%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP778+1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:41:14 PM UTC 2026
% Result : Theorem 77.24s 11.62s
% Output : CNFRefutation 77.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 14
% Syntax : Number of formulae : 175 ( 169 unt; 0 def)
% Number of atoms : 185 ( 163 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 20 ( 10 ~; 6 |; 2 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 1 avg)
% Maximal term depth : 4 ( 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 : 255 ( 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/benchmark/theBenchmark.p',sos05) ).
fof(sos06,axiom,
! [X2] : product(X2,X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos06) ).
fof(sos03,axiom,
! [X1,X2] : quotient(product(X2,X1),X1) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos03) ).
fof(sos01,axiom,
! [X1,X2] : difference(X2,product(X2,X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos01) ).
fof(sos07,axiom,
! [X1,X2] : product(product(product(X2,X1),X1),product(X1,product(X1,X2))) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos07) ).
fof(sos04,axiom,
! [X1,X2] : product(quotient(X2,X1),X1) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos04) ).
fof(sos02,axiom,
! [X1,X2] : product(X2,difference(X2,X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos02) ).
fof(sos08,axiom,
! [X5,X6,X7] :
( d(X5,X6,X7)
<=> product(X5,X6) = product(X6,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos08) ).
fof(sos11,axiom,
d(a,b1,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos11) ).
fof(sos10,axiom,
d(a1,b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos10) ).
fof(sos12,axiom,
d(a,b,c1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos12) ).
fof(sos14,axiom,
d(a1,b2,c1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos14) ).
fof(goals,conjecture,
m(b1,b,b2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(sos09,axiom,
! [X8,X9,X10] :
( m(X8,X9,X10)
<=> product(product(X8,X9),product(X9,X10)) = product(X8,X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos09) ).
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]) ).
fof(c_0_20,plain,
! [X11,X12] : difference(X12,product(X12,X11)) = X11,
inference(variable_rename,[status(thm)],[sos01]) ).
fof(c_0_21,plain,
! [X24,X25] : product(product(product(X25,X24),X24),product(X24,product(X24,X25))) = X24,
inference(variable_rename,[status(thm)],[sos07]) ).
cnf(c_0_22,plain,
quotient(product(X1,X2),X2) = X1,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,plain,
product(product(X1,X2),X1) = product(X1,product(X2,X1)),
inference(spm,[status(thm)],[c_0_19,c_0_17]) ).
fof(c_0_24,plain,
! [X17,X18] : product(quotient(X18,X17),X17) = X18,
inference(variable_rename,[status(thm)],[sos04]) ).
cnf(c_0_25,plain,
difference(X1,product(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_26,plain,
product(product(product(X1,X2),X2),product(X2,product(X2,X1))) = X2,
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_27,plain,
quotient(product(X1,product(X2,X1)),X1) = product(X1,X2),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_28,plain,
product(quotient(X1,X2),X2) = X1,
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_29,plain,
difference(product(product(X1,X2),X2),X2) = product(X2,product(X2,X1)),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
fof(c_0_30,plain,
! [X13,X14] : product(X14,difference(X14,X13)) = X13,
inference(variable_rename,[status(thm)],[sos02]) ).
cnf(c_0_31,plain,
quotient(product(X1,X2),X1) = product(X1,quotient(X2,X1)),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,plain,
product(X1,product(X1,quotient(X2,X1))) = difference(product(X2,X1),X1),
inference(spm,[status(thm)],[c_0_29,c_0_28]) ).
cnf(c_0_33,plain,
product(X1,difference(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_34,plain,
quotient(difference(product(X1,X2),X2),X2) = difference(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_31]),c_0_32]),c_0_28]) ).
fof(c_0_35,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(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos08])])]) ).
cnf(c_0_36,plain,
quotient(X1,difference(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_22,c_0_33]) ).
cnf(c_0_37,plain,
difference(product(X1,X2),X2) = product(difference(X1,X2),X2),
inference(spm,[status(thm)],[c_0_28,c_0_34]) ).
