%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : KLE024+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n018.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 : 600s
% DateTime : Sun Jul 17 02:14:43 EDT 2022
% Result : Theorem 54.39s 54.56s
% Output : CNFRefutation 54.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 49
% Syntax : Number of formulae : 208 ( 110 unt; 0 def)
% Number of atoms : 371 ( 305 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 313 ( 150 ~; 131 |; 18 &)
% ( 9 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 242 ( 12 sgn 93 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_commutativity,axiom,
! [A,B] : addition(A,B) = addition(B,A) ).
fof(additive_associativity,axiom,
! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C) ).
fof(additive_identity,axiom,
! [A] : addition(A,zero) = A ).
fof(multiplicative_associativity,axiom,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C) ).
fof(multiplicative_right_identity,axiom,
! [A] : multiplication(A,one) = A ).
fof(multiplicative_left_identity,axiom,
! [A] : multiplication(one,A) = A ).
fof(right_distributivity,axiom,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) ).
fof(left_distributivity,axiom,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) ).
fof(left_annihilation,axiom,
! [A] : multiplication(zero,A) = zero ).
fof(test_1,axiom,
! [X0] :
( test(X0)
<=> ? [X1] : complement(X1,X0) ) ).
fof(test_2,axiom,
! [X0,X1] :
( complement(X1,X0)
<=> ( multiplication(X0,X1) = zero
& multiplication(X1,X0) = zero
& addition(X0,X1) = one ) ) ).
fof(test_3,axiom,
! [X0,X1] :
( test(X0)
=> ( c(X0) = X1
<=> complement(X0,X1) ) ) ).
fof(goals,conjecture,
! [X0,X1,X2] :
( ( test(X1)
& test(X2) )
=> ( addition(multiplication(X0,c(X2)),multiplication(c(X1),X0)) = multiplication(c(X1),X0)
=> multiplication(multiplication(X1,X0),c(X2)) = zero ) ) ).
fof(subgoal_0,plain,
! [X0,X1,X2] :
( ( test(X1)
& test(X2)
& addition(multiplication(X0,c(X2)),multiplication(c(X1),X0)) = multiplication(c(X1),X0) )
=> multiplication(multiplication(X1,X0),c(X2)) = zero ),
inference(strip,[],[goals]) ).
fof(negate_0_0,plain,
~ ! [X0,X1,X2] :
( ( test(X1)
& test(X2)
& addition(multiplication(X0,c(X2)),multiplication(c(X1),X0)) = multiplication(c(X1),X0) )
=> multiplication(multiplication(X1,X0),c(X2)) = zero ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(canonicalize,[],[right_distributivity]) ).
fof(normalize_0_1,plain,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
inference(canonicalize,[],[multiplicative_associativity]) ).
fof(normalize_0_3,plain,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
? [X0,X1,X2] :
( multiplication(multiplication(X1,X0),c(X2)) != zero
& addition(multiplication(X0,c(X2)),multiplication(c(X1),X0)) = multiplication(c(X1),X0)
& test(X1)
& test(X2) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_5,plain,
( multiplication(multiplication(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X2)) != zero
& addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)),multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0)) = multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0)
& test(skolemFOFtoCNF_X1_1)
& test(skolemFOFtoCNF_X2) ),
inference(skolemize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
test(skolemFOFtoCNF_X1_1),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [X0] :
( ~ test(X0)
<=> ! [X1] : ~ complement(X1,X0) ),
inference(canonicalize,[],[test_1]) ).
fof(normalize_0_8,plain,
! [X0] :
( ~ test(X0)
<=> ! [X1] : ~ complement(X1,X0) ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [X0,X1] :
( ( ~ complement(X1,X0)
| test(X0) )
& ( ~ test(X0)
| complement(skolemFOFtoCNF_X1(X0),X0) ) ),
inference(clausify,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [X0] :
( ~ test(X0)
| complement(skolemFOFtoCNF_X1(X0),X0) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [X0,X1] :
( ~ complement(X1,X0)
<=> ( addition(X0,X1) != one
| multiplication(X0,X1) != zero
| multiplication(X1,X0) != zero ) ),
inference(canonicalize,[],[test_2]) ).
fof(normalize_0_12,plain,
! [X0,X1] :
( ~ complement(X1,X0)
<=> ( addition(X0,X1) != one
| multiplication(X0,X1) != zero
| multiplication(X1,X0) != zero ) ),
inference(specialize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [X0,X1] :
( ( ~ complement(X1,X0)
| addition(X0,X1) = one )
& ( ~ complement(X1,X0)
| multiplication(X0,X1) = zero )
& ( ~ complement(X1,X0)
| multiplication(X1,X0) = zero )
& ( addition(X0,X1) != one
| multiplication(X0,X1) != zero
| multiplication(X1,X0) != zero
| complement(X1,X0) ) ),
inference(clausify,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| multiplication(X0,X1) = zero ),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [A] : multiplication(zero,A) = zero,
inference(canonicalize,[],[left_annihilation]) ).
fof(normalize_0_16,plain,
! [A] : multiplication(zero,A) = zero,
inference(specialize,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
! [A] : addition(A,zero) = A,
inference(canonicalize,[],[additive_identity]) ).
fof(normalize_0_18,plain,
! [A] : addition(A,zero) = A,
inference(specialize,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
! [X0] :
( ~ test(X0)
| ! [X1] :
( c(X0) != X1
<=> ~ complement(X0,X1) ) ),
inference(canonicalize,[],[test_3]) ).
fof(normalize_0_20,plain,
! [X0] :
( ~ test(X0)
| ! [X1] :
( c(X0) != X1
<=> ~ complement(X0,X1) ) ),
inference(specialize,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
! [X0,X1] :
( ( c(X0) != X1
| ~ test(X0)
| complement(X0,X1) )
& ( ~ complement(X0,X1)
| ~ test(X0)
| c(X0) = X1 ) ),
inference(clausify,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
! [X0,X1] :
( c(X0) != X1
| ~ test(X0)
| complement(X0,X1) ),
inference(conjunct,[],[normalize_0_21]) ).
fof(normalize_0_23,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(canonicalize,[],[additive_commutativity]) ).
fof(normalize_0_24,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(specialize,[],[normalize_0_23]) ).
fof(normalize_0_25,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_26,plain,
! [A] : multiplication(A,one) = A,
inference(canonicalize,[],[multiplicative_right_identity]) ).
fof(normalize_0_27,plain,
! [A] : multiplication(A,one) = A,
inference(specialize,[],[normalize_0_26]) ).
fof(normalize_0_28,plain,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(canonicalize,[],[left_distributivity]) ).
fof(normalize_0_29,plain,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(specialize,[],[normalize_0_28]) ).
fof(normalize_0_30,plain,
! [A] : multiplication(one,A) = A,
inference(canonicalize,[],[multiplicative_left_identity]) ).
fof(normalize_0_31,plain,
! [A] : multiplication(one,A) = A,
inference(specialize,[],[normalize_0_30]) ).
fof(normalize_0_32,plain,
! [A,B,C] : addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(canonicalize,[],[additive_associativity]) ).
