TSTP Solution File: KLE102+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : KLE102+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 05:26:08 EDT 2023
% Result : Theorem 47.40s 48.02s
% Output : CNFRefutation 47.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 40
% Syntax : Number of formulae : 190 ( 169 unt; 18 typ; 0 def)
% Number of atoms : 175 ( 174 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 5 ~; 0 |; 1 &)
% ( 0 <=>; 1 =>; 1 <=; 0 <~>)
% Maximal formula depth : 6 ( 1 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 21 ( 13 >; 8 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 5 con; 0-2 aty)
% Number of variables : 224 ( 16 sgn; 74 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
addition: ( $i * $i ) > $i ).
tff(decl_23,type,
zero: $i ).
tff(decl_24,type,
multiplication: ( $i * $i ) > $i ).
tff(decl_25,type,
one: $i ).
tff(decl_26,type,
leq: ( $i * $i ) > $o ).
tff(decl_27,type,
antidomain: $i > $i ).
tff(decl_28,type,
domain: $i > $i ).
tff(decl_29,type,
coantidomain: $i > $i ).
tff(decl_30,type,
codomain: $i > $i ).
tff(decl_31,type,
c: $i > $i ).
tff(decl_32,type,
domain_difference: ( $i * $i ) > $i ).
tff(decl_33,type,
forward_diamond: ( $i * $i ) > $i ).
tff(decl_34,type,
backward_diamond: ( $i * $i ) > $i ).
tff(decl_35,type,
forward_box: ( $i * $i ) > $i ).
tff(decl_36,type,
backward_box: ( $i * $i ) > $i ).
tff(decl_37,type,
esk1_0: $i ).
tff(decl_38,type,
esk2_0: $i ).
tff(decl_39,type,
esk3_0: $i ).
fof(goals,conjecture,
! [X4,X5,X6] :
( multiplication(forward_diamond(X4,domain(X5)),domain(X6)) = zero
<= multiplication(domain(X5),backward_diamond(X4,domain(X6))) = zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(backward_diamond,axiom,
! [X4,X5] : backward_diamond(X4,X5) = codomain(multiplication(codomain(X5),X4)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+6.ax',backward_diamond) ).
fof(codomain4,axiom,
! [X4] : codomain(X4) = coantidomain(coantidomain(X4)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',codomain4) ).
fof(domain4,axiom,
! [X4] : domain(X4) = antidomain(antidomain(X4)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',domain4) ).
fof(right_distributivity,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',right_distributivity) ).
fof(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
fof(codomain3,axiom,
! [X4] : addition(coantidomain(coantidomain(X4)),coantidomain(X4)) = one,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',codomain3) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
fof(codomain1,axiom,
! [X4] : multiplication(X4,coantidomain(X4)) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',codomain1) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
fof(additive_associativity,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_associativity) ).
fof(additive_idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
fof(domain3,axiom,
! [X4] : addition(antidomain(antidomain(X4)),antidomain(X4)) = one,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',domain3) ).
fof(left_distributivity,axiom,
! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',left_distributivity) ).
fof(domain1,axiom,
! [X4] : multiplication(antidomain(X4),X4) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',domain1) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
fof(multiplicative_associativity,axiom,
! [X1,X2,X3] : multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_associativity) ).
fof(domain2,axiom,
! [X4,X5] : addition(antidomain(multiplication(X4,X5)),antidomain(multiplication(X4,antidomain(antidomain(X5))))) = antidomain(multiplication(X4,antidomain(antidomain(X5)))),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',domain2) ).
fof(right_annihilation,axiom,
! [X1] : multiplication(X1,zero) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',right_annihilation) ).
fof(codomain2,axiom,
! [X4,X5] : addition(coantidomain(multiplication(X4,X5)),coantidomain(multiplication(coantidomain(coantidomain(X4)),X5))) = coantidomain(multiplication(coantidomain(coantidomain(X4)),X5)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',codomain2) ).
fof(left_annihilation,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',left_annihilation) ).
