TSTP Solution File: HAL002+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : HAL002+1 : TPTP v5.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art11.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 3.00GHz @ 3000MHz
% Memory : 2006MB
% OS : Linux 2.6.31.5-127.fc12.i686.PAE
% CPULimit : 300s
% DateTime : Sat Dec 25 11:39:03 EST 2010
% Result : Theorem 9.89s
% Output : CNFRefutation 9.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 11
% Syntax : Number of formulae : 124 ( 11 unt; 0 def)
% Number of atoms : 437 ( 122 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 538 ( 225 ~; 257 |; 39 &)
% ( 2 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 267 ( 6 sgn 133 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2,X3] :
( ( injection(X1)
& morphism(X1,X2,X3) )
=> ! [X4,X5] :
( ( element(X4,X2)
& element(X5,X2)
& apply(X1,X4) = apply(X1,X5) )
=> X4 = X5 ) ),
file('/tmp/tmpbrbZqO/sel_HAL002+1.p_1',injection_properties) ).
fof(2,axiom,
! [X2,X4,X5] :
( ( element(X4,X2)
& element(X5,X2) )
=> subtract(X2,X4,subtract(X2,X4,X5)) = X5 ),
file('/tmp/tmpbrbZqO/sel_HAL002+1.p_1',subtract_cancellation) ).
fof(3,axiom,
! [X1,X2,X3] :
( morphism(X1,X2,X3)
=> ! [X4,X5] :
( ( element(X4,X2)
& element(X5,X2) )
=> apply(X1,subtract(X2,X4,X5)) = subtract(X3,apply(X1,X4),apply(X1,X5)) ) ),
file('/tmp/tmpbrbZqO/sel_HAL002+1.p_1',subtract_distribution) ).
fof(4,axiom,
! [X2,X4,X5] :
( ( element(X4,X2)
& element(X5,X2) )
=> element(subtract(X2,X4,X5),X2) ),
file('/tmp/tmpbrbZqO/sel_HAL002+1.p_1',subtract_in_domain) ).
fof(5,axiom,
! [X2,X6] :
( element(X6,X2)
=> subtract(X2,X6,X6) = zero(X2) ),
file('/tmp/tmpbrbZqO/sel_HAL002+1.p_1',subtract_to_0) ).
fof(6,axiom,
! [X1,X2,X3] :
( ( morphism(X1,X2,X3)
& ! [X4,X5] :
( ( element(X4,X2)
& element(X5,X2)
& apply(X1,X4) = apply(X1,X5) )
=> X4 = X5 ) )
=> injection(X1) ),
file('/tmp/tmpbrbZqO/sel_HAL002+1.p_1',properties_for_injection) ).
fof(7,axiom,
! [X1,X2,X3] :
( morphism(X1,X2,X3)
=> ( ! [X6] :
( element(X6,X2)
=> element(apply(X1,X6),X3) )
& apply(X1,zero(X2)) = zero(X3) ) ),
file('/tmp/tmpbrbZqO/sel_HAL002+1.p_1',morphism) ).
fof(8,axiom,
! [X1,X2,X3] :
( ( morphism(X1,X2,X3)
& ! [X6] :
( ( element(X6,X2)
& apply(X1,X6) = zero(X3) )
=> X6 = zero(X2) ) )
=> injection_2(X1) ),
file('/tmp/tmpbrbZqO/sel_HAL002+1.p_1',properties_for_injection_2) ).
fof(9,conjecture,
( injection(x)
<=> injection_2(x) ),
file('/tmp/tmpbrbZqO/sel_HAL002+1.p_1',my) ).
fof(10,axiom,
morphism(x,any1,any2),
file('/tmp/tmpbrbZqO/sel_HAL002+1.p_1',x_morphism) ).
fof(11,axiom,
! [X1,X2,X3] :
( ( injection_2(X1)
& morphism(X1,X2,X3) )
=> ! [X6] :
( ( element(X6,X2)
& apply(X1,X6) = zero(X3) )
=> X6 = zero(X2) ) ),
file('/tmp/tmpbrbZqO/sel_HAL002+1.p_1',injection_properties_2) ).
fof(12,negated_conjecture,
~ ( injection(x)
<=> injection_2(x) ),
inference(assume_negation,[status(cth)],[9]) ).