fof(normalize_0_33,plain,
! [A,B,C] : addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(specialize,[],[normalize_0_32]) ).
fof(normalize_0_34,plain,
addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)),multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0)) = multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_35,plain,
multiplication(multiplication(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X2)) != zero,
inference(conjunct,[],[normalize_0_5]) ).
cnf(refute_0_0,plain,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
multiplication(skolemFOFtoCNF_X1_1,addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),X_287))) = addition(multiplication(skolemFOFtoCNF_X1_1,B),multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),X_287))),
inference(subst,[],[refute_0_0:[bind(A,$fot(skolemFOFtoCNF_X1_1)),bind(C,$fot(multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),X_287)))]]) ).
cnf(refute_0_2,plain,
multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_3,plain,
multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),C)) = multiplication(multiplication(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)),C),
inference(subst,[],[refute_0_2:[bind(A,$fot(skolemFOFtoCNF_X1_1)),bind(B,$fot(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)))]]) ).
cnf(refute_0_4,plain,
test(skolemFOFtoCNF_X1_1),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_5,plain,
( ~ test(X0)
| complement(skolemFOFtoCNF_X1(X0),X0) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_6,plain,
( ~ test(skolemFOFtoCNF_X1_1)
| complement(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1_1) ),
inference(subst,[],[refute_0_5:[bind(X0,$fot(skolemFOFtoCNF_X1_1))]]) ).
cnf(refute_0_7,plain,
complement(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1_1),
inference(resolve,[$cnf( test(skolemFOFtoCNF_X1_1) )],[refute_0_4,refute_0_6]) ).
cnf(refute_0_8,plain,
( ~ complement(X1,X0)
| multiplication(X0,X1) = zero ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_9,plain,
( ~ complement(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1_1)
| multiplication(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)) = zero ),
inference(subst,[],[refute_0_8:[bind(X0,$fot(skolemFOFtoCNF_X1_1)),bind(X1,$fot(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)))]]) ).
cnf(refute_0_10,plain,
multiplication(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)) = zero,
inference(resolve,[$cnf( complement(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1_1) )],[refute_0_7,refute_0_9]) ).
cnf(refute_0_11,plain,
( multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),C)) != multiplication(multiplication(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)),C)
| multiplication(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)) != zero
| multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),C)) = multiplication(zero,C) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),C)),multiplication(multiplication(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)),C)) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_12,plain,
( multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),C)) != multiplication(multiplication(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)),C)
| multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),C)) = multiplication(zero,C) ),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)),zero) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),C)) = multiplication(zero,C),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),C)),multiplication(multiplication(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)),C)) )],[refute_0_3,refute_0_12]) ).
cnf(refute_0_14,plain,
multiplication(zero,A) = zero,
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_15,plain,
multiplication(zero,C) = zero,
inference(subst,[],[refute_0_14:[bind(A,$fot(C))]]) ).
cnf(refute_0_16,plain,
( multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),C)) != multiplication(zero,C)
| multiplication(zero,C) != zero
| multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),C)) = zero ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),C)),zero) ),[0],$fot(multiplication(zero,C))]]) ).
cnf(refute_0_17,plain,
( multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),C)) != multiplication(zero,C)
| multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),C)) = zero ),
inference(resolve,[$cnf( $equal(multiplication(zero,C),zero) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),C)) = zero,
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),C)),multiplication(zero,C)) )],[refute_0_13,refute_0_17]) ).
cnf(refute_0_19,plain,
multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),X_287)) = zero,
inference(subst,[],[refute_0_18:[bind(C,$fot(X_287))]]) ).
cnf(refute_0_20,plain,
( multiplication(skolemFOFtoCNF_X1_1,addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),X_287))) != addition(multiplication(skolemFOFtoCNF_X1_1,B),multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),X_287)))
| multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),X_287)) != zero
| multiplication(skolemFOFtoCNF_X1_1,addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),X_287))) = addition(multiplication(skolemFOFtoCNF_X1_1,B),zero) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(skolemFOFtoCNF_X1_1,addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),X_287))),addition(multiplication(skolemFOFtoCNF_X1_1,B),multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),X_287)))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_21,plain,
( multiplication(skolemFOFtoCNF_X1_1,addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),X_287))) != addition(multiplication(skolemFOFtoCNF_X1_1,B),multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),X_287)))
| multiplication(skolemFOFtoCNF_X1_1,addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),X_287))) = addition(multiplication(skolemFOFtoCNF_X1_1,B),zero) ),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),X_287)),zero) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
multiplication(skolemFOFtoCNF_X1_1,addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),X_287))) = addition(multiplication(skolemFOFtoCNF_X1_1,B),zero),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X1_1,addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),X_287))),addition(multiplication(skolemFOFtoCNF_X1_1,B),multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),X_287)))) )],[refute_0_1,refute_0_21]) ).
cnf(refute_0_23,plain,
addition(A,zero) = A,
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_24,plain,
addition(multiplication(skolemFOFtoCNF_X1_1,B),zero) = multiplication(skolemFOFtoCNF_X1_1,B),
inference(subst,[],[refute_0_23:[bind(A,$fot(multiplication(skolemFOFtoCNF_X1_1,B)))]]) ).
cnf(refute_0_25,plain,
( addition(multiplication(skolemFOFtoCNF_X1_1,B),zero) != multiplication(skolemFOFtoCNF_X1_1,B)
| multiplication(skolemFOFtoCNF_X1_1,addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),X_287))) != addition(multiplication(skolemFOFtoCNF_X1_1,B),zero)
| multiplication(skolemFOFtoCNF_X1_1,addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),X_287))) = multiplication(skolemFOFtoCNF_X1_1,B) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(skolemFOFtoCNF_X1_1,addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),X_287))),addition(multiplication(skolemFOFtoCNF_X1_1,B),zero)) ),[1],$fot(multiplication(skolemFOFtoCNF_X1_1,B))]]) ).
cnf(refute_0_26,plain,
( multiplication(skolemFOFtoCNF_X1_1,addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),X_287))) != addition(multiplication(skolemFOFtoCNF_X1_1,B),zero)
| multiplication(skolemFOFtoCNF_X1_1,addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),X_287))) = multiplication(skolemFOFtoCNF_X1_1,B) ),
inference(resolve,[$cnf( $equal(addition(multiplication(skolemFOFtoCNF_X1_1,B),zero),multiplication(skolemFOFtoCNF_X1_1,B)) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
multiplication(skolemFOFtoCNF_X1_1,addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),X_287))) = multiplication(skolemFOFtoCNF_X1_1,B),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X1_1,addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),X_287))),addition(multiplication(skolemFOFtoCNF_X1_1,B),zero)) )],[refute_0_22,refute_0_26]) ).
cnf(refute_0_28,plain,
multiplication(c(skolemFOFtoCNF_X1_1),addition(skolemFOFtoCNF_X1_1,C)) = addition(multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1_1),multiplication(c(skolemFOFtoCNF_X1_1),C)),
inference(subst,[],[refute_0_0:[bind(A,$fot(c(skolemFOFtoCNF_X1_1))),bind(B,$fot(skolemFOFtoCNF_X1_1))]]) ).