fof(forward_diamond,axiom,
! [X4,X5] : forward_diamond(X4,X5) = domain(multiplication(X4,domain(X5))),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+6.ax',forward_diamond) ).
fof(c_0_22,negated_conjecture,
~ ! [X4,X5,X6] :
( multiplication(domain(X5),backward_diamond(X4,domain(X6))) = zero
=> multiplication(forward_diamond(X4,domain(X5)),domain(X6)) = zero ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[goals])]) ).
fof(c_0_23,plain,
! [X44,X45] : backward_diamond(X44,X45) = codomain(multiplication(codomain(X45),X44)),
inference(variable_rename,[status(thm)],[backward_diamond]) ).
fof(c_0_24,plain,
! [X38] : codomain(X38) = coantidomain(coantidomain(X38)),
inference(variable_rename,[status(thm)],[codomain4]) ).
fof(c_0_25,negated_conjecture,
( multiplication(domain(esk2_0),backward_diamond(esk1_0,domain(esk3_0))) = zero
& multiplication(forward_diamond(esk1_0,domain(esk2_0)),domain(esk3_0)) != zero ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_22])])]) ).
fof(c_0_26,plain,
! [X33] : domain(X33) = antidomain(antidomain(X33)),
inference(variable_rename,[status(thm)],[domain4]) ).
cnf(c_0_27,plain,
backward_diamond(X1,X2) = codomain(multiplication(codomain(X2),X1)),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_28,plain,
codomain(X1) = coantidomain(coantidomain(X1)),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_29,plain,
! [X19,X20,X21] : multiplication(X19,addition(X20,X21)) = addition(multiplication(X19,X20),multiplication(X19,X21)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
cnf(c_0_30,negated_conjecture,
multiplication(domain(esk2_0),backward_diamond(esk1_0,domain(esk3_0))) = zero,
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_31,plain,
domain(X1) = antidomain(antidomain(X1)),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_32,plain,
backward_diamond(X1,X2) = coantidomain(coantidomain(multiplication(coantidomain(coantidomain(X2)),X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28]),c_0_28]) ).
fof(c_0_33,plain,
! [X12] : addition(X12,zero) = X12,
inference(variable_rename,[status(thm)],[additive_identity]) ).
fof(c_0_34,plain,
! [X37] : addition(coantidomain(coantidomain(X37)),coantidomain(X37)) = one,
inference(variable_rename,[status(thm)],[codomain3]) ).
fof(c_0_35,plain,
! [X7,X8] : addition(X7,X8) = addition(X8,X7),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_36,plain,
! [X34] : multiplication(X34,coantidomain(X34)) = zero,
inference(variable_rename,[status(thm)],[codomain1]) ).
cnf(c_0_37,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_38,negated_conjecture,
multiplication(antidomain(antidomain(esk2_0)),coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(esk3_0)))),esk1_0)))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31]),c_0_31]),c_0_32]) ).
cnf(c_0_39,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_40,plain,
addition(coantidomain(coantidomain(X1)),coantidomain(X1)) = one,
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_41,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
fof(c_0_42,plain,
! [X17] : multiplication(X17,one) = X17,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
fof(c_0_43,plain,
! [X9,X10,X11] : addition(X11,addition(X10,X9)) = addition(addition(X11,X10),X9),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_44,plain,
! [X13] : addition(X13,X13) = X13,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
fof(c_0_45,plain,
! [X32] : addition(antidomain(antidomain(X32)),antidomain(X32)) = one,
inference(variable_rename,[status(thm)],[domain3]) ).
cnf(c_0_46,plain,
multiplication(X1,coantidomain(X1)) = zero,
inference(split_conjunct,[status(thm)],[c_0_36]) ).
fof(c_0_47,plain,
! [X22,X23,X24] : multiplication(addition(X22,X23),X24) = addition(multiplication(X22,X24),multiplication(X23,X24)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
cnf(c_0_48,negated_conjecture,
multiplication(antidomain(antidomain(esk2_0)),addition(X1,coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(esk3_0)))),esk1_0))))) = multiplication(antidomain(antidomain(esk2_0)),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]) ).