fof(13,plain,
! [X1,X2,X3] :
( ~ injection(X1)
| ~ morphism(X1,X2,X3)
| ! [X4,X5] :
( ~ element(X4,X2)
| ~ element(X5,X2)
| apply(X1,X4) != apply(X1,X5)
| X4 = X5 ) ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(14,plain,
! [X6,X7,X8] :
( ~ injection(X6)
| ~ morphism(X6,X7,X8)
| ! [X9,X10] :
( ~ element(X9,X7)
| ~ element(X10,X7)
| apply(X6,X9) != apply(X6,X10)
| X9 = X10 ) ),
inference(variable_rename,[status(thm)],[13]) ).
fof(15,plain,
! [X6,X7,X8,X9,X10] :
( ~ element(X9,X7)
| ~ element(X10,X7)
| apply(X6,X9) != apply(X6,X10)
| X9 = X10
| ~ injection(X6)
| ~ morphism(X6,X7,X8) ),
inference(shift_quantors,[status(thm)],[14]) ).
cnf(16,plain,
( X4 = X5
| ~ morphism(X1,X2,X3)
| ~ injection(X1)
| apply(X1,X4) != apply(X1,X5)
| ~ element(X5,X2)
| ~ element(X4,X2) ),
inference(split_conjunct,[status(thm)],[15]) ).
fof(17,plain,
! [X2,X4,X5] :
( ~ element(X4,X2)
| ~ element(X5,X2)
| subtract(X2,X4,subtract(X2,X4,X5)) = X5 ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(18,plain,
! [X6,X7,X8] :
( ~ element(X7,X6)
| ~ element(X8,X6)
| subtract(X6,X7,subtract(X6,X7,X8)) = X8 ),
inference(variable_rename,[status(thm)],[17]) ).
cnf(19,plain,
( subtract(X1,X2,subtract(X1,X2,X3)) = X3
| ~ element(X3,X1)
| ~ element(X2,X1) ),
inference(split_conjunct,[status(thm)],[18]) ).
fof(20,plain,
! [X1,X2,X3] :
( ~ morphism(X1,X2,X3)
| ! [X4,X5] :
( ~ element(X4,X2)
| ~ element(X5,X2)
| apply(X1,subtract(X2,X4,X5)) = subtract(X3,apply(X1,X4),apply(X1,X5)) ) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(21,plain,
! [X6,X7,X8] :
( ~ morphism(X6,X7,X8)
| ! [X9,X10] :
( ~ element(X9,X7)
| ~ element(X10,X7)
| apply(X6,subtract(X7,X9,X10)) = subtract(X8,apply(X6,X9),apply(X6,X10)) ) ),
inference(variable_rename,[status(thm)],[20]) ).
fof(22,plain,
! [X6,X7,X8,X9,X10] :
( ~ element(X9,X7)
| ~ element(X10,X7)
| apply(X6,subtract(X7,X9,X10)) = subtract(X8,apply(X6,X9),apply(X6,X10))
| ~ morphism(X6,X7,X8) ),
inference(shift_quantors,[status(thm)],[21]) ).
cnf(23,plain,
( apply(X1,subtract(X2,X4,X5)) = subtract(X3,apply(X1,X4),apply(X1,X5))
| ~ morphism(X1,X2,X3)
| ~ element(X5,X2)
| ~ element(X4,X2) ),
inference(split_conjunct,[status(thm)],[22]) ).
fof(24,plain,
! [X2,X4,X5] :
( ~ element(X4,X2)
| ~ element(X5,X2)
| element(subtract(X2,X4,X5),X2) ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(25,plain,
! [X6,X7,X8] :
( ~ element(X7,X6)
| ~ element(X8,X6)
| element(subtract(X6,X7,X8),X6) ),
inference(variable_rename,[status(thm)],[24]) ).
cnf(26,plain,
( element(subtract(X1,X2,X3),X1)
| ~ element(X3,X1)
| ~ element(X2,X1) ),
inference(split_conjunct,[status(thm)],[25]) ).
fof(27,plain,
! [X2,X6] :
( ~ element(X6,X2)
| subtract(X2,X6,X6) = zero(X2) ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(28,plain,
! [X7,X8] :
( ~ element(X8,X7)
| subtract(X7,X8,X8) = zero(X7) ),
inference(variable_rename,[status(thm)],[27]) ).
