_37,c_0_65]) ).
cnf(c_0_70,plain,
product(difference(b1,a),b1) = c,
inference(spm,[status(thm)],[c_0_25,c_0_66]) ).
cnf(c_0_71,plain,
difference(a,product(X1,c1)) = product(difference(b,X1),b),
inference(spm,[status(thm)],[c_0_32,c_0_67]) ).
cnf(c_0_72,plain,
product(product(difference(b2,b),b2),c1) = product(a,b2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_68]),c_0_25]) ).
cnf(c_0_73,plain,
product(a1,product(difference(b,X1),b)) = product(X1,c),
inference(spm,[status(thm)],[c_0_69,c_0_34]) ).
cnf(c_0_74,plain,
product(product(b1,X1),c) = product(a,product(X1,b1)),
inference(spm,[status(thm)],[c_0_37,c_0_70]) ).
cnf(c_0_75,plain,
product(difference(b,product(difference(b2,b),b2)),b) = b2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_32]) ).
cnf(c_0_76,plain,
difference(a1,product(X1,c)) = product(difference(b,X1),b),
inference(spm,[status(thm)],[c_0_32,c_0_73]) ).
cnf(c_0_77,plain,
quotient(product(a,product(X1,b1)),c) = product(b1,X1),
inference(spm,[status(thm)],[c_0_20,c_0_74]) ).
cnf(c_0_78,plain,
product(product(product(difference(X1,X2),X1),X1),product(X1,X2)) = X1,
inference(spm,[status(thm)],[c_0_48,c_0_34]) ).
cnf(c_0_79,plain,
difference(b,product(difference(b2,b),b2)) = quotient(b2,b),
inference(spm,[status(thm)],[c_0_20,c_0_75]) ).
cnf(c_0_80,plain,
product(difference(b,quotient(X1,c)),b) = difference(a1,X1),
inference(spm,[status(thm)],[c_0_76,c_0_25]) ).
cnf(c_0_81,plain,
quotient(product(a,X1),c) = product(b1,quotient(X1,b1)),
inference(spm,[status(thm)],[c_0_77,c_0_25]) ).
cnf(c_0_82,plain,
product(product(b2,b),product(b,product(difference(b2,b),b2))) = b,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_25]) ).
cnf(c_0_83,plain,
product(quotient(X1,c),b) = product(b,difference(a1,X1)),
inference(spm,[status(thm)],[c_0_59,c_0_80]) ).
cnf(c_0_84,plain,
quotient(product(b,c1),c) = product(b1,quotient(b,b1)),
inference(spm,[status(thm)],[c_0_81,c_0_39]) ).
cnf(c_0_85,plain,
product(b,product(difference(b2,b),b2)) = difference(product(b2,b),b),
inference(spm,[status(thm)],[c_0_32,c_0_82]) ).
cnf(c_0_86,plain,
product(product(b1,quotient(b,b1)),b) = difference(product(b2,b),b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_49]),c_0_85]) ).
cnf(c_0_87,plain,
product(difference(product(b2,b),b),b) = product(b,product(b,b2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_85]),c_0_64]) ).
cnf(c_0_88,plain,
product(product(X1,X2),product(X1,X3)) = product(X1,product(X2,X3)),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_89,plain,
product(b,product(b,product(b2,product(b1,quotient(b,b1))))) = b,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_86]),c_0_87]),c_0_88]),c_0_88]) ).
cnf(c_0_90,plain,
difference(X1,X1) = X1,
inference(spm,[status(thm)],[c_0_32,c_0_17]) ).
cnf(c_0_91,plain,
product(b,product(b2,product(b1,quotient(b,b1)))) = b,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_89]),c_0_90]) ).
cnf(c_0_92,plain,
product(b2,product(b1,quotient(b,b1))) = b,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_91]),c_0_90]) ).
cnf(c_0_93,plain,
product(b1,quotient(b,b1)) = difference(b2,b),
inference(spm,[status(thm)],[c_0_32,c_0_92]) ).
cnf(c_0_94,plain,
difference(b,difference(product(b2,b),b)) = product(difference(b2,b),b2),
inference(spm,[status(thm)],[c_0_32,c_0_85]) ).
cnf(c_0_95,plain,
difference(product(b2,b),b) = product(difference(b2,b),b),
inference(rw,[status(thm)],[c_0_86,c_0_93]) ).
cnf(c_0_96,plain,
difference(X1,product(X2,X1)) = product(difference(X1,X2),X1),
inference(spm,[status(thm)],[c_0_32,c_0_59]) ).