cnf(c_0_49,plain,
addition(coantidomain(X1),coantidomain(coantidomain(X1))) = one,
inference(rw,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_50,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_51,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_52,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_53,plain,
addition(antidomain(antidomain(X1)),antidomain(X1)) = one,
inference(split_conjunct,[status(thm)],[c_0_45]) ).
fof(c_0_54,plain,
! [X29] : multiplication(antidomain(X29),X29) = zero,
inference(variable_rename,[status(thm)],[domain1]) ).
cnf(c_0_55,plain,
multiplication(X1,addition(X2,coantidomain(X1))) = multiplication(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_46]),c_0_39]) ).
cnf(c_0_56,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_57,negated_conjecture,
multiplication(antidomain(antidomain(esk2_0)),coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(esk3_0)))),esk1_0))) = antidomain(antidomain(esk2_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50]) ).
fof(c_0_58,plain,
! [X18] : multiplication(one,X18) = X18,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_0_59,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_60,plain,
addition(antidomain(X1),antidomain(antidomain(X1))) = one,
inference(rw,[status(thm)],[c_0_53,c_0_41]) ).
cnf(c_0_61,plain,
multiplication(antidomain(X1),X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_54]) ).
fof(c_0_62,plain,
! [X14,X15,X16] : multiplication(X14,multiplication(X15,X16)) = multiplication(multiplication(X14,X15),X16),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
cnf(c_0_63,plain,
multiplication(X1,addition(coantidomain(X1),X2)) = multiplication(X1,X2),
inference(spm,[status(thm)],[c_0_55,c_0_41]) ).
cnf(c_0_64,negated_conjecture,
addition(antidomain(antidomain(esk2_0)),multiplication(X1,coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(esk3_0)))),esk1_0)))) = multiplication(addition(antidomain(antidomain(esk2_0)),X1),coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(esk3_0)))),esk1_0))),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_65,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_66,plain,
addition(one,antidomain(X1)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_41]) ).
fof(c_0_67,plain,
! [X30,X31] : addition(antidomain(multiplication(X30,X31)),antidomain(multiplication(X30,antidomain(antidomain(X31))))) = antidomain(multiplication(X30,antidomain(antidomain(X31)))),
inference(variable_rename,[status(thm)],[domain2]) ).
cnf(c_0_68,plain,
antidomain(one) = zero,
inference(spm,[status(thm)],[c_0_61,c_0_50]) ).
cnf(c_0_69,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_39,c_0_41]) ).
cnf(c_0_70,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_71,plain,
multiplication(X1,coantidomain(coantidomain(X1))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_49]),c_0_50]) ).
cnf(c_0_72,negated_conjecture,
addition(antidomain(antidomain(esk2_0)),coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(esk3_0)))),esk1_0))) = coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(esk3_0)))),esk1_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_41]),c_0_66]),c_0_65]) ).
fof(c_0_73,plain,
! [X25] : multiplication(X25,zero) = zero,
inference(variable_rename,[status(thm)],[right_annihilation]) ).
cnf(c_0_74,plain,
addition(antidomain(multiplication(X1,X2)),antidomain(multiplication(X1,antidomain(antidomain(X2))))) = antidomain(multiplication(X1,antidomain(antidomain(X2)))),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_75,plain,
antidomain(zero) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_68]),c_0_69]) ).
fof(c_0_76,plain,
! [X35,X36] : addition(coantidomain(multiplication(X35,X36)),coantidomain(multiplication(coantidomain(coantidomain(X35)),X36))) = coantidomain(multiplication(coantidomain(coantidomain(X35)),X36)),
inference(variable_rename,[status(thm)],[codomain2]) ).