cnf(29,plain,
( subtract(X1,X2,X2) = zero(X1)
| ~ element(X2,X1) ),
inference(split_conjunct,[status(thm)],[28]) ).
fof(30,plain,
! [X1,X2,X3] :
( ~ morphism(X1,X2,X3)
| ? [X4,X5] :
( element(X4,X2)
& element(X5,X2)
& apply(X1,X4) = apply(X1,X5)
& X4 != X5 )
| injection(X1) ),
inference(fof_nnf,[status(thm)],[6]) ).
fof(31,plain,
! [X6,X7,X8] :
( ~ morphism(X6,X7,X8)
| ? [X9,X10] :
( element(X9,X7)
& element(X10,X7)
& apply(X6,X9) = apply(X6,X10)
& X9 != X10 )
| injection(X6) ),
inference(variable_rename,[status(thm)],[30]) ).
fof(32,plain,
! [X6,X7,X8] :
( ~ morphism(X6,X7,X8)
| ( element(esk1_3(X6,X7,X8),X7)
& element(esk2_3(X6,X7,X8),X7)
& apply(X6,esk1_3(X6,X7,X8)) = apply(X6,esk2_3(X6,X7,X8))
& esk1_3(X6,X7,X8) != esk2_3(X6,X7,X8) )
| injection(X6) ),
inference(skolemize,[status(esa)],[31]) ).
fof(33,plain,
! [X6,X7,X8] :
( ( element(esk1_3(X6,X7,X8),X7)
| ~ morphism(X6,X7,X8)
| injection(X6) )
& ( element(esk2_3(X6,X7,X8),X7)
| ~ morphism(X6,X7,X8)
| injection(X6) )
& ( apply(X6,esk1_3(X6,X7,X8)) = apply(X6,esk2_3(X6,X7,X8))
| ~ morphism(X6,X7,X8)
| injection(X6) )
& ( esk1_3(X6,X7,X8) != esk2_3(X6,X7,X8)
| ~ morphism(X6,X7,X8)
| injection(X6) ) ),
inference(distribute,[status(thm)],[32]) ).
cnf(34,plain,
( injection(X1)
| ~ morphism(X1,X2,X3)
| esk1_3(X1,X2,X3) != esk2_3(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[33]) ).
cnf(35,plain,
( injection(X1)
| apply(X1,esk1_3(X1,X2,X3)) = apply(X1,esk2_3(X1,X2,X3))
| ~ morphism(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[33]) ).
cnf(36,plain,
( injection(X1)
| element(esk2_3(X1,X2,X3),X2)
| ~ morphism(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[33]) ).
cnf(37,plain,
( injection(X1)
| element(esk1_3(X1,X2,X3),X2)
| ~ morphism(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[33]) ).
fof(38,plain,
! [X1,X2,X3] :
( ~ morphism(X1,X2,X3)
| ( ! [X6] :
( ~ element(X6,X2)
| element(apply(X1,X6),X3) )
& apply(X1,zero(X2)) = zero(X3) ) ),
inference(fof_nnf,[status(thm)],[7]) ).
fof(39,plain,
! [X7,X8,X9] :
( ~ morphism(X7,X8,X9)
| ( ! [X10] :
( ~ element(X10,X8)
| element(apply(X7,X10),X9) )
& apply(X7,zero(X8)) = zero(X9) ) ),
inference(variable_rename,[status(thm)],[38]) ).
fof(40,plain,
! [X7,X8,X9,X10] :
( ( ( ~ element(X10,X8)
| element(apply(X7,X10),X9) )
& apply(X7,zero(X8)) = zero(X9) )
| ~ morphism(X7,X8,X9) ),
inference(shift_quantors,[status(thm)],[39]) ).
fof(41,plain,
! [X7,X8,X9,X10] :
( ( ~ element(X10,X8)
| element(apply(X7,X10),X9)
| ~ morphism(X7,X8,X9) )
& ( apply(X7,zero(X8)) = zero(X9)
| ~ morphism(X7,X8,X9) ) ),
inference(distribute,[status(thm)],[40]) ).
cnf(42,plain,
( apply(X1,zero(X2)) = zero(X3)
| ~ morphism(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[41]) ).