cnf(c_0_97,plain,
product(difference(b,difference(b2,b)),b) = product(difference(b2,b),b2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_94,c_0_95]),c_0_96]) ).
cnf(c_0_98,plain,
difference(X1,product(difference(b2,X1),b2)) = quotient(b2,X1),
inference(spm,[status(thm)],[c_0_32,c_0_68]) ).
cnf(c_0_99,plain,
product(b1,quotient(quotient(b,b1),b1)) = quotient(difference(b2,b),b1),
inference(spm,[status(thm)],[c_0_29,c_0_93]) ).
cnf(c_0_100,plain,
product(product(X1,X2),product(X2,product(X2,quotient(X1,X2)))) = X2,
inference(spm,[status(thm)],[c_0_48,c_0_25]) ).
cnf(c_0_101,plain,
product(difference(b,difference(b,difference(b2,b))),b) = quotient(b2,b),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_98]) ).
cnf(c_0_102,plain,
quotient(difference(X1,X2),X1) = difference(X1,quotient(X2,X1)),
inference(spm,[status(thm)],[c_0_32,c_0_44]) ).
cnf(c_0_103,plain,
product(b,product(b1,quotient(difference(b2,b),b1))) = b1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_99]),c_0_25]),c_0_25]) ).
cnf(c_0_104,plain,
product(quotient(b2,b),quotient(difference(b2,b),b)) = b,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_102]),c_0_102]),c_0_34]),c_0_34]) ).
cnf(c_0_105,plain,
product(b1,quotient(difference(b2,b),b1)) = difference(b,b1),
inference(spm,[status(thm)],[c_0_32,c_0_103]) ).
cnf(c_0_106,plain,
quotient(difference(b2,b),b) = difference(quotient(b2,b),b),
inference(spm,[status(thm)],[c_0_32,c_0_104]) ).
cnf(c_0_107,plain,
product(product(X1,quotient(X2,X3)),product(X4,X3)) = product(product(X1,X4),X2),
inference(spm,[status(thm)],[c_0_16,c_0_25]) ).
cnf(c_0_108,plain,
quotient(difference(b2,b),b1) = difference(b1,difference(b,b1)),
inference(spm,[status(thm)],[c_0_32,c_0_105]) ).
cnf(c_0_109,plain,
product(difference(quotient(b2,b),b),b) = difference(b2,b),
inference(spm,[status(thm)],[c_0_25,c_0_106]) ).
cnf(c_0_110,plain,
product(difference(b2,b),product(X1,b1)) = product(product(b1,X1),b),
inference(spm,[status(thm)],[c_0_107,c_0_93]) ).
cnf(c_0_111,plain,
product(difference(b1,difference(b,b1)),b1) = difference(b2,b),
inference(spm,[status(thm)],[c_0_25,c_0_108]) ).
cnf(c_0_112,plain,
difference(product(b,b2),b) = product(b,difference(b2,b)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_97]),c_0_64]),c_0_34]) ).
cnf(c_0_113,plain,
product(difference(b,difference(quotient(b2,b),b)),b) = difference(b,difference(b2,b)),
inference(spm,[status(thm)],[c_0_96,c_0_109]) ).
cnf(c_0_114,plain,
product(difference(b,b1),b) = difference(b2,b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_17]),c_0_34]) ).
cnf(c_0_115,plain,
difference(product(X1,X2),product(product(X1,X3),product(X2,X4))) = product(X3,X4),
inference(spm,[status(thm)],[c_0_32,c_0_16]) ).
cnf(c_0_116,plain,
product(product(b,b2),product(difference(b2,b),b)) = product(b,product(b,b2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_112]),c_0_88]),c_0_85]),c_0_95]) ).
cnf(c_0_117,plain,
product(b,difference(quotient(b2,b),b)) = difference(product(difference(b2,b),b2),b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_113]),c_0_97]),c_0_34]) ).
cnf(c_0_118,plain,
difference(quotient(b2,b),b) = difference(b,b1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_114]),c_0_106]) ).
cnf(c_0_119,plain,
difference(product(b,difference(b2,b)),product(b,product(b,b2))) = product(b2,b),
inference(spm,[status(thm)],[c_0_115,c_0_116]) ).
cnf(c_0_120,plain,
product(b,difference(b2,b)) = product(b1,b),
inference(spm,[status(thm)],[c_0_59,c_0_114]) ).
cnf(c_0_121,plain,
quotient(X1,difference(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_20,c_0_34]) ).
cnf(c_0_122,plain,
difference(product(difference(b2,b),b2),b) = b1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_117,c_0_118]),c_0_34]) ).