cnf(c_0_38,plain,
product(X1,product(difference(X1,X2),X1)) = product(X2,X1),
inference(spm,[status(thm)],[c_0_23,c_0_33]) ).
cnf(c_0_39,plain,
quotient(X1,product(X1,product(X1,X2))) = product(product(X2,X1),X1),
inference(spm,[status(thm)],[c_0_22,c_0_26]) ).
cnf(c_0_40,plain,
( ~ d(X1,X2,X3)
| product(X1,X2) = product(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_41,plain,
d(a,b1,c),
inference(split_conjunct,[status(thm)],[sos11]) ).
cnf(c_0_42,plain,
d(a1,b,c),
inference(split_conjunct,[status(thm)],[sos10]) ).
cnf(c_0_43,plain,
quotient(X1,product(difference(X2,X1),X1)) = product(X2,X1),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_44,plain,
difference(quotient(X1,X2),X1) = X2,
inference(spm,[status(thm)],[c_0_25,c_0_28]) ).
cnf(c_0_45,plain,
difference(X1,product(X2,X1)) = product(difference(X1,X2),X1),
inference(spm,[status(thm)],[c_0_25,c_0_38]) ).
cnf(c_0_46,plain,
product(product(difference(X1,X2),X1),X1) = quotient(X1,product(X1,X2)),
inference(spm,[status(thm)],[c_0_39,c_0_33]) ).
cnf(c_0_47,plain,
product(a,b1) = product(b1,c),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_48,plain,
product(b,c) = product(a1,b),
inference(spm,[status(thm)],[c_0_40,c_0_42]) ).
cnf(c_0_49,plain,
quotient(X1,product(X2,X1)) = product(quotient(X1,X2),X1),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_50,plain,
difference(X1,quotient(X1,product(X1,X2))) = quotient(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_45]),c_0_46]),c_0_33]) ).
cnf(c_0_51,plain,
product(product(quotient(X1,X2),X3),X2) = product(X1,product(X3,X2)),
inference(spm,[status(thm)],[c_0_19,c_0_28]) ).
cnf(c_0_52,plain,
product(product(product(b1,c),b1),product(b1,product(b1,a))) = b1,
inference(spm,[status(thm)],[c_0_26,c_0_47]) ).
cnf(c_0_53,plain,
d(a,b,c1),
inference(split_conjunct,[status(thm)],[sos12]) ).
cnf(c_0_54,plain,
product(b,quotient(c,b)) = a1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_48]),c_0_22]) ).
cnf(c_0_55,plain,
product(quotient(X1,quotient(X2,X1)),X1) = quotient(X1,X2),
inference(spm,[status(thm)],[c_0_49,c_0_28]) ).
cnf(c_0_56,plain,
quotient(X1,product(X1,X2)) = product(X1,quotient(X1,X2)),
inference(spm,[status(thm)],[c_0_33,c_0_50]) ).
cnf(c_0_57,plain,
quotient(product(X1,product(X2,X3)),X3) = product(quotient(X1,X3),X2),
inference(spm,[status(thm)],[c_0_22,c_0_51]) ).
cnf(c_0_58,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_59,plain,
product(b1,product(product(c,b1),product(b1,a))) = b1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_52,c_0_23]),c_0_16]),c_0_17]) ).
cnf(c_0_60,plain,
difference(X1,X1) = X1,
inference(spm,[status(thm)],[c_0_25,c_0_17]) ).
cnf(c_0_61,plain,
product(a,b) = product(b,c1),
inference(spm,[status(thm)],[c_0_40,c_0_53]) ).
cnf(c_0_62,plain,
quotient(c,b) = difference(b,a1),
inference(spm,[status(thm)],[c_0_25,c_0_54]) ).
cnf(c_0_63,plain,
product(product(X1,quotient(X2,X3)),product(X4,X3)) = product(product(X1,X4),X2),
inference(spm,[status(thm)],[c_0_16,c_0_28]) ).
cnf(c_0_64,plain,
product(quotient(X1,X2),quotient(X2,X1)) = product(difference(X2,X1),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_55]),c_0_32]),c_0_37]) ).