cnf(43,plain,
( element(apply(X1,X4),X3)
| ~ morphism(X1,X2,X3)
| ~ element(X4,X2) ),
inference(split_conjunct,[status(thm)],[41]) ).
fof(44,plain,
! [X1,X2,X3] :
( ~ morphism(X1,X2,X3)
| ? [X6] :
( element(X6,X2)
& apply(X1,X6) = zero(X3)
& X6 != zero(X2) )
| injection_2(X1) ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(45,plain,
! [X7,X8,X9] :
( ~ morphism(X7,X8,X9)
| ? [X10] :
( element(X10,X8)
& apply(X7,X10) = zero(X9)
& X10 != zero(X8) )
| injection_2(X7) ),
inference(variable_rename,[status(thm)],[44]) ).
fof(46,plain,
! [X7,X8,X9] :
( ~ morphism(X7,X8,X9)
| ( element(esk3_3(X7,X8,X9),X8)
& apply(X7,esk3_3(X7,X8,X9)) = zero(X9)
& esk3_3(X7,X8,X9) != zero(X8) )
| injection_2(X7) ),
inference(skolemize,[status(esa)],[45]) ).
fof(47,plain,
! [X7,X8,X9] :
( ( element(esk3_3(X7,X8,X9),X8)
| ~ morphism(X7,X8,X9)
| injection_2(X7) )
& ( apply(X7,esk3_3(X7,X8,X9)) = zero(X9)
| ~ morphism(X7,X8,X9)
| injection_2(X7) )
& ( esk3_3(X7,X8,X9) != zero(X8)
| ~ morphism(X7,X8,X9)
| injection_2(X7) ) ),
inference(distribute,[status(thm)],[46]) ).
cnf(48,plain,
( injection_2(X1)
| ~ morphism(X1,X2,X3)
| esk3_3(X1,X2,X3) != zero(X2) ),
inference(split_conjunct,[status(thm)],[47]) ).
cnf(49,plain,
( injection_2(X1)
| apply(X1,esk3_3(X1,X2,X3)) = zero(X3)
| ~ morphism(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[47]) ).
cnf(50,plain,
( injection_2(X1)
| element(esk3_3(X1,X2,X3),X2)
| ~ morphism(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[47]) ).
fof(51,negated_conjecture,
( ( ~ injection(x)
| ~ injection_2(x) )
& ( injection(x)
| injection_2(x) ) ),
inference(fof_nnf,[status(thm)],[12]) ).
cnf(52,negated_conjecture,
( injection_2(x)
| injection(x) ),
inference(split_conjunct,[status(thm)],[51]) ).
cnf(53,negated_conjecture,
( ~ injection_2(x)
| ~ injection(x) ),
inference(split_conjunct,[status(thm)],[51]) ).
cnf(54,plain,
morphism(x,any1,any2),
inference(split_conjunct,[status(thm)],[10]) ).
fof(55,plain,
! [X1,X2,X3] :
( ~ injection_2(X1)
| ~ morphism(X1,X2,X3)
| ! [X6] :
( ~ element(X6,X2)
| apply(X1,X6) != zero(X3)
| X6 = zero(X2) ) ),
inference(fof_nnf,[status(thm)],[11]) ).
fof(56,plain,
! [X7,X8,X9] :
( ~ injection_2(X7)
| ~ morphism(X7,X8,X9)
| ! [X10] :
( ~ element(X10,X8)
| apply(X7,X10) != zero(X9)
| X10 = zero(X8) ) ),
inference(variable_rename,[status(thm)],[55]) ).
fof(57,plain,
! [X7,X8,X9,X10] :
( ~ element(X10,X8)
| apply(X7,X10) != zero(X9)
| X10 = zero(X8)
| ~ injection_2(X7)
| ~ morphism(X7,X8,X9) ),
inference(shift_quantors,[status(thm)],[56]) ).
cnf(58,plain,
( X4 = zero(X2)
| ~ morphism(X1,X2,X3)
| ~ injection_2(X1)
| apply(X1,X4) != zero(X3)
| ~ element(X4,X2) ),
inference(split_conjunct,[status(thm)],[57]) ).
cnf(60,plain,
apply(x,zero(any1)) = zero(any2),
inference(spm,[status(thm)],[42,54,theory(equality)]) ).
cnf(61,plain,
( element(apply(x,X1),any2)
| ~ element(X1,any1) ),
inference(spm,[status(thm)],[43,54,theory(equality)]) ).