fof(c_0_123,plain,
! [X29,X30,X31] :
( ( ~ m(X29,X30,X31)
| product(product(X29,X30),product(X30,X31)) = product(X29,X31) )
& ( product(product(X29,X30),product(X30,X31)) != product(X29,X31)
| m(X29,X30,X31) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos09])]) ).
cnf(c_0_124,plain,
difference(product(b1,b),product(b,product(b,b2))) = product(b2,b),
inference(rw,[status(thm)],[c_0_119,c_0_120]) ).
cnf(c_0_125,plain,
product(b,product(difference(b2,b),b2)) = product(difference(b2,b),b),
inference(rw,[status(thm)],[c_0_85,c_0_95]) ).
cnf(c_0_126,plain,
product(difference(b2,b),b2) = quotient(b,b1),
inference(spm,[status(thm)],[c_0_121,c_0_122]) ).
cnf(c_0_127,plain,
( m(X1,X2,X3)
| product(product(X1,X2),product(X2,X3)) != product(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_123]) ).
cnf(c_0_128,plain,
product(product(b1,b2),b) = product(b,product(b,b2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_124]),c_0_19]) ).
cnf(c_0_129,plain,
product(b,quotient(b,b1)) = product(difference(b2,b),b),
inference(rw,[status(thm)],[c_0_125,c_0_126]) ).
fof(c_0_130,negated_conjecture,
~ m(b1,b,b2),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[goals])]) ).
cnf(c_0_131,plain,
( m(X1,product(X2,X3),X2)
| product(product(X1,X2),product(product(X2,X3),product(X3,X2))) != product(X1,X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_21]),c_0_16]) ).
cnf(c_0_132,plain,
product(difference(b2,b),b) = product(b1,b2),
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_20,c_0_128]),c_0_29]),c_0_29]),c_0_68]),c_0_126]),c_0_129]) ).
cnf(c_0_133,negated_conjecture,
~ m(b1,b,b2),
inference(split_conjunct,[status(thm)],[c_0_130]) ).
cnf(c_0_134,plain,
( m(X1,b,b2)
| product(product(X1,b1),b2) != product(X1,b2) ),
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_131,c_0_126]),c_0_34]),c_0_34]),c_0_129]),c_0_132]),c_0_19]) ).
cnf(c_0_135,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_134]),c_0_17])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.14 % Problem : GRP778+1 : TPTP v8.1.2. Released v4.1.0.
% 0.13/0.15 % Command : run_E %s %d THM
% 0.13/0.36 % Computer : n010.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 2400
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Tue Oct 3 02:38:35 EDT 2023
% 0.13/0.36 % CPUTime :
% 0.20/0.50 Running first-order theorem proving
% 0.20/0.50 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.07gUmgRvo9/E---3.1_8945.p
% 258.96/33.21 # Version: 3.1pre001
% 258.96/33.21 # Preprocessing class: FSMSSMSMSSSNFFN.
% 258.96/33.21 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 258.96/33.21 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 258.96/33.21 # Starting new_bool_3 with 300s (1) cores
% 258.96/33.21 # Starting new_bool_1 with 300s (1) cores
% 258.96/33.21 # Starting sh5l with 300s (1) cores
% 258.96/33.21 # G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 9023 completed with status 0
% 258.96/33.21 # Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 258.96/33.21 # Preprocessing class: FSMSSMSMSSSNFFN.
% 258.96/33.21 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 258.96/33.21 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 258.96/33.21 # No SInE strategy applied
% 258.96/33.21 # Search class: FHUSM-FFSM22-MFFFFFNN
% 258.96/33.21 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 258.96/33.21 # Starting G-E--_207_C41_F1_AE_CS_SP_PI_S0Y with 811s (1) cores
% 258.96/33.21 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 258.96/33.21 # Starting new_bool_3 with 136s (1) cores
% 258.96/33.21 # Starting new_bool_1 with 136s (1) cores
% 258.96/33.21 # Starting sh5l with 136s (1) cores
% 258.96/33.21 # G-E--_207_C41_F1_AE_CS_SP_PI_S0Y with pid 9028 completed with status 0
% 258.96/33.21 # Result found by G-E--_207_C41_F1_AE_CS_SP_PI_S0Y
% 258.96/33.21 # Preprocessing class: FSMSSMSMSSSNFFN.