cnf(c_0_77,plain,
multiplication(X1,multiplication(coantidomain(coantidomain(X1)),X2)) = multiplication(X1,X2),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_78,negated_conjecture,
multiplication(coantidomain(coantidomain(antidomain(antidomain(esk3_0)))),multiplication(esk1_0,antidomain(antidomain(esk2_0)))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_72]),c_0_46]),c_0_70]) ).
cnf(c_0_79,plain,
multiplication(X1,zero) = zero,
inference(split_conjunct,[status(thm)],[c_0_73]) ).
fof(c_0_80,plain,
! [X26] : multiplication(zero,X26) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
cnf(c_0_81,plain,
multiplication(addition(X1,antidomain(X2)),X2) = multiplication(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_61]),c_0_39]) ).
cnf(c_0_82,plain,
addition(one,antidomain(multiplication(X1,antidomain(antidomain(coantidomain(X1)))))) = antidomain(multiplication(X1,antidomain(antidomain(coantidomain(X1))))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_46]),c_0_75]) ).
cnf(c_0_83,plain,
addition(coantidomain(multiplication(X1,X2)),coantidomain(multiplication(coantidomain(coantidomain(X1)),X2))) = coantidomain(multiplication(coantidomain(coantidomain(X1)),X2)),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_84,negated_conjecture,
multiplication(antidomain(antidomain(esk3_0)),multiplication(esk1_0,antidomain(antidomain(esk2_0)))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_79]) ).
cnf(c_0_85,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_86,plain,
multiplication(addition(antidomain(X1),X2),X1) = multiplication(X2,X1),
inference(spm,[status(thm)],[c_0_81,c_0_41]) ).
cnf(c_0_87,plain,
multiplication(X1,antidomain(antidomain(coantidomain(X1)))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_61]),c_0_65]) ).
cnf(c_0_88,plain,
multiplication(addition(X1,X2),coantidomain(X2)) = multiplication(X1,coantidomain(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_46]),c_0_39]) ).
cnf(c_0_89,plain,
addition(coantidomain(X1),coantidomain(coantidomain(coantidomain(X1)))) = coantidomain(coantidomain(coantidomain(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_50]),c_0_50]) ).
cnf(c_0_90,negated_conjecture,
multiplication(antidomain(antidomain(esk3_0)),multiplication(esk1_0,multiplication(antidomain(antidomain(esk2_0)),X1))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_84]),c_0_85]),c_0_70]) ).
cnf(c_0_91,plain,
multiplication(antidomain(antidomain(X1)),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_60]),c_0_65]) ).
cnf(c_0_92,plain,
coantidomain(one) = zero,
inference(spm,[status(thm)],[c_0_46,c_0_65]) ).
cnf(c_0_93,plain,
multiplication(addition(X1,X2),antidomain(antidomain(coantidomain(X2)))) = multiplication(X1,antidomain(antidomain(coantidomain(X2)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_87]),c_0_39]) ).
cnf(c_0_94,plain,
coantidomain(coantidomain(coantidomain(X1))) = coantidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_49]),c_0_65]),c_0_71]) ).
cnf(c_0_95,plain,
addition(coantidomain(multiplication(X1,X2)),addition(coantidomain(multiplication(coantidomain(coantidomain(X1)),X2)),X3)) = addition(coantidomain(multiplication(coantidomain(coantidomain(X1)),X2)),X3),
inference(spm,[status(thm)],[c_0_51,c_0_83]) ).
cnf(c_0_96,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(X2,one)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_50]),c_0_41]) ).
cnf(c_0_97,plain,
multiplication(coantidomain(coantidomain(X1)),coantidomain(X1)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_89]),c_0_46]) ).
cnf(c_0_98,plain,
multiplication(antidomain(multiplication(X1,X2)),multiplication(X1,antidomain(antidomain(X2)))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_74]),c_0_61]) ).
cnf(c_0_99,negated_conjecture,
multiplication(antidomain(antidomain(esk3_0)),multiplication(esk1_0,esk2_0)) = zero,
inference(spm,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_100,plain,
coantidomain(zero) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_92]),c_0_69]) ).