cnf(c_0_65,plain,
difference(product(X1,quotient(X1,X2)),X1) = product(X1,X2),
inference(spm,[status(thm)],[c_0_44,c_0_56]) ).
cnf(c_0_66,plain,
product(quotient(product(X1,X2),X3),X1) = product(quotient(X1,X3),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_57]) ).
cnf(c_0_67,plain,
d(a1,b2,c1),
inference(split_conjunct,[status(thm)],[sos14]) ).
cnf(c_0_68,plain,
product(product(c,b1),product(b1,a)) = b1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_59]),c_0_60]) ).
cnf(c_0_69,plain,
product(product(X1,X2),product(X3,difference(X2,X4))) = product(product(X1,X3),X4),
inference(spm,[status(thm)],[c_0_16,c_0_33]) ).
cnf(c_0_70,plain,
product(product(X1,a),product(X2,b)) = product(product(X1,X2),product(b,c1)),
inference(spm,[status(thm)],[c_0_16,c_0_61]) ).
cnf(c_0_71,plain,
product(product(a,X1),product(b,X2)) = product(product(b,c1),product(X1,X2)),
inference(spm,[status(thm)],[c_0_16,c_0_61]) ).
cnf(c_0_72,plain,
difference(product(c,b),b) = product(b,a1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_62]),c_0_33]) ).
cnf(c_0_73,plain,
product(product(difference(X1,X2),X3),X2) = product(X2,product(X3,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_19]),c_0_51]) ).
cnf(c_0_74,plain,
product(difference(b,a1),b) = c,
inference(spm,[status(thm)],[c_0_28,c_0_62]) ).
cnf(c_0_75,plain,
difference(product(X1,X2),X1) = product(X1,difference(X2,X1)),
inference(spm,[status(thm)],[c_0_65,c_0_36]) ).
cnf(c_0_76,plain,
quotient(product(quotient(X1,X2),X3),X1) = quotient(product(X1,X3),X2),
inference(spm,[status(thm)],[c_0_22,c_0_66]) ).
cnf(c_0_77,plain,
product(product(difference(X1,X2),X1),X1) = product(X1,quotient(X1,X2)),
inference(rw,[status(thm)],[c_0_46,c_0_56]) ).
cnf(c_0_78,plain,
quotient(quotient(X1,X2),X1) = quotient(X1,quotient(X2,X1)),
inference(spm,[status(thm)],[c_0_22,c_0_55]) ).
cnf(c_0_79,plain,
product(b2,c1) = product(a1,b2),
inference(spm,[status(thm)],[c_0_40,c_0_67]) ).
cnf(c_0_80,plain,
difference(product(c,b1),b1) = product(b1,a),
inference(spm,[status(thm)],[c_0_25,c_0_68]) ).
cnf(c_0_81,plain,
product(X1,product(X2,difference(X1,X3))) = product(product(X1,X2),X3),
inference(spm,[status(thm)],[c_0_69,c_0_17]) ).
cnf(c_0_82,plain,
product(product(b,X1),c1) = product(a,product(X1,b)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_17]),c_0_19]) ).
cnf(c_0_83,plain,
product(b,quotient(a1,b)) = difference(c,b),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_72]),c_0_31]) ).
cnf(c_0_84,plain,
product(c,a1) = product(a1,b),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_17]) ).
cnf(c_0_85,plain,
difference(c,product(a1,b)) = product(difference(c,b),c),
inference(spm,[status(thm)],[c_0_45,c_0_48]) ).
cnf(c_0_86,plain,
product(X1,difference(difference(X1,X2),X1)) = difference(X2,X1),
inference(spm,[status(thm)],[c_0_75,c_0_33]) ).
cnf(c_0_87,plain,
product(X1,product(X1,quotient(X2,X1))) = product(difference(X2,X1),X1),
inference(rw,[status(thm)],[c_0_32,c_0_37]) ).
cnf(c_0_88,plain,
quotient(product(X1,quotient(X2,X1)),X2) = difference(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_64]),c_0_22]) ).