cnf(refute_0_29,plain,
( c(X0) != X1
| ~ test(X0)
| complement(X0,X1) ),
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_30,plain,
( c(X0) != c(X0)
| ~ test(X0)
| complement(X0,c(X0)) ),
inference(subst,[],[refute_0_29:[bind(X1,$fot(c(X0)))]]) ).
cnf(refute_0_31,plain,
c(X0) = c(X0),
introduced(tautology,[refl,[$fot(c(X0))]]) ).
cnf(refute_0_32,plain,
( ~ test(X0)
| complement(X0,c(X0)) ),
inference(resolve,[$cnf( $equal(c(X0),c(X0)) )],[refute_0_31,refute_0_30]) ).
cnf(refute_0_33,plain,
( ~ test(skolemFOFtoCNF_X1_1)
| complement(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)) ),
inference(subst,[],[refute_0_32:[bind(X0,$fot(skolemFOFtoCNF_X1_1))]]) ).
cnf(refute_0_34,plain,
complement(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)),
inference(resolve,[$cnf( test(skolemFOFtoCNF_X1_1) )],[refute_0_4,refute_0_33]) ).
cnf(refute_0_35,plain,
( ~ complement(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))
| multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1_1) = zero ),
inference(subst,[],[refute_0_8:[bind(X0,$fot(c(skolemFOFtoCNF_X1_1))),bind(X1,$fot(skolemFOFtoCNF_X1_1))]]) ).
cnf(refute_0_36,plain,
multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1_1) = zero,
inference(resolve,[$cnf( complement(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
( multiplication(c(skolemFOFtoCNF_X1_1),addition(skolemFOFtoCNF_X1_1,C)) != addition(multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1_1),multiplication(c(skolemFOFtoCNF_X1_1),C))
| multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1_1) != zero
| multiplication(c(skolemFOFtoCNF_X1_1),addition(skolemFOFtoCNF_X1_1,C)) = addition(zero,multiplication(c(skolemFOFtoCNF_X1_1),C)) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(c(skolemFOFtoCNF_X1_1),addition(skolemFOFtoCNF_X1_1,C)),addition(multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1_1),multiplication(c(skolemFOFtoCNF_X1_1),C))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_38,plain,
( multiplication(c(skolemFOFtoCNF_X1_1),addition(skolemFOFtoCNF_X1_1,C)) != addition(multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1_1),multiplication(c(skolemFOFtoCNF_X1_1),C))
| multiplication(c(skolemFOFtoCNF_X1_1),addition(skolemFOFtoCNF_X1_1,C)) = addition(zero,multiplication(c(skolemFOFtoCNF_X1_1),C)) ),
inference(resolve,[$cnf( $equal(multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1_1),zero) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
multiplication(c(skolemFOFtoCNF_X1_1),addition(skolemFOFtoCNF_X1_1,C)) = addition(zero,multiplication(c(skolemFOFtoCNF_X1_1),C)),
inference(resolve,[$cnf( $equal(multiplication(c(skolemFOFtoCNF_X1_1),addition(skolemFOFtoCNF_X1_1,C)),addition(multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1_1),multiplication(c(skolemFOFtoCNF_X1_1),C))) )],[refute_0_28,refute_0_38]) ).
cnf(refute_0_40,plain,
addition(A,B) = addition(B,A),
inference(canonicalize,[],[normalize_0_24]) ).
cnf(refute_0_41,plain,
addition(A,zero) = addition(zero,A),
inference(subst,[],[refute_0_40:[bind(B,$fot(zero))]]) ).
cnf(refute_0_42,plain,
( addition(A,zero) != A
| addition(A,zero) != addition(zero,A)
| addition(zero,A) = A ),
introduced(tautology,[equality,[$cnf( $equal(addition(A,zero),A) ),[0],$fot(addition(zero,A))]]) ).
cnf(refute_0_43,plain,
( addition(A,zero) != A
| addition(zero,A) = A ),
inference(resolve,[$cnf( $equal(addition(A,zero),addition(zero,A)) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
addition(zero,A) = A,
inference(resolve,[$cnf( $equal(addition(A,zero),A) )],[refute_0_23,refute_0_43]) ).
cnf(refute_0_45,plain,
addition(zero,multiplication(c(skolemFOFtoCNF_X1_1),C)) = multiplication(c(skolemFOFtoCNF_X1_1),C),
inference(subst,[],[refute_0_44:[bind(A,$fot(multiplication(c(skolemFOFtoCNF_X1_1),C)))]]) ).
cnf(refute_0_46,plain,
( addition(zero,multiplication(c(skolemFOFtoCNF_X1_1),C)) != multiplication(c(skolemFOFtoCNF_X1_1),C)
| multiplication(c(skolemFOFtoCNF_X1_1),addition(skolemFOFtoCNF_X1_1,C)) != addition(zero,multiplication(c(skolemFOFtoCNF_X1_1),C))
| multiplication(c(skolemFOFtoCNF_X1_1),addition(skolemFOFtoCNF_X1_1,C)) = multiplication(c(skolemFOFtoCNF_X1_1),C) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(c(skolemFOFtoCNF_X1_1),addition(skolemFOFtoCNF_X1_1,C)),addition(zero,multiplication(c(skolemFOFtoCNF_X1_1),C))) ),[1],$fot(multiplication(c(skolemFOFtoCNF_X1_1),C))]]) ).
cnf(refute_0_47,plain,
( multiplication(c(skolemFOFtoCNF_X1_1),addition(skolemFOFtoCNF_X1_1,C)) != addition(zero,multiplication(c(skolemFOFtoCNF_X1_1),C))
| multiplication(c(skolemFOFtoCNF_X1_1),addition(skolemFOFtoCNF_X1_1,C)) = multiplication(c(skolemFOFtoCNF_X1_1),C) ),
inference(resolve,[$cnf( $equal(addition(zero,multiplication(c(skolemFOFtoCNF_X1_1),C)),multiplication(c(skolemFOFtoCNF_X1_1),C)) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
multiplication(c(skolemFOFtoCNF_X1_1),addition(skolemFOFtoCNF_X1_1,C)) = multiplication(c(skolemFOFtoCNF_X1_1),C),
inference(resolve,[$cnf( $equal(multiplication(c(skolemFOFtoCNF_X1_1),addition(skolemFOFtoCNF_X1_1,C)),addition(zero,multiplication(c(skolemFOFtoCNF_X1_1),C))) )],[refute_0_39,refute_0_47]) ).
cnf(refute_0_49,plain,
multiplication(c(skolemFOFtoCNF_X1_1),addition(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1))) = multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)),
inference(subst,[],[refute_0_48:[bind(C,$fot(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)))]]) ).
cnf(refute_0_50,plain,
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(canonicalize,[],[normalize_0_25]) ).
cnf(refute_0_51,plain,
( ~ complement(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1_1)
| addition(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)) = one ),
inference(subst,[],[refute_0_50:[bind(X0,$fot(skolemFOFtoCNF_X1_1)),bind(X1,$fot(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)))]]) ).