cnf(c_0_101,plain,
multiplication(antidomain(X1),addition(X2,X1)) = multiplication(antidomain(X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_61]),c_0_39]) ).
cnf(c_0_102,plain,
multiplication(antidomain(X1),antidomain(X1)) = antidomain(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_60]),c_0_65]) ).
cnf(c_0_103,plain,
multiplication(coantidomain(X1),antidomain(antidomain(coantidomain(X1)))) = antidomain(antidomain(coantidomain(X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_49]),c_0_94]),c_0_65]),c_0_94]) ).
cnf(c_0_104,plain,
addition(one,coantidomain(multiplication(X1,X2))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_49]),c_0_41]) ).
cnf(c_0_105,plain,
multiplication(coantidomain(coantidomain(X1)),addition(one,coantidomain(X1))) = coantidomain(coantidomain(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_39]),c_0_41]) ).
cnf(c_0_106,negated_conjecture,
multiplication(antidomain(antidomain(esk3_0)),antidomain(antidomain(multiplication(esk1_0,esk2_0)))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_75]),c_0_65]) ).
cnf(c_0_107,plain,
addition(one,coantidomain(multiplication(coantidomain(coantidomain(antidomain(X1))),X1))) = coantidomain(multiplication(coantidomain(coantidomain(antidomain(X1))),X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_61]),c_0_100]) ).
cnf(c_0_108,plain,
multiplication(antidomain(X1),coantidomain(antidomain(antidomain(X1)))) = coantidomain(antidomain(antidomain(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_60]),c_0_65]) ).
cnf(c_0_109,plain,
antidomain(antidomain(antidomain(X1))) = antidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_60]),c_0_50]),c_0_91]) ).
cnf(c_0_110,plain,
multiplication(antidomain(X1),addition(X2,antidomain(X1))) = multiplication(antidomain(X1),addition(X2,one)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_102]),c_0_41]),c_0_96]) ).
cnf(c_0_111,plain,
addition(coantidomain(X1),antidomain(antidomain(coantidomain(X1)))) = coantidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_103]),c_0_41]),c_0_66]),c_0_50]) ).
cnf(c_0_112,plain,
addition(one,coantidomain(X1)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_94]) ).
cnf(c_0_113,plain,
multiplication(antidomain(X1),addition(X1,X2)) = multiplication(antidomain(X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_61]),c_0_69]) ).
cnf(c_0_114,negated_conjecture,
multiplication(antidomain(antidomain(esk3_0)),multiplication(antidomain(antidomain(multiplication(esk1_0,esk2_0))),X1)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_106]),c_0_85]) ).
cnf(c_0_115,plain,
multiplication(coantidomain(coantidomain(antidomain(X1))),X1) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_107]),c_0_46]),c_0_50]) ).
cnf(c_0_116,plain,
multiplication(antidomain(antidomain(X1)),coantidomain(antidomain(X1))) = coantidomain(antidomain(X1)),
inference(spm,[status(thm)],[c_0_108,c_0_109]) ).
cnf(c_0_117,plain,
antidomain(antidomain(coantidomain(X1))) = coantidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_91]),c_0_41]),c_0_112]),c_0_50]) ).
cnf(c_0_118,plain,
multiplication(antidomain(coantidomain(X1)),coantidomain(coantidomain(X1))) = antidomain(coantidomain(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_49]),c_0_50]) ).
cnf(c_0_119,plain,
addition(X1,multiplication(antidomain(antidomain(X1)),X2)) = multiplication(antidomain(antidomain(X1)),addition(X1,X2)),
inference(spm,[status(thm)],[c_0_37,c_0_91]) ).
cnf(c_0_120,negated_conjecture,
multiplication(antidomain(antidomain(esk3_0)),coantidomain(antidomain(multiplication(esk1_0,esk2_0)))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_108]),c_0_109]) ).
cnf(c_0_121,plain,
multiplication(coantidomain(coantidomain(antidomain(X1))),multiplication(X1,X2)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_115]),c_0_85]) ).