cnf(c_0_89,plain,
product(X1,quotient(X1,quotient(X2,X1))) = product(difference(X1,X2),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_77]),c_0_31]),c_0_78]) ).
cnf(c_0_90,plain,
product(b2,quotient(c1,b2)) = a1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_79]),c_0_22]) ).
cnf(c_0_91,plain,
quotient(a,product(b1,c)) = product(a,quotient(a,b1)),
inference(spm,[status(thm)],[c_0_56,c_0_47]) ).
cnf(c_0_92,plain,
product(product(a,X1),product(b1,X2)) = product(product(b1,c),product(X1,X2)),
inference(spm,[status(thm)],[c_0_16,c_0_47]) ).
cnf(c_0_93,plain,
product(b1,quotient(a,b1)) = difference(c,b1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_80]),c_0_31]) ).
cnf(c_0_94,plain,
difference(X1,product(product(X1,X2),X3)) = product(X2,difference(X1,X3)),
inference(spm,[status(thm)],[c_0_25,c_0_81]) ).
cnf(c_0_95,plain,
product(difference(c,b),c1) = product(a,a1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_28]) ).
cnf(c_0_96,plain,
product(difference(c,b),c) = a1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_84]),c_0_85]) ).
cnf(c_0_97,plain,
product(X1,product(difference(X1,X2),X3)) = product(X2,product(X1,X3)),
inference(spm,[status(thm)],[c_0_58,c_0_33]) ).
cnf(c_0_98,plain,
product(product(X1,quotient(X2,X3)),X3) = product(product(X1,X3),X2),
inference(spm,[status(thm)],[c_0_19,c_0_28]) ).
cnf(c_0_99,plain,
product(difference(quotient(X1,X2),X2),X2) = difference(X1,X2),
inference(spm,[status(thm)],[c_0_37,c_0_28]) ).
cnf(c_0_100,plain,
difference(difference(X1,X2),X1) = difference(X1,difference(X2,X1)),
inference(spm,[status(thm)],[c_0_25,c_0_86]) ).
cnf(c_0_101,plain,
product(difference(X1,difference(X2,X1)),X1) = product(X1,quotient(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_87]),c_0_45]) ).
cnf(c_0_102,plain,
difference(product(X1,quotient(X2,X1)),X2) = product(difference(X1,X2),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_88]),c_0_33]),c_0_56]),c_0_89]) ).
cnf(c_0_103,plain,
quotient(c1,b2) = difference(b2,a1),
inference(spm,[status(thm)],[c_0_25,c_0_90]) ).
cnf(c_0_104,plain,
product(difference(c,b1),c) = a,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_91]),c_0_92]),c_0_19]),c_0_93]) ).
cnf(c_0_105,plain,
product(X1,difference(X2,product(X3,X1))) = product(X3,difference(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_19]),c_0_94]) ).
cnf(c_0_106,plain,
difference(difference(c,b),product(a,a1)) = c1,
inference(spm,[status(thm)],[c_0_25,c_0_95]) ).
cnf(c_0_107,plain,
difference(difference(c,b),a1) = c,
inference(spm,[status(thm)],[c_0_25,c_0_96]) ).
cnf(c_0_108,plain,
product(quotient(X1,X2),difference(X1,X3)) = product(quotient(X3,X2),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_97]),c_0_57]) ).
cnf(c_0_109,plain,
quotient(product(product(X1,X2),X3),X2) = product(X1,quotient(X3,X2)),
inference(spm,[status(thm)],[c_0_22,c_0_98]) ).
cnf(c_0_110,plain,
product(X1,quotient(product(X2,X3),X1)) = product(difference(X3,X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_73]),c_0_31]) ).
cnf(c_0_111,plain,
product(difference(X1,X2),X1) = product(X2,quotient(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_88]),c_0_100]),c_0_101]),c_0_102]) ).
cnf(c_0_112,plain,
product(difference(X1,X2),difference(X1,X3)) = difference(X1,product(X2,X3)),
inference(spm,[status(thm)],[c_0_94,c_0_33]) ).