cnf(refute_0_52,plain,
addition(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)) = one,
inference(resolve,[$cnf( complement(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1_1) )],[refute_0_7,refute_0_51]) ).
cnf(refute_0_53,plain,
( addition(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)) != one
| multiplication(c(skolemFOFtoCNF_X1_1),addition(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1))) != multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1))
| multiplication(c(skolemFOFtoCNF_X1_1),one) = multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(c(skolemFOFtoCNF_X1_1),addition(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1))),multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1))) ),[0,1],$fot(one)]]) ).
cnf(refute_0_54,plain,
( multiplication(c(skolemFOFtoCNF_X1_1),addition(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1))) != multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1))
| multiplication(c(skolemFOFtoCNF_X1_1),one) = multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)) ),
inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)),one) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
multiplication(c(skolemFOFtoCNF_X1_1),one) = multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)),
inference(resolve,[$cnf( $equal(multiplication(c(skolemFOFtoCNF_X1_1),addition(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1))),multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1))) )],[refute_0_49,refute_0_54]) ).
cnf(refute_0_56,plain,
multiplication(A,one) = A,
inference(canonicalize,[],[normalize_0_27]) ).
cnf(refute_0_57,plain,
multiplication(c(skolemFOFtoCNF_X1_1),one) = c(skolemFOFtoCNF_X1_1),
inference(subst,[],[refute_0_56:[bind(A,$fot(c(skolemFOFtoCNF_X1_1)))]]) ).
cnf(refute_0_58,plain,
( multiplication(c(skolemFOFtoCNF_X1_1),one) != c(skolemFOFtoCNF_X1_1)
| multiplication(c(skolemFOFtoCNF_X1_1),one) != multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1))
| c(skolemFOFtoCNF_X1_1) = multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(c(skolemFOFtoCNF_X1_1),one),multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1))) ),[0],$fot(c(skolemFOFtoCNF_X1_1))]]) ).
cnf(refute_0_59,plain,
( multiplication(c(skolemFOFtoCNF_X1_1),one) != multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1))
| c(skolemFOFtoCNF_X1_1) = multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)) ),
inference(resolve,[$cnf( $equal(multiplication(c(skolemFOFtoCNF_X1_1),one),c(skolemFOFtoCNF_X1_1)) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(canonicalize,[],[normalize_0_29]) ).
cnf(refute_0_61,plain,
multiplication(addition(skolemFOFtoCNF_X1_1,B),skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)) = addition(multiplication(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)),multiplication(B,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1))),
inference(subst,[],[refute_0_60:[bind(A,$fot(skolemFOFtoCNF_X1_1)),bind(C,$fot(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)))]]) ).
cnf(refute_0_62,plain,
( multiplication(addition(skolemFOFtoCNF_X1_1,B),skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)) != addition(multiplication(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)),multiplication(B,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)))
| multiplication(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)) != zero
| multiplication(addition(skolemFOFtoCNF_X1_1,B),skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)) = addition(zero,multiplication(B,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1))) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(addition(skolemFOFtoCNF_X1_1,B),skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)),addition(multiplication(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)),multiplication(B,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_63,plain,
( multiplication(addition(skolemFOFtoCNF_X1_1,B),skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)) != addition(multiplication(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)),multiplication(B,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)))
| multiplication(addition(skolemFOFtoCNF_X1_1,B),skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)) = addition(zero,multiplication(B,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1))) ),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)),zero) )],[refute_0_10,refute_0_62]) ).
cnf(refute_0_64,plain,
multiplication(addition(skolemFOFtoCNF_X1_1,B),skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)) = addition(zero,multiplication(B,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1))),
inference(resolve,[$cnf( $equal(multiplication(addition(skolemFOFtoCNF_X1_1,B),skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)),addition(multiplication(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)),multiplication(B,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)))) )],[refute_0_61,refute_0_63]) ).
cnf(refute_0_65,plain,
addition(zero,multiplication(B,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1))) = multiplication(B,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)),
inference(subst,[],[refute_0_44:[bind(A,$fot(multiplication(B,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1))))]]) ).
cnf(refute_0_66,plain,
( addition(zero,multiplication(B,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1))) != multiplication(B,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1))
| multiplication(addition(skolemFOFtoCNF_X1_1,B),skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)) != addition(zero,multiplication(B,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)))
| multiplication(addition(skolemFOFtoCNF_X1_1,B),skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)) = multiplication(B,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(addition(skolemFOFtoCNF_X1_1,B),skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)),addition(zero,multiplication(B,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)))) ),[1],$fot(multiplication(B,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)))]]) ).
cnf(refute_0_67,plain,
( multiplication(addition(skolemFOFtoCNF_X1_1,B),skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)) != addition(zero,multiplication(B,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)))
| multiplication(addition(skolemFOFtoCNF_X1_1,B),skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)) = multiplication(B,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)) ),
inference(resolve,[$cnf( $equal(addition(zero,multiplication(B,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1))),multiplication(B,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1))) )],[refute_0_65,refute_0_66]) ).
cnf(refute_0_68,plain,
multiplication(addition(skolemFOFtoCNF_X1_1,B),skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)) = multiplication(B,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)),
inference(resolve,[$cnf( $equal(multiplication(addition(skolemFOFtoCNF_X1_1,B),skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)),addition(zero,multiplication(B,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)))) )],[refute_0_64,refute_0_67]) ).
cnf(refute_0_69,plain,
multiplication(addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)),skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)) = multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)),
inference(subst,[],[refute_0_68:[bind(B,$fot(c(skolemFOFtoCNF_X1_1)))]]) ).
cnf(refute_0_70,plain,
( ~ complement(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))
| addition(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1_1) = one ),
inference(subst,[],[refute_0_50:[bind(X0,$fot(c(skolemFOFtoCNF_X1_1))),bind(X1,$fot(skolemFOFtoCNF_X1_1))]]) ).
cnf(refute_0_71,plain,
addition(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1_1) = one,
inference(resolve,[$cnf( complement(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)) )],[refute_0_34,refute_0_70]) ).
cnf(refute_0_72,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_73,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_74,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_72,refute_0_73]) ).
cnf(refute_0_75,plain,
( addition(A,B) != addition(B,A)
| addition(B,A) = addition(A,B) ),
inference(subst,[],[refute_0_74:[bind(X,$fot(addition(A,B))),bind(Y,$fot(addition(B,A)))]]) ).
cnf(refute_0_76,plain,
addition(B,A) = addition(A,B),
inference(resolve,[$cnf( $equal(addition(A,B),addition(B,A)) )],[refute_0_40,refute_0_75]) ).
cnf(refute_0_77,plain,
addition(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1_1) = addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)),
inference(subst,[],[refute_0_76:[bind(A,$fot(skolemFOFtoCNF_X1_1)),bind(B,$fot(c(skolemFOFtoCNF_X1_1)))]]) ).
cnf(refute_0_78,plain,
( addition(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1_1) != addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))
| addition(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1_1) != one
| addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)) = one ),
introduced(tautology,[equality,[$cnf( $equal(addition(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1_1),one) ),[0],$fot(addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))]]) ).