cnf(62,plain,
( zero(any1) = X1
| apply(x,X1) != zero(any2)
| ~ injection_2(x)
| ~ element(X1,any1) ),
inference(spm,[status(thm)],[58,54,theory(equality)]) ).
cnf(63,plain,
( element(zero(X1),X1)
| ~ element(X2,X1) ),
inference(spm,[status(thm)],[26,29,theory(equality)]) ).
cnf(64,plain,
( subtract(X1,X2,zero(X1)) = X2
| ~ element(X2,X1) ),
inference(spm,[status(thm)],[19,29,theory(equality)]) ).
cnf(66,plain,
( X1 = X2
| apply(x,X1) != apply(x,X2)
| ~ element(X2,any1)
| ~ element(X1,any1)
| ~ injection(x) ),
inference(spm,[status(thm)],[16,54,theory(equality)]) ).
cnf(67,plain,
( subtract(any2,apply(x,X1),apply(x,X2)) = apply(x,subtract(any1,X1,X2))
| ~ element(X2,any1)
| ~ element(X1,any1) ),
inference(spm,[status(thm)],[23,54,theory(equality)]) ).
cnf(70,plain,
( element(zero(X1),X1)
| injection_2(X2)
| ~ morphism(X2,X1,X3) ),
inference(spm,[status(thm)],[63,50,theory(equality)]) ).
cnf(77,plain,
( element(zero(any2),any2)
| ~ element(X1,any1) ),
inference(spm,[status(thm)],[63,61,theory(equality)]) ).
cnf(84,negated_conjecture,
( zero(any1) = X1
| injection(x)
| apply(x,X1) != zero(any2)
| ~ element(X1,any1) ),
inference(spm,[status(thm)],[62,52,theory(equality)]) ).
cnf(88,plain,
( injection_2(x)
| element(zero(any1),any1) ),
inference(spm,[status(thm)],[70,54,theory(equality)]) ).
cnf(96,plain,
( subtract(any2,apply(x,X1),zero(any2)) = apply(x,subtract(any1,X1,zero(any1)))
| ~ element(zero(any1),any1)
| ~ element(X1,any1) ),
inference(spm,[status(thm)],[67,60,theory(equality)]) ).
cnf(97,plain,
( apply(x,subtract(any1,X1,X1)) = zero(any2)
| ~ element(apply(x,X1),any2)
| ~ element(X1,any1) ),
inference(spm,[status(thm)],[29,67,theory(equality)]) ).
cnf(99,plain,
( subtract(any2,zero(X2),apply(x,X3)) = apply(x,subtract(any1,esk3_3(x,X1,X2),X3))
| injection_2(x)
| ~ element(X3,any1)
| ~ element(esk3_3(x,X1,X2),any1)
| ~ morphism(x,X1,X2) ),
inference(spm,[status(thm)],[67,49,theory(equality)]) ).
cnf(101,plain,
( subtract(any2,apply(x,X1),apply(x,subtract(any1,X1,X2))) = apply(x,X2)
| ~ element(apply(x,X2),any2)
| ~ element(apply(x,X1),any2)
| ~ element(X2,any1)
| ~ element(X1,any1) ),
inference(spm,[status(thm)],[19,67,theory(equality)]) ).
cnf(111,plain,
( apply(x,subtract(any1,X1,X1)) = zero(any2)
| ~ element(X1,any1) ),
inference(csr,[status(thm)],[97,61]) ).
cnf(149,plain,
( subtract(any2,apply(x,X1),zero(any2)) = apply(x,subtract(any1,X1,zero(any1)))
| ~ element(X1,any1) ),
inference(csr,[status(thm)],[96,63]) ).
cnf(153,plain,
( subtract(any2,apply(x,X1),apply(x,subtract(any1,X1,zero(any1)))) = zero(any2)
| ~ element(zero(any2),any2)
| ~ element(apply(x,X1),any2)
| ~ element(X1,any1) ),
inference(spm,[status(thm)],[19,149,theory(equality)]) ).
cnf(154,plain,
( subtract(any2,apply(x,esk1_3(x,X1,X2)),zero(any2)) = apply(x,subtract(any1,esk2_3(x,X1,X2),zero(any1)))
| injection(x)
| ~ element(esk2_3(x,X1,X2),any1)
| ~ morphism(x,X1,X2) ),
inference(spm,[status(thm)],[149,35,theory(equality)]) ).