cnf(c_0_113,plain,
difference(product(X1,X2),product(X1,product(X2,X1))) = X1,
inference(spm,[status(thm)],[c_0_25,c_0_23]) ).
cnf(c_0_114,plain,
product(difference(c,b),b) = product(b,a1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_83]),c_0_28]) ).
cnf(c_0_115,plain,
product(difference(b2,a1),b2) = c1,
inference(spm,[status(thm)],[c_0_28,c_0_103]) ).
cnf(c_0_116,plain,
product(product(a,c),product(c,b1)) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_104]),c_0_33]) ).
cnf(c_0_117,plain,
product(a,c) = product(a1,c1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_107]) ).
cnf(c_0_118,plain,
quotient(a1,c) = difference(c,b),
inference(spm,[status(thm)],[c_0_22,c_0_96]) ).
cnf(c_0_119,plain,
product(quotient(X1,difference(X2,X3)),X3) = product(X2,difference(X3,X1)),
inference(spm,[status(thm)],[c_0_108,c_0_36]) ).
cnf(c_0_120,plain,
quotient(product(X1,X2),product(X1,X3)) = product(X1,quotient(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_22]),c_0_109]) ).
cnf(c_0_121,plain,
product(difference(quotient(X1,X2),X3),X2) = difference(X1,product(X3,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_110]),c_0_112]) ).
cnf(c_0_122,plain,
product(difference(a1,b),a1) = difference(c,b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_96]),c_0_33]),c_0_114]),c_0_45]) ).
cnf(c_0_123,plain,
product(c1,a1) = product(a1,b2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_115]),c_0_17]) ).
cnf(c_0_124,plain,
difference(product(X1,X2),product(product(X1,X3),product(X2,X4))) = product(X3,X4),
inference(spm,[status(thm)],[c_0_25,c_0_16]) ).
cnf(c_0_125,plain,
product(product(a1,c1),product(c,b1)) = c,
inference(rw,[status(thm)],[c_0_116,c_0_117]) ).
cnf(c_0_126,plain,
product(difference(a1,c),c) = product(c,b),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_118]),c_0_33]) ).
cnf(c_0_127,plain,
quotient(product(X1,difference(X2,X3)),X2) = quotient(X3,difference(X1,X2)),
inference(spm,[status(thm)],[c_0_22,c_0_119]) ).
cnf(c_0_128,plain,
difference(product(X1,X2),product(X1,X3)) = product(X1,difference(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_120]),c_0_58]),c_0_120]),c_0_88]) ).
cnf(c_0_129,plain,
quotient(difference(X1,product(X2,X3)),X3) = difference(quotient(X1,X3),X2),
inference(spm,[status(thm)],[c_0_22,c_0_121]) ).
cnf(c_0_130,plain,
quotient(difference(c,b),a1) = difference(a1,b),
inference(spm,[status(thm)],[c_0_22,c_0_122]) ).
cnf(c_0_131,plain,
product(difference(a1,c1),a1) = b2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_123]),c_0_25]) ).
cnf(c_0_132,plain,
product(difference(X1,quotient(X2,X1)),X1) = difference(X1,X2),
inference(spm,[status(thm)],[c_0_45,c_0_28]) ).
cnf(c_0_133,plain,
product(c,b) = product(c1,b1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_125]),c_0_37]),c_0_126]) ).
cnf(c_0_134,plain,
quotient(product(X1,X2),difference(X2,X3)) = quotient(X2,difference(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_105]),c_0_127]) ).
cnf(c_0_135,plain,
product(X1,difference(difference(X1,X2),X3)) = difference(X2,product(X1,X3)),
inference(spm,[status(thm)],[c_0_128,c_0_33]) ).
cnf(c_0_136,plain,
difference(difference(a1,b),a) = quotient(c1,a1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_106]),c_0_130]) ).
cnf(c_0_137,plain,
product(a1,quotient(c1,a1)) = difference(b2,a1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_131]),c_0_100]),c_0_101]) ).
cnf(c_0_138,plain,
product(difference(X1,X2),quotient(X2,X1)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_132]),c_0_17]),c_0_28]) ).