cnf(refute_0_79,plain,
( addition(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1_1) != one
| addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)) = one ),
inference(resolve,[$cnf( $equal(addition(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1_1),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) )],[refute_0_77,refute_0_78]) ).
cnf(refute_0_80,plain,
addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)) = one,
inference(resolve,[$cnf( $equal(addition(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1_1),one) )],[refute_0_71,refute_0_79]) ).
cnf(refute_0_81,plain,
( addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)) != one
| multiplication(addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)),skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)) != multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1))
| multiplication(one,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)) = multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)),skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)),multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1))) ),[0,0],$fot(one)]]) ).
cnf(refute_0_82,plain,
( multiplication(addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)),skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)) != multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1))
| multiplication(one,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)) = multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)) ),
inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)),one) )],[refute_0_80,refute_0_81]) ).
cnf(refute_0_83,plain,
multiplication(one,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)) = multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)),
inference(resolve,[$cnf( $equal(multiplication(addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)),skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)),multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1))) )],[refute_0_69,refute_0_82]) ).
cnf(refute_0_84,plain,
multiplication(one,A) = A,
inference(canonicalize,[],[normalize_0_31]) ).
cnf(refute_0_85,plain,
multiplication(one,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)) = skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),
inference(subst,[],[refute_0_84:[bind(A,$fot(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)))]]) ).
cnf(refute_0_86,plain,
( multiplication(one,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)) != multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1))
| multiplication(one,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)) != skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)
| skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1) = multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(one,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)),multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1))) ),[0],$fot(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1))]]) ).
cnf(refute_0_87,plain,
( multiplication(one,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)) != multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1))
| skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1) = multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)) ),
inference(resolve,[$cnf( $equal(multiplication(one,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)),skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)) )],[refute_0_85,refute_0_86]) ).
cnf(refute_0_88,plain,
skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1) = multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)),
inference(resolve,[$cnf( $equal(multiplication(one,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)),multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1))) )],[refute_0_83,refute_0_87]) ).
cnf(refute_0_89,plain,
( skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1) != multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1))
| multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)) = skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1) ),
inference(subst,[],[refute_0_74:[bind(X,$fot(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1))),bind(Y,$fot(multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1))))]]) ).
cnf(refute_0_90,plain,
multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)) = skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1))) )],[refute_0_88,refute_0_89]) ).
cnf(refute_0_91,plain,
( c(skolemFOFtoCNF_X1_1) != multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1))
| multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)) != skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)
| c(skolemFOFtoCNF_X1_1) = skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1) ),
introduced(tautology,[equality,[$cnf( ~ $equal(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)) ),[0],$fot(multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)))]]) ).
cnf(refute_0_92,plain,
( c(skolemFOFtoCNF_X1_1) != multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1))
| c(skolemFOFtoCNF_X1_1) = skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1) ),
inference(resolve,[$cnf( $equal(multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)),skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)) )],[refute_0_90,refute_0_91]) ).
cnf(refute_0_93,plain,
( multiplication(c(skolemFOFtoCNF_X1_1),one) != multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1))
| c(skolemFOFtoCNF_X1_1) = skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1) ),
inference(resolve,[$cnf( $equal(c(skolemFOFtoCNF_X1_1),multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1))) )],[refute_0_59,refute_0_92]) ).
cnf(refute_0_94,plain,
c(skolemFOFtoCNF_X1_1) = skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),
inference(resolve,[$cnf( $equal(multiplication(c(skolemFOFtoCNF_X1_1),one),multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1))) )],[refute_0_55,refute_0_93]) ).
cnf(refute_0_95,plain,
( c(skolemFOFtoCNF_X1_1) != skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)
| skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1) = c(skolemFOFtoCNF_X1_1) ),
inference(subst,[],[refute_0_74:[bind(X,$fot(c(skolemFOFtoCNF_X1_1))),bind(Y,$fot(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)))]]) ).
cnf(refute_0_96,plain,
skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1) = c(skolemFOFtoCNF_X1_1),
inference(resolve,[$cnf( $equal(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)) )],[refute_0_94,refute_0_95]) ).
cnf(refute_0_97,plain,
multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),X_287) = multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),X_287),
introduced(tautology,[refl,[$fot(multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),X_287))]]) ).
cnf(refute_0_98,plain,
( multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),X_287) != multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),X_287)
| skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1) != c(skolemFOFtoCNF_X1_1)
| multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),X_287) = multiplication(c(skolemFOFtoCNF_X1_1),X_287) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),X_287),multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),X_287)) ),[1,0],$fot(c(skolemFOFtoCNF_X1_1))]]) ).
cnf(refute_0_99,plain,
( skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1) != c(skolemFOFtoCNF_X1_1)
| multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),X_287) = multiplication(c(skolemFOFtoCNF_X1_1),X_287) ),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),X_287),multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),X_287)) )],[refute_0_97,refute_0_98]) ).
cnf(refute_0_100,plain,
multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),X_287) = multiplication(c(skolemFOFtoCNF_X1_1),X_287),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),c(skolemFOFtoCNF_X1_1)) )],[refute_0_96,refute_0_99]) ).
cnf(refute_0_101,plain,
addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),X_287)) = addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),X_287)),
introduced(tautology,[refl,[$fot(addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),X_287)))]]) ).
cnf(refute_0_102,plain,
( addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),X_287)) != addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),X_287))
| multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),X_287) != multiplication(c(skolemFOFtoCNF_X1_1),X_287)
| addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),X_287)) = addition(B,multiplication(c(skolemFOFtoCNF_X1_1),X_287)) ),
introduced(tautology,[equality,[$cnf( $equal(addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),X_287)),addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),X_287))) ),[1,1],$fot(multiplication(c(skolemFOFtoCNF_X1_1),X_287))]]) ).
cnf(refute_0_103,plain,
( multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),X_287) != multiplication(c(skolemFOFtoCNF_X1_1),X_287)
| addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),X_287)) = addition(B,multiplication(c(skolemFOFtoCNF_X1_1),X_287)) ),
inference(resolve,[$cnf( $equal(addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),X_287)),addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),X_287))) )],[refute_0_101,refute_0_102]) ).
cnf(refute_0_104,plain,
addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),X_287)) = addition(B,multiplication(c(skolemFOFtoCNF_X1_1),X_287)),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),X_287),multiplication(c(skolemFOFtoCNF_X1_1),X_287)) )],[refute_0_100,refute_0_103]) ).
cnf(refute_0_105,plain,
multiplication(skolemFOFtoCNF_X1_1,addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),X_287))) = multiplication(skolemFOFtoCNF_X1_1,addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),X_287))),
introduced(tautology,[refl,[$fot(multiplication(skolemFOFtoCNF_X1_1,addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),X_287))))]]) ).