% 258.96/33.21 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 258.96/33.21 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 258.96/33.21 # No SInE strategy applied
% 258.96/33.21 # Search class: FHUSM-FFSM22-MFFFFFNN
% 258.96/33.21 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 258.96/33.21 # Starting G-E--_207_C41_F1_AE_CS_SP_PI_S0Y with 811s (1) cores
% 258.96/33.21 # Preprocessing time : 0.001 s
% 258.96/33.21
% 258.96/33.21 # Proof found!
% 258.96/33.21 # SZS status Theorem
% 258.96/33.21 # SZS output start CNFRefutation
% See solution above
% 258.96/33.21 # Parsed axioms : 16
% 258.96/33.21 # Removed by relevancy pruning/SinE : 0
% 258.96/33.21 # Initial clauses : 18
% 258.96/33.21 # Removed in clause preprocessing : 0
% 258.96/33.21 # Initial clauses in saturation : 18
% 258.96/33.21 # Processed clauses : 8841
% 258.96/33.21 # ...of these trivial : 1011
% 258.96/33.21 # ...subsumed : 3087
% 258.96/33.21 # ...remaining for further processing : 4743
% 258.96/33.21 # Other redundant clauses eliminated : 0
% 258.96/33.21 # Clauses deleted for lack of memory : 0
% 258.96/33.21 # Backward-subsumed : 18
% 258.96/33.21 # Backward-rewritten : 898
% 258.96/33.21 # Generated clauses : 1792769
% 258.96/33.21 # ...of the previous two non-redundant : 1774777
% 258.96/33.21 # ...aggressively subsumed : 0
% 258.96/33.21 # Contextual simplify-reflections : 15
% 258.96/33.21 # Paramodulations : 1792769
% 258.96/33.21 # Factorizations : 0
% 258.96/33.21 # NegExts : 0
% 258.96/33.21 # Equation resolutions : 0
% 258.96/33.21 # Total rewrite steps : 307623
% 258.96/33.21 # Propositional unsat checks : 0
% 258.96/33.21 # Propositional check models : 0
% 258.96/33.21 # Propositional check unsatisfiable : 0
% 258.96/33.21 # Propositional clauses : 0
% 258.96/33.21 # Propositional clauses after purity: 0
% 258.96/33.21 # Propositional unsat core size : 0
% 258.96/33.21 # Propositional preprocessing time : 0.000
% 258.96/33.21 # Propositional encoding time : 0.000
% 258.96/33.21 # Propositional solver time : 0.000
% 258.96/33.21 # Success case prop preproc time : 0.000
% 258.96/33.21 # Success case prop encoding time : 0.000
% 258.96/33.21 # Success case prop solver time : 0.000
% 258.96/33.21 # Current number of processed clauses : 3827
% 258.96/33.21 # Positive orientable unit clauses : 1715
% 258.96/33.21 # Positive unorientable unit clauses: 143
% 258.96/33.21 # Negative unit clauses : 1
% 258.96/33.21 # Non-unit-clauses : 1968
% 258.96/33.21 # Current number of unprocessed clauses: 1765191
% 258.96/33.21 # ...number of literals in the above : 1952499
% 258.96/33.21 # Current number of archived formulas : 0
% 258.96/33.21 # Current number of archived clauses : 916
% 258.96/33.21 # Clause-clause subsumption calls (NU) : 93765
% 258.96/33.21 # Rec. Clause-clause subsumption calls : 90145
% 258.96/33.21 # Non-unit clause-clause subsumptions : 2995
% 258.96/33.21 # Unit Clause-clause subsumption calls : 3831
% 258.96/33.21 # Rewrite failures with RHS unbound : 0
% 258.96/33.21 # BW rewrite match attempts : 21915
% 258.96/33.21 # BW rewrite match successes : 1907
% 258.96/33.21 # Condensation attempts : 0
% 258.96/33.21 # Condensation successes : 0
% 258.96/33.21 # Termbank termtop insertions : 43055759
% 258.96/33.21
% 258.96/33.21 # -------------------------------------------------
% 258.96/33.21 # User time : 30.540 s
% 258.96/33.21 # System time : 1.168 s
% 258.96/33.21 # Total time : 31.708 s
% 258.96/33.21 # Maximum resident set size: 1712 pages
% 258.96/33.21
% 258.96/33.21 # -------------------------------------------------
% 258.96/33.21 # User time : 158.969 s
% 258.96/33.21 # System time : 1.938 s
% 258.96/33.21 # Total time : 160.907 s
% 258.96/33.21 # Maximum resident set size: 1688 pages
% 258.96/33.21 % E---3.1 exiting
% 258.96/33.21 % E---3.1 exiting
%------------------------------------------------------------------------------