cnf(c_0_139,plain,
quotient(product(c1,b1),b) = c,
inference(spm,[status(thm)],[c_0_22,c_0_133]) ).
cnf(c_0_140,plain,
quotient(product(b,c1),b) = a,
inference(spm,[status(thm)],[c_0_22,c_0_61]) ).
cnf(c_0_141,plain,
product(X1,quotient(X2,difference(X1,X3))) = quotient(product(X1,X2),X3),
inference(spm,[status(thm)],[c_0_120,c_0_33]) ).
cnf(c_0_142,plain,
quotient(X1,difference(X2,product(X1,X3))) = quotient(product(X2,X1),X3),
inference(spm,[status(thm)],[c_0_134,c_0_25]) ).
cnf(c_0_143,plain,
difference(b,product(a1,a)) = difference(b2,a1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_136]),c_0_137]) ).
cnf(c_0_144,plain,
difference(difference(X1,X2),X2) = quotient(X2,X1),
inference(spm,[status(thm)],[c_0_25,c_0_138]) ).
cnf(c_0_145,plain,
product(difference(b1,b),c1) = product(a1,b),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_139]),c_0_48]) ).
cnf(c_0_146,plain,
product(b,quotient(c1,b)) = a,
inference(rw,[status(thm)],[c_0_140,c_0_31]) ).
cnf(c_0_147,plain,
difference(X1,quotient(product(X1,X2),X3)) = quotient(X2,difference(X1,X3)),
inference(spm,[status(thm)],[c_0_25,c_0_141]) ).
cnf(c_0_148,plain,
quotient(product(b,a1),a) = b2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_143]),c_0_36]) ).
cnf(c_0_149,plain,
quotient(quotient(product(X1,X2),X3),X2) = quotient(X1,quotient(X3,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_144]),c_0_129]),c_0_144]) ).
cnf(c_0_150,plain,
quotient(product(a1,b),c1) = difference(b1,b),
inference(spm,[status(thm)],[c_0_22,c_0_145]) ).
cnf(c_0_151,plain,
quotient(difference(X1,X2),X2) = difference(quotient(X1,X2),X2),
inference(spm,[status(thm)],[c_0_22,c_0_99]) ).
cnf(c_0_152,plain,
quotient(c1,b) = difference(b,a),
inference(spm,[status(thm)],[c_0_25,c_0_146]) ).
cnf(c_0_153,plain,
quotient(a1,difference(b,a)) = difference(b,b2),
inference(spm,[status(thm)],[c_0_147,c_0_148]) ).
cnf(c_0_154,plain,
product(X1,quotient(X1,difference(X1,X2))) = quotient(X1,X2),
inference(spm,[status(thm)],[c_0_56,c_0_33]) ).
cnf(c_0_155,plain,
product(product(X1,X2),product(difference(X1,X3),X4)) = product(X3,product(X2,X4)),
inference(spm,[status(thm)],[c_0_16,c_0_33]) ).
cnf(c_0_156,plain,
product(X1,product(difference(X2,X1),X2)) = product(difference(X2,X1),X1),
inference(spm,[status(thm)],[c_0_73,c_0_17]) ).
cnf(c_0_157,plain,
difference(quotient(b1,b),b) = difference(b,b2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_150]),c_0_151]),c_0_152]),c_0_153]) ).
cnf(c_0_158,plain,
quotient(X1,difference(X1,X2)) = difference(X1,quotient(X1,X2)),
inference(spm,[status(thm)],[c_0_25,c_0_154]) ).
cnf(c_0_159,plain,
product(product(X1,X2),product(X2,X1)) = product(X2,product(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_156]),c_0_25]) ).
cnf(c_0_160,plain,
product(b2,quotient(b,b2)) = difference(b1,b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_157]),c_0_17]),c_0_111]) ).
cnf(c_0_161,plain,
difference(b,quotient(b,b2)) = quotient(b1,b),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_157]),c_0_158]) ).