cnf(refute_0_106,plain,
( addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),X_287)) != addition(B,multiplication(c(skolemFOFtoCNF_X1_1),X_287))
| multiplication(skolemFOFtoCNF_X1_1,addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),X_287))) != multiplication(skolemFOFtoCNF_X1_1,addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),X_287)))
| multiplication(skolemFOFtoCNF_X1_1,addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),X_287))) = multiplication(skolemFOFtoCNF_X1_1,addition(B,multiplication(c(skolemFOFtoCNF_X1_1),X_287))) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(skolemFOFtoCNF_X1_1,addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),X_287))),multiplication(skolemFOFtoCNF_X1_1,addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),X_287)))) ),[1,1],$fot(addition(B,multiplication(c(skolemFOFtoCNF_X1_1),X_287)))]]) ).
cnf(refute_0_107,plain,
( addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),X_287)) != addition(B,multiplication(c(skolemFOFtoCNF_X1_1),X_287))
| multiplication(skolemFOFtoCNF_X1_1,addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),X_287))) = multiplication(skolemFOFtoCNF_X1_1,addition(B,multiplication(c(skolemFOFtoCNF_X1_1),X_287))) ),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X1_1,addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),X_287))),multiplication(skolemFOFtoCNF_X1_1,addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),X_287)))) )],[refute_0_105,refute_0_106]) ).
cnf(refute_0_108,plain,
multiplication(skolemFOFtoCNF_X1_1,addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),X_287))) = multiplication(skolemFOFtoCNF_X1_1,addition(B,multiplication(c(skolemFOFtoCNF_X1_1),X_287))),
inference(resolve,[$cnf( $equal(addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),X_287)),addition(B,multiplication(c(skolemFOFtoCNF_X1_1),X_287))) )],[refute_0_104,refute_0_107]) ).
cnf(refute_0_109,plain,
( multiplication(skolemFOFtoCNF_X1_1,addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),X_287))) != multiplication(skolemFOFtoCNF_X1_1,B)
| multiplication(skolemFOFtoCNF_X1_1,addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),X_287))) != multiplication(skolemFOFtoCNF_X1_1,addition(B,multiplication(c(skolemFOFtoCNF_X1_1),X_287)))
| multiplication(skolemFOFtoCNF_X1_1,addition(B,multiplication(c(skolemFOFtoCNF_X1_1),X_287))) = multiplication(skolemFOFtoCNF_X1_1,B) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(skolemFOFtoCNF_X1_1,addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),X_287))),multiplication(skolemFOFtoCNF_X1_1,B)) ),[0],$fot(multiplication(skolemFOFtoCNF_X1_1,addition(B,multiplication(c(skolemFOFtoCNF_X1_1),X_287))))]]) ).
cnf(refute_0_110,plain,
( multiplication(skolemFOFtoCNF_X1_1,addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),X_287))) != multiplication(skolemFOFtoCNF_X1_1,B)
| multiplication(skolemFOFtoCNF_X1_1,addition(B,multiplication(c(skolemFOFtoCNF_X1_1),X_287))) = multiplication(skolemFOFtoCNF_X1_1,B) ),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X1_1,addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),X_287))),multiplication(skolemFOFtoCNF_X1_1,addition(B,multiplication(c(skolemFOFtoCNF_X1_1),X_287)))) )],[refute_0_108,refute_0_109]) ).
cnf(refute_0_111,plain,
multiplication(skolemFOFtoCNF_X1_1,addition(B,multiplication(c(skolemFOFtoCNF_X1_1),X_287))) = multiplication(skolemFOFtoCNF_X1_1,B),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X1_1,addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),X_287))),multiplication(skolemFOFtoCNF_X1_1,B)) )],[refute_0_27,refute_0_110]) ).
cnf(refute_0_112,plain,
multiplication(skolemFOFtoCNF_X1_1,addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)),multiplication(c(skolemFOFtoCNF_X1_1),addition(skolemFOFtoCNF_X0,X_28)))) = multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2))),
inference(subst,[],[refute_0_111:[bind(B,$fot(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)))),bind(X_287,$fot(addition(skolemFOFtoCNF_X0,X_28)))]]) ).
cnf(refute_0_113,plain,
addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(canonicalize,[],[normalize_0_33]) ).
cnf(refute_0_114,plain,
addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)),addition(multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0),X_14)) = addition(addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)),multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0)),X_14),
inference(subst,[],[refute_0_113:[bind(A,$fot(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)))),bind(B,$fot(multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0))),bind(C,$fot(X_14))]]) ).
cnf(refute_0_115,plain,
addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)),multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0)) = multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0),
inference(canonicalize,[],[normalize_0_34]) ).
cnf(refute_0_116,plain,
( addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)),addition(multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0),X_14)) != addition(addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)),multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0)),X_14)
| addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)),multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0)) != multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0)
| addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)),addition(multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0),X_14)) = addition(multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0),X_14) ),
introduced(tautology,[equality,[$cnf( $equal(addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)),addition(multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0),X_14)),addition(addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)),multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0)),X_14)) ),[1,0],$fot(multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0))]]) ).
cnf(refute_0_117,plain,
( addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)),addition(multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0),X_14)) != addition(addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)),multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0)),X_14)
| addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)),addition(multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0),X_14)) = addition(multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0),X_14) ),
inference(resolve,[$cnf( $equal(addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)),multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0)),multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0)) )],[refute_0_115,refute_0_116]) ).
cnf(refute_0_118,plain,
addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)),addition(multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0),X_14)) = addition(multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0),X_14),
inference(resolve,[$cnf( $equal(addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)),addition(multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0),X_14)),addition(addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)),multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0)),X_14)) )],[refute_0_114,refute_0_117]) ).
cnf(refute_0_119,plain,
addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)),addition(multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X1_1),X_28))) = addition(multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X1_1),X_28)),
inference(subst,[],[refute_0_118:[bind(X_14,$fot(multiplication(c(skolemFOFtoCNF_X1_1),X_28)))]]) ).
cnf(refute_0_120,plain,
multiplication(c(skolemFOFtoCNF_X1_1),addition(skolemFOFtoCNF_X0,X_28)) = addition(multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X1_1),X_28)),
inference(subst,[],[refute_0_0:[bind(A,$fot(c(skolemFOFtoCNF_X1_1))),bind(B,$fot(skolemFOFtoCNF_X0)),bind(C,$fot(X_28))]]) ).
cnf(refute_0_121,plain,
( multiplication(c(skolemFOFtoCNF_X1_1),addition(skolemFOFtoCNF_X0,X_28)) != addition(multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X1_1),X_28))
| addition(multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X1_1),X_28)) = multiplication(c(skolemFOFtoCNF_X1_1),addition(skolemFOFtoCNF_X0,X_28)) ),
inference(subst,[],[refute_0_74:[bind(X,$fot(multiplication(c(skolemFOFtoCNF_X1_1),addition(skolemFOFtoCNF_X0,X_28)))),bind(Y,$fot(addition(multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X1_1),X_28))))]]) ).