cnf(c_0_122,plain,
coantidomain(coantidomain(X1)) = antidomain(coantidomain(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_117]),c_0_118]) ).
cnf(c_0_123,negated_conjecture,
multiplication(antidomain(antidomain(esk3_0)),addition(esk3_0,coantidomain(antidomain(multiplication(esk1_0,esk2_0))))) = esk3_0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_120]),c_0_39]) ).
cnf(c_0_124,plain,
multiplication(antidomain(coantidomain(antidomain(X1))),multiplication(X1,X2)) = zero,
inference(rw,[status(thm)],[c_0_121,c_0_122]) ).
cnf(c_0_125,negated_conjecture,
multiplication(antidomain(antidomain(esk3_0)),addition(one,esk3_0)) = addition(esk3_0,antidomain(antidomain(esk3_0))),
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_96,c_0_123]),c_0_51]),c_0_41]),c_0_112]),c_0_41]),c_0_41]) ).
cnf(c_0_126,negated_conjecture,
multiplication(antidomain(coantidomain(antidomain(esk3_0))),addition(esk3_0,antidomain(antidomain(esk3_0)))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_125]),c_0_109]) ).
cnf(c_0_127,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_65]),c_0_41]) ).
cnf(c_0_128,negated_conjecture,
multiplication(antidomain(coantidomain(antidomain(esk3_0))),multiplication(addition(esk3_0,antidomain(antidomain(esk3_0))),X1)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_126]),c_0_85]) ).
cnf(c_0_129,plain,
multiplication(addition(X1,antidomain(antidomain(X2))),X2) = multiplication(addition(X1,one),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_91]),c_0_41]),c_0_127]) ).
cnf(c_0_130,plain,
multiplication(antidomain(antidomain(X1)),multiplication(X1,X2)) = multiplication(X1,X2),
inference(spm,[status(thm)],[c_0_70,c_0_91]) ).
cnf(c_0_131,plain,
addition(multiplication(X1,multiplication(X2,X3)),multiplication(X4,X3)) = multiplication(addition(multiplication(X1,X2),X4),X3),
inference(spm,[status(thm)],[c_0_56,c_0_70]) ).
cnf(c_0_132,negated_conjecture,
multiplication(antidomain(coantidomain(antidomain(esk3_0))),multiplication(addition(one,esk3_0),esk3_0)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_129]),c_0_41]) ).
cnf(c_0_133,negated_conjecture,
multiplication(antidomain(coantidomain(antidomain(esk3_0))),addition(one,esk3_0)) = antidomain(coantidomain(antidomain(esk3_0))),
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_96,c_0_126]),c_0_39]),c_0_51]),c_0_41]),c_0_66]),c_0_41]) ).
cnf(c_0_134,plain,
multiplication(coantidomain(X1),coantidomain(X1)) = coantidomain(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_49]),c_0_50]) ).
cnf(c_0_135,plain,
multiplication(antidomain(antidomain(X1)),addition(one,multiplication(X1,X2))) = addition(antidomain(antidomain(X1)),multiplication(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_130]),c_0_41]) ).
cnf(c_0_136,negated_conjecture,
multiplication(addition(antidomain(coantidomain(antidomain(esk3_0))),X1),esk3_0) = multiplication(X1,esk3_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_132]),c_0_69]),c_0_133]) ).
cnf(c_0_137,plain,
multiplication(coantidomain(X1),addition(X2,coantidomain(X1))) = multiplication(coantidomain(X1),addition(X2,one)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_134]),c_0_41]),c_0_96]) ).
cnf(c_0_138,plain,
addition(antidomain(X1),coantidomain(antidomain(antidomain(X1)))) = antidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_108]),c_0_109]),c_0_112]),c_0_50]),c_0_109]) ).
cnf(c_0_139,plain,
multiplication(antidomain(X1),multiplication(X1,X2)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_61]),c_0_85]) ).
cnf(c_0_140,negated_conjecture,
multiplication(coantidomain(antidomain(esk3_0)),esk3_0) = esk3_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_60]),c_0_65]),c_0_117]) ).