cnf(c_0_162,plain,
quotient(X1,quotient(X1,X2)) = difference(X2,X1),
inference(spm,[status(thm)],[c_0_22,c_0_138]) ).
fof(c_0_163,negated_conjecture,
~ m(b1,b,b2),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_164,plain,
product(b,difference(b1,b)) = product(b2,b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_159,c_0_160]),c_0_28]),c_0_28]) ).
cnf(c_0_165,plain,
product(b,difference(b2,b)) = product(b1,b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_161]),c_0_28]),c_0_162]) ).
fof(c_0_166,negated_conjecture,
~ m(b1,b,b2),
inference(fof_simplification,[status(thm)],[c_0_163]) ).
fof(c_0_167,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(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos09])])]) ).
cnf(c_0_168,plain,
product(product(b1,b),b) = product(b1,product(b2,b)),
inference(spm,[status(thm)],[c_0_81,c_0_164]) ).
cnf(c_0_169,plain,
product(quotient(b,b1),b) = product(b,b2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_165]),c_0_49]),c_0_36]) ).
fof(c_0_170,negated_conjecture,
~ m(b1,b,b2),
inference(fof_nnf,[status(thm)],[c_0_166]) ).
cnf(c_0_171,plain,
( product(product(X1,X2),product(X2,X3)) != product(X1,X3)
| m(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_167]) ).
cnf(c_0_172,plain,
product(product(b1,b),product(b,b2)) = product(b1,b2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_168]),c_0_120]),c_0_22]),c_0_49]),c_0_169]) ).
cnf(c_0_173,negated_conjecture,
~ m(b1,b,b2),
inference(split_conjunct,[status(thm)],[c_0_170]) ).
cnf(c_0_174,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_171,c_0_172]),c_0_173]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP778+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n016.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 20 20:44:22 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 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/benchmark/theBenchmark.p
% 77.24/11.62 % Version: 3.5.1
% 77.24/11.62 % Preprocessing class: FSMSSMSMSSSNFFN.
% 77.24/11.62 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 77.24/11.62 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 77.24/11.62 % Starting new_bool_3 with 300s (1) cores
% 77.24/11.62 % Starting new_bool_1 with 300s (1) cores
% 77.24/11.62 % Starting sh5l with 300s (1) cores
% 77.24/11.62 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 773292 completed with status 0
% 77.24/11.62 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 77.24/11.62 % Preprocessing class: FSMSSMSMSSSNFFN.
% 77.24/11.62 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 77.24/11.62 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 77.24/11.62 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 77.24/11.62 % No SInE strategy applied
% 77.24/11.62 % Search class: FHUSM-FFSM22-MFFFFFNN
% 77.24/11.62 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 77.24/11.62 % Starting SubtermCWHack with 136s (1) cores
% 77.24/11.62 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 77.24/11.62 % Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 136s (1) cores
% 77.24/11.62 % Starting new_bool_3 with 136s (1) cores
% 77.24/11.62 % Starting new_bool_1 with 136s (1) cores
% 77.24/11.62 % G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with pid 773300 completed with status 0
% 77.24/11.62 % Result found by G-E--_300_C18_F1_SE_CS_SP_PS_S0Y
% 77.24/11.62 % Preprocessing class: FSMSSMSMSSSNFFN.
% 77.24/11.62 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 77.24/11.62 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 77.24/11.62 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 77.24/11.62 % No SInE strategy applied
% 77.24/11.62 % Search class: FHUSM-FFSM22-MFFFFFNN
% 77.24/11.62 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 77.24/11.62 % Starting SubtermCWHack with 136s (1) cores
% 77.24/11.62 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 77.24/11.62 % Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 136s (1) cores
% 77.24/11.62 % Preprocessing time : 0.001 s
% 77.24/11.62 % Presaturation interreduction done
% 77.24/11.62
% 77.24/11.62 % Proof found!