cnf(refute_0_122,plain,
addition(multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X1_1),X_28)) = multiplication(c(skolemFOFtoCNF_X1_1),addition(skolemFOFtoCNF_X0,X_28)),
inference(resolve,[$cnf( $equal(multiplication(c(skolemFOFtoCNF_X1_1),addition(skolemFOFtoCNF_X0,X_28)),addition(multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X1_1),X_28))) )],[refute_0_120,refute_0_121]) ).
cnf(refute_0_123,plain,
( addition(multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X1_1),X_28)) != multiplication(c(skolemFOFtoCNF_X1_1),addition(skolemFOFtoCNF_X0,X_28))
| addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)),addition(multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X1_1),X_28))) != addition(multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X1_1),X_28))
| addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)),multiplication(c(skolemFOFtoCNF_X1_1),addition(skolemFOFtoCNF_X0,X_28))) = addition(multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X1_1),X_28)) ),
introduced(tautology,[equality,[$cnf( $equal(addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)),addition(multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X1_1),X_28))),addition(multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X1_1),X_28))) ),[0,1],$fot(multiplication(c(skolemFOFtoCNF_X1_1),addition(skolemFOFtoCNF_X0,X_28)))]]) ).
cnf(refute_0_124,plain,
( addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)),addition(multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X1_1),X_28))) != addition(multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X1_1),X_28))
| addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)),multiplication(c(skolemFOFtoCNF_X1_1),addition(skolemFOFtoCNF_X0,X_28))) = addition(multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X1_1),X_28)) ),
inference(resolve,[$cnf( $equal(addition(multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X1_1),X_28)),multiplication(c(skolemFOFtoCNF_X1_1),addition(skolemFOFtoCNF_X0,X_28))) )],[refute_0_122,refute_0_123]) ).
cnf(refute_0_125,plain,
addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)),multiplication(c(skolemFOFtoCNF_X1_1),addition(skolemFOFtoCNF_X0,X_28))) = addition(multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X1_1),X_28)),
inference(resolve,[$cnf( $equal(addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)),addition(multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X1_1),X_28))),addition(multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X1_1),X_28))) )],[refute_0_119,refute_0_124]) ).
cnf(refute_0_126,plain,
( addition(multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X1_1),X_28)) != multiplication(c(skolemFOFtoCNF_X1_1),addition(skolemFOFtoCNF_X0,X_28))
| addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)),multiplication(c(skolemFOFtoCNF_X1_1),addition(skolemFOFtoCNF_X0,X_28))) != addition(multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X1_1),X_28))
| addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)),multiplication(c(skolemFOFtoCNF_X1_1),addition(skolemFOFtoCNF_X0,X_28))) = multiplication(c(skolemFOFtoCNF_X1_1),addition(skolemFOFtoCNF_X0,X_28)) ),
introduced(tautology,[equality,[$cnf( $equal(addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)),multiplication(c(skolemFOFtoCNF_X1_1),addition(skolemFOFtoCNF_X0,X_28))),addition(multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X1_1),X_28))) ),[1],$fot(multiplication(c(skolemFOFtoCNF_X1_1),addition(skolemFOFtoCNF_X0,X_28)))]]) ).
cnf(refute_0_127,plain,
( addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)),multiplication(c(skolemFOFtoCNF_X1_1),addition(skolemFOFtoCNF_X0,X_28))) != addition(multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X1_1),X_28))
| addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)),multiplication(c(skolemFOFtoCNF_X1_1),addition(skolemFOFtoCNF_X0,X_28))) = multiplication(c(skolemFOFtoCNF_X1_1),addition(skolemFOFtoCNF_X0,X_28)) ),
inference(resolve,[$cnf( $equal(addition(multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X1_1),X_28)),multiplication(c(skolemFOFtoCNF_X1_1),addition(skolemFOFtoCNF_X0,X_28))) )],[refute_0_122,refute_0_126]) ).
cnf(refute_0_128,plain,
addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)),multiplication(c(skolemFOFtoCNF_X1_1),addition(skolemFOFtoCNF_X0,X_28))) = multiplication(c(skolemFOFtoCNF_X1_1),addition(skolemFOFtoCNF_X0,X_28)),
inference(resolve,[$cnf( $equal(addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)),multiplication(c(skolemFOFtoCNF_X1_1),addition(skolemFOFtoCNF_X0,X_28))),addition(multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X1_1),X_28))) )],[refute_0_125,refute_0_127]) ).
cnf(refute_0_129,plain,
( addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)),multiplication(c(skolemFOFtoCNF_X1_1),addition(skolemFOFtoCNF_X0,X_28))) != multiplication(c(skolemFOFtoCNF_X1_1),addition(skolemFOFtoCNF_X0,X_28))
| multiplication(skolemFOFtoCNF_X1_1,addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)),multiplication(c(skolemFOFtoCNF_X1_1),addition(skolemFOFtoCNF_X0,X_28)))) != multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)))
| multiplication(skolemFOFtoCNF_X1_1,multiplication(c(skolemFOFtoCNF_X1_1),addition(skolemFOFtoCNF_X0,X_28))) = multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2))) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(skolemFOFtoCNF_X1_1,addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)),multiplication(c(skolemFOFtoCNF_X1_1),addition(skolemFOFtoCNF_X0,X_28)))),multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)))) ),[0,1],$fot(multiplication(c(skolemFOFtoCNF_X1_1),addition(skolemFOFtoCNF_X0,X_28)))]]) ).
cnf(refute_0_130,plain,
( multiplication(skolemFOFtoCNF_X1_1,addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)),multiplication(c(skolemFOFtoCNF_X1_1),addition(skolemFOFtoCNF_X0,X_28)))) != multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)))
| multiplication(skolemFOFtoCNF_X1_1,multiplication(c(skolemFOFtoCNF_X1_1),addition(skolemFOFtoCNF_X0,X_28))) = multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2))) ),
inference(resolve,[$cnf( $equal(addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)),multiplication(c(skolemFOFtoCNF_X1_1),addition(skolemFOFtoCNF_X0,X_28))),multiplication(c(skolemFOFtoCNF_X1_1),addition(skolemFOFtoCNF_X0,X_28))) )],[refute_0_128,refute_0_129]) ).
cnf(refute_0_131,plain,
multiplication(skolemFOFtoCNF_X1_1,multiplication(c(skolemFOFtoCNF_X1_1),addition(skolemFOFtoCNF_X0,X_28))) = multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2))),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X1_1,addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)),multiplication(c(skolemFOFtoCNF_X1_1),addition(skolemFOFtoCNF_X0,X_28)))),multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)))) )],[refute_0_112,refute_0_130]) ).
cnf(refute_0_132,plain,
multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),C) = multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),C),
introduced(tautology,[refl,[$fot(multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),C))]]) ).
cnf(refute_0_133,plain,
( multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),C) != multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),C)
| skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1) != c(skolemFOFtoCNF_X1_1)
| multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),C) = multiplication(c(skolemFOFtoCNF_X1_1),C) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),C),multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),C)) ),[1,0],$fot(c(skolemFOFtoCNF_X1_1))]]) ).