cnf(c_0_141,plain,
multiplication(coantidomain(antidomain(antidomain(X1))),antidomain(X1)) = coantidomain(antidomain(antidomain(X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_138]),c_0_41]),c_0_66]),c_0_50]) ).
cnf(c_0_142,plain,
multiplication(antidomain(X1),antidomain(antidomain(multiplication(X1,X2)))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_139]),c_0_75]),c_0_65]) ).
cnf(c_0_143,negated_conjecture,
addition(antidomain(esk3_0),antidomain(multiplication(coantidomain(antidomain(esk3_0)),antidomain(antidomain(esk3_0))))) = antidomain(multiplication(coantidomain(antidomain(esk3_0)),antidomain(antidomain(esk3_0)))),
inference(spm,[status(thm)],[c_0_74,c_0_140]) ).
cnf(c_0_144,plain,
multiplication(coantidomain(antidomain(X1)),antidomain(antidomain(X1))) = coantidomain(antidomain(X1)),
inference(spm,[status(thm)],[c_0_141,c_0_109]) ).
cnf(c_0_145,plain,
multiplication(X1,multiplication(X2,coantidomain(multiplication(X1,X2)))) = zero,
inference(spm,[status(thm)],[c_0_46,c_0_70]) ).
cnf(c_0_146,plain,
multiplication(antidomain(X1),addition(antidomain(antidomain(multiplication(X1,X2))),X3)) = multiplication(antidomain(X1),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_142]),c_0_69]) ).
cnf(c_0_147,plain,
multiplication(addition(antidomain(X1),X2),antidomain(X1)) = multiplication(addition(X2,one),antidomain(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_102]),c_0_127]) ).
cnf(c_0_148,negated_conjecture,
addition(antidomain(esk3_0),antidomain(coantidomain(antidomain(esk3_0)))) = antidomain(coantidomain(antidomain(esk3_0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_143,c_0_144]),c_0_144]) ).
cnf(c_0_149,plain,
multiplication(addition(X1,X2),multiplication(X3,coantidomain(multiplication(X2,X3)))) = multiplication(X1,multiplication(X3,coantidomain(multiplication(X2,X3)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_145]),c_0_39]) ).
cnf(c_0_150,plain,
multiplication(antidomain(X1),antidomain(multiplication(X1,X2))) = antidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_60]),c_0_50]),c_0_109]) ).
cnf(c_0_151,negated_conjecture,
multiplication(antidomain(coantidomain(antidomain(esk3_0))),antidomain(esk3_0)) = antidomain(esk3_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_148]),c_0_41]),c_0_66]),c_0_65]) ).
cnf(c_0_152,negated_conjecture,
multiplication(addition(X1,antidomain(antidomain(esk3_0))),multiplication(esk1_0,esk2_0)) = multiplication(X1,multiplication(esk1_0,esk2_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_99]),c_0_100]),c_0_50]),c_0_100]),c_0_50]) ).
cnf(c_0_153,negated_conjecture,
antidomain(coantidomain(antidomain(esk3_0))) = antidomain(esk3_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_140]),c_0_151]) ).
cnf(c_0_154,negated_conjecture,
multiplication(antidomain(esk3_0),multiplication(esk1_0,esk2_0)) = multiplication(esk1_0,esk2_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_60]),c_0_65]) ).
cnf(c_0_155,negated_conjecture,
coantidomain(antidomain(esk3_0)) = antidomain(antidomain(esk3_0)),
inference(spm,[status(thm)],[c_0_117,c_0_153]) ).
fof(c_0_156,plain,
! [X42,X43] : forward_diamond(X42,X43) = domain(multiplication(X42,domain(X43))),
inference(variable_rename,[status(thm)],[forward_diamond]) ).
cnf(c_0_157,plain,
addition(X1,addition(coantidomain(X2),multiplication(X2,X1))) = multiplication(addition(X2,one),addition(X1,coantidomain(X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_55]),c_0_51]) ).