% 77.24/11.62 % SZS status Theorem
% 77.24/11.62 % SZS output start CNFRefutation
% See solution above
% 77.24/11.62 % Parsed axioms : 16
% 77.24/11.62 % Removed by relevancy pruning/SinE : 0
% 77.24/11.62 % Initial clauses : 18
% 77.24/11.62 % Removed in clause preprocessing : 0
% 77.24/11.62 % Initial clauses in saturation : 18
% 77.24/11.62 % Processed clauses : 12240
% 77.24/11.62 % ...of these trivial : 3791
% 77.24/11.62 % ...subsumed : 1887
% 77.24/11.62 % ...remaining for further processing : 6562
% 77.24/11.62 % Other redundant clauses eliminated : 6
% 77.24/11.62 % Clauses deleted for lack of memory : 0
% 77.24/11.62 % Backward-subsumed : 76
% 77.24/11.62 % Backward-rewritten : 1744
% 77.24/11.62 % Generated clauses : 532793
% 77.24/11.62 % ...of the previous two non-redundant : 512023
% 77.24/11.62 % ...aggressively subsumed : 0
% 77.24/11.62 % Contextual simplify-reflections : 1
% 77.24/11.62 % Paramodulations : 532787
% 77.24/11.62 % Factorizations : 0
% 77.24/11.62 % NegExts : 0
% 77.24/11.62 % Equation resolutions : 6
% 77.24/11.62 % Disequality decompositions : 0
% 77.24/11.62 % Total rewrite steps : 848052
% 77.24/11.62 % ...of those cached : 806883
% 77.24/11.62 % Propositional unsat checks : 0
% 77.24/11.62 % Propositional check models : 0
% 77.24/11.62 % Propositional check unsatisfiable : 0
% 77.24/11.62 % Propositional clauses : 0
% 77.24/11.62 % Propositional clauses after purity: 0
% 77.24/11.62 % Propositional unsat core size : 0
% 77.24/11.62 % Propositional preprocessing time : 0.000
% 77.24/11.62 % Propositional encoding time : 0.000
% 77.24/11.62 % Propositional solver time : 0.000
% 77.24/11.62 % Success case prop preproc time : 0.000
% 77.24/11.62 % Success case prop encoding time : 0.000
% 77.24/11.62 % Success case prop solver time : 0.000
% 77.24/11.62 % Current number of processed clauses : 4724
% 77.24/11.62 % Positive orientable unit clauses : 2707
% 77.24/11.62 % Positive unorientable unit clauses: 12
% 77.24/11.62 % Negative unit clauses : 2
% 77.24/11.62 % Non-unit-clauses : 2003
% 77.24/11.62 % Current number of unprocessed clauses: 496544
% 77.24/11.62 % ...number of literals in the above : 589958
% 77.24/11.62 % Current number of archived formulas : 0
% 77.24/11.62 % Current number of archived clauses : 1838
% 77.24/11.62 % Clause-clause subsumption calls (NU) : 84319
% 77.24/11.62 % Rec. Clause-clause subsumption calls : 78853
% 77.24/11.62 % Non-unit clause-clause subsumptions : 1868
% 77.24/11.62 % Unit Clause-clause subsumption calls : 260
% 77.24/11.62 % Rewrite failures with RHS unbound : 0
% 77.24/11.62 % BW rewrite match attempts : 3608
% 77.24/11.62 % BW rewrite match successes : 1220
% 77.24/11.62 % Condensation attempts : 0
% 77.24/11.62 % Condensation successes : 0
% 77.24/11.62 % Termbank termtop insertions : 16261755
% 77.24/11.62 % Search garbage collected termcells : 46
% 77.24/11.62
% 77.24/11.62 % -------------------------------------------------
% 77.24/11.63 % User time : 10.445 s
% 77.24/11.63 % System time : 0.425 s
% 77.24/11.63 % Total time : 10.869 s
% 77.24/11.63 % Maximum resident set size: 3644 pages
% 77.24/11.63
% 77.24/11.63 % -------------------------------------------------
% 77.24/11.63 % User time : 53.072 s
% 77.24/11.63 % System time : 1.746 s
% 77.24/11.63 % Total time : 54.818 s
% 77.24/11.63 % Maximum resident set size: 4608 pages
% 77.24/11.63 % E exiting
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