cnf(refute_0_134,plain,
( skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1) != c(skolemFOFtoCNF_X1_1)
| multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),C) = multiplication(c(skolemFOFtoCNF_X1_1),C) ),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),C),multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),C)) )],[refute_0_132,refute_0_133]) ).
cnf(refute_0_135,plain,
multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),C) = multiplication(c(skolemFOFtoCNF_X1_1),C),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),c(skolemFOFtoCNF_X1_1)) )],[refute_0_96,refute_0_134]) ).
cnf(refute_0_136,plain,
multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),C)) = multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),C)),
introduced(tautology,[refl,[$fot(multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),C)))]]) ).
cnf(refute_0_137,plain,
( multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),C) != multiplication(c(skolemFOFtoCNF_X1_1),C)
| multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),C)) != multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),C))
| multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),C)) = multiplication(skolemFOFtoCNF_X1_1,multiplication(c(skolemFOFtoCNF_X1_1),C)) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),C)),multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),C))) ),[1,1],$fot(multiplication(c(skolemFOFtoCNF_X1_1),C))]]) ).
cnf(refute_0_138,plain,
( multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),C) != multiplication(c(skolemFOFtoCNF_X1_1),C)
| multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),C)) = multiplication(skolemFOFtoCNF_X1_1,multiplication(c(skolemFOFtoCNF_X1_1),C)) ),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),C)),multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),C))) )],[refute_0_136,refute_0_137]) ).
cnf(refute_0_139,plain,
multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),C)) = multiplication(skolemFOFtoCNF_X1_1,multiplication(c(skolemFOFtoCNF_X1_1),C)),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),C),multiplication(c(skolemFOFtoCNF_X1_1),C)) )],[refute_0_135,refute_0_138]) ).
cnf(refute_0_140,plain,
( multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),C)) != multiplication(skolemFOFtoCNF_X1_1,multiplication(c(skolemFOFtoCNF_X1_1),C))
| multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),C)) != zero
| multiplication(skolemFOFtoCNF_X1_1,multiplication(c(skolemFOFtoCNF_X1_1),C)) = zero ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),C)),zero) ),[0],$fot(multiplication(skolemFOFtoCNF_X1_1,multiplication(c(skolemFOFtoCNF_X1_1),C)))]]) ).
cnf(refute_0_141,plain,
( multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),C)) != zero
| multiplication(skolemFOFtoCNF_X1_1,multiplication(c(skolemFOFtoCNF_X1_1),C)) = zero ),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),C)),multiplication(skolemFOFtoCNF_X1_1,multiplication(c(skolemFOFtoCNF_X1_1),C))) )],[refute_0_139,refute_0_140]) ).
cnf(refute_0_142,plain,
multiplication(skolemFOFtoCNF_X1_1,multiplication(c(skolemFOFtoCNF_X1_1),C)) = zero,
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),C)),zero) )],[refute_0_18,refute_0_141]) ).
cnf(refute_0_143,plain,
multiplication(skolemFOFtoCNF_X1_1,multiplication(c(skolemFOFtoCNF_X1_1),addition(skolemFOFtoCNF_X0,X_28))) = zero,
inference(subst,[],[refute_0_142:[bind(C,$fot(addition(skolemFOFtoCNF_X0,X_28)))]]) ).
cnf(refute_0_144,plain,
( multiplication(skolemFOFtoCNF_X1_1,multiplication(c(skolemFOFtoCNF_X1_1),addition(skolemFOFtoCNF_X0,X_28))) != multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)))
| multiplication(skolemFOFtoCNF_X1_1,multiplication(c(skolemFOFtoCNF_X1_1),addition(skolemFOFtoCNF_X0,X_28))) != zero
| zero = multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2))) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(skolemFOFtoCNF_X1_1,multiplication(c(skolemFOFtoCNF_X1_1),addition(skolemFOFtoCNF_X0,X_28))),multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)))) ),[0],$fot(zero)]]) ).
cnf(refute_0_145,plain,
( multiplication(skolemFOFtoCNF_X1_1,multiplication(c(skolemFOFtoCNF_X1_1),addition(skolemFOFtoCNF_X0,X_28))) != multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)))
| zero = multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2))) ),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X1_1,multiplication(c(skolemFOFtoCNF_X1_1),addition(skolemFOFtoCNF_X0,X_28))),zero) )],[refute_0_143,refute_0_144]) ).
cnf(refute_0_146,plain,
zero = multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2))),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X1_1,multiplication(c(skolemFOFtoCNF_X1_1),addition(skolemFOFtoCNF_X0,X_28))),multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)))) )],[refute_0_131,refute_0_145]) ).
cnf(refute_0_147,plain,
multiplication(multiplication(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X2)) != zero,
inference(canonicalize,[],[normalize_0_35]) ).
cnf(refute_0_148,plain,
( multiplication(A,multiplication(B,C)) != multiplication(multiplication(A,B),C)
| multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) ),
inference(subst,[],[refute_0_74:[bind(X,$fot(multiplication(A,multiplication(B,C)))),bind(Y,$fot(multiplication(multiplication(A,B),C)))]]) ).
cnf(refute_0_149,plain,
multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)),
inference(resolve,[$cnf( $equal(multiplication(A,multiplication(B,C)),multiplication(multiplication(A,B),C)) )],[refute_0_2,refute_0_148]) ).
cnf(refute_0_150,plain,
multiplication(multiplication(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X2)) = multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2))),
inference(subst,[],[refute_0_149:[bind(A,$fot(skolemFOFtoCNF_X1_1)),bind(B,$fot(skolemFOFtoCNF_X0)),bind(C,$fot(c(skolemFOFtoCNF_X2)))]]) ).
cnf(refute_0_151,plain,
( multiplication(multiplication(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X2)) != multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)))
| multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2))) != zero
| multiplication(multiplication(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X2)) = zero ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiplication(multiplication(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X2)),zero) ),[0],$fot(multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2))))]]) ).
cnf(refute_0_152,plain,
( multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2))) != zero
| multiplication(multiplication(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X2)) = zero ),
inference(resolve,[$cnf( $equal(multiplication(multiplication(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X2)),multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)))) )],[refute_0_150,refute_0_151]) ).
cnf(refute_0_153,plain,
multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2))) != zero,
inference(resolve,[$cnf( $equal(multiplication(multiplication(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X2)),zero) )],[refute_0_152,refute_0_147]) ).
cnf(refute_0_154,plain,
( zero != multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)))
| multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2))) = zero ),
inference(subst,[],[refute_0_74:[bind(X,$fot(zero)),bind(Y,$fot(multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)))))]]) ).
cnf(refute_0_155,plain,
zero != multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2))),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2))),zero) )],[refute_0_154,refute_0_153]) ).
cnf(refute_0_156,plain,
$false,
inference(resolve,[$cnf( $equal(zero,multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)))) )],[refute_0_146,refute_0_155]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : KLE024+1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n018.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jun 16 08:09:45 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 54.39/54.56 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 54.39/54.56
% 54.39/54.56 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 54.39/54.57
%------------------------------------------------------------------------------