cnf(c_0_158,negated_conjecture,
multiplication(antidomain(antidomain(esk3_0)),antidomain(multiplication(esk1_0,esk2_0))) = antidomain(antidomain(esk3_0)),
inference(spm,[status(thm)],[c_0_150,c_0_154]) ).
cnf(c_0_159,negated_conjecture,
coantidomain(antidomain(antidomain(esk3_0))) = antidomain(esk3_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_155]),c_0_109]) ).
cnf(c_0_160,plain,
forward_diamond(X1,X2) = domain(multiplication(X1,domain(X2))),
inference(split_conjunct,[status(thm)],[c_0_156]) ).
cnf(c_0_161,plain,
multiplication(addition(X1,antidomain(multiplication(X2,X3))),multiplication(X2,antidomain(antidomain(X3)))) = multiplication(X1,multiplication(X2,antidomain(antidomain(X3)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_98]),c_0_39]) ).
cnf(c_0_162,negated_conjecture,
addition(antidomain(esk3_0),antidomain(multiplication(esk1_0,esk2_0))) = one,
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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_158]),c_0_159]),c_0_60]),c_0_41]),c_0_66]),c_0_159]),c_0_41]),c_0_65]),c_0_41]),c_0_66]) ).
cnf(c_0_163,negated_conjecture,
multiplication(forward_diamond(esk1_0,domain(esk2_0)),domain(esk3_0)) != zero,
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_164,plain,
forward_diamond(X1,X2) = antidomain(antidomain(multiplication(X1,antidomain(antidomain(X2))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_160,c_0_31]),c_0_31]) ).
cnf(c_0_165,plain,
multiplication(antidomain(multiplication(X1,X2)),multiplication(addition(X1,X3),X2)) = multiplication(antidomain(multiplication(X1,X2)),multiplication(X3,X2)),
inference(spm,[status(thm)],[c_0_113,c_0_56]) ).
cnf(c_0_166,negated_conjecture,
multiplication(antidomain(esk3_0),multiplication(esk1_0,antidomain(antidomain(esk2_0)))) = multiplication(esk1_0,antidomain(antidomain(esk2_0))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_162]),c_0_65]) ).
cnf(c_0_167,negated_conjecture,
multiplication(antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(antidomain(antidomain(esk2_0))))))),antidomain(antidomain(esk3_0))) != zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_163,c_0_31]),c_0_31]),c_0_164]) ).
cnf(c_0_168,plain,
multiplication(antidomain(X1),multiplication(antidomain(X2),X1)) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_66]),c_0_65]),c_0_65]),c_0_61]),c_0_65]) ).
cnf(c_0_169,negated_conjecture,
multiplication(antidomain(antidomain(esk3_0)),antidomain(multiplication(esk1_0,antidomain(antidomain(esk2_0))))) = antidomain(antidomain(esk3_0)),
inference(spm,[status(thm)],[c_0_150,c_0_166]) ).
cnf(c_0_170,negated_conjecture,
multiplication(antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(esk2_0))))),antidomain(antidomain(esk3_0))) != zero,
inference(spm,[status(thm)],[c_0_167,c_0_109]) ).
cnf(c_0_171,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_168,c_0_169]),c_0_170]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : KLE102+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.10 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.09/0.29 % Computer : n002.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Tue Aug 29 12:43:35 EDT 2023
% 0.09/0.29 % CPUTime :
% 0.13/0.51 start to proof: theBenchmark
% 47.40/48.02 % Version : CSE_E---1.5
% 47.40/48.02 % Problem : theBenchmark.p
% 47.40/48.02 % Proof found
% 47.40/48.02 % SZS status Theorem for theBenchmark.p
% 47.40/48.02 % SZS output start Proof
% See solution above
% 47.40/48.03 % Total time : 46.961000 s
% 47.40/48.03 % SZS output end Proof
% 47.40/48.03 % Total time : 46.965000 s
%------------------------------------------------------------------------------