cnf(155,plain,
( apply(x,subtract(any1,X1,zero(any1))) = apply(x,X1)
| ~ element(apply(x,X1),any2)
| ~ element(X1,any1) ),
inference(spm,[status(thm)],[64,149,theory(equality)]) ).
cnf(158,plain,
( apply(x,subtract(any1,X1,zero(any1))) = apply(x,X1)
| ~ element(X1,any1) ),
inference(csr,[status(thm)],[155,61]) ).
cnf(160,plain,
( subtract(any2,apply(x,X1),apply(x,X2)) = apply(x,subtract(any1,subtract(any1,X1,zero(any1)),X2))
| ~ element(X2,any1)
| ~ element(subtract(any1,X1,zero(any1)),any1)
| ~ element(X1,any1) ),
inference(spm,[status(thm)],[67,158,theory(equality)]) ).
cnf(192,plain,
( apply(x,esk3_3(x,X1,X2)) = subtract(any2,zero(X2),apply(x,zero(any1)))
| injection_2(x)
| ~ element(esk3_3(x,X1,X2),any1)
| ~ element(zero(any1),any1)
| ~ morphism(x,X1,X2) ),
inference(spm,[status(thm)],[99,64,theory(equality)]) ).
cnf(203,plain,
( apply(x,esk3_3(x,X1,X2)) = subtract(any2,zero(X2),zero(any2))
| injection_2(x)
| ~ element(esk3_3(x,X1,X2),any1)
| ~ element(zero(any1),any1)
| ~ morphism(x,X1,X2) ),
inference(rw,[status(thm)],[192,60,theory(equality)]) ).
cnf(269,plain,
( subtract(any2,apply(x,X1),apply(x,subtract(any1,X1,X2))) = apply(x,X2)
| ~ element(apply(x,X2),any2)
| ~ element(X2,any1)
| ~ element(X1,any1) ),
inference(csr,[status(thm)],[101,61]) ).
cnf(270,plain,
( subtract(any2,apply(x,X1),apply(x,subtract(any1,X1,X2))) = apply(x,X2)
| ~ element(X2,any1)
| ~ element(X1,any1) ),
inference(csr,[status(thm)],[269,61]) ).
cnf(272,plain,
( subtract(any2,apply(x,X1),apply(x,zero(any1))) = apply(x,X1)
| ~ element(X1,any1) ),
inference(spm,[status(thm)],[270,29,theory(equality)]) ).
cnf(291,plain,
( subtract(any2,apply(x,X1),zero(any2)) = apply(x,X1)
| ~ element(X1,any1) ),
inference(rw,[status(thm)],[272,60,theory(equality)]) ).
cnf(302,plain,
( subtract(any2,apply(x,esk1_3(x,X1,X2)),zero(any2)) = apply(x,esk1_3(x,X1,X2))
| injection(x)
| ~ element(esk2_3(x,X1,X2),any1)
| ~ morphism(x,X1,X2) ),
inference(spm,[status(thm)],[291,35,theory(equality)]) ).
cnf(303,plain,
( subtract(any2,zero(any2),zero(any2)) = zero(any2)
| ~ element(subtract(any1,X1,X1),any1)
| ~ element(X1,any1) ),
inference(spm,[status(thm)],[291,111,theory(equality)]) ).
cnf(379,plain,
( subtract(any2,zero(any2),zero(any2)) = zero(any2)
| ~ element(X1,any1) ),
inference(spm,[status(thm)],[303,26,theory(equality)]) ).
cnf(835,plain,
( subtract(any2,apply(x,X1),apply(x,subtract(any1,X1,zero(any1)))) = zero(any2)
| ~ element(zero(any2),any2)
| ~ element(X1,any1) ),
inference(csr,[status(thm)],[153,61]) ).
cnf(836,plain,
( subtract(any2,apply(x,X1),apply(x,subtract(any1,X1,zero(any1)))) = zero(any2)
| ~ element(X1,any1) ),
inference(csr,[status(thm)],[835,77]) ).
cnf(1079,plain,
( zero(any1) = subtract(any1,subtract(any1,X1,zero(any1)),X2)
| injection(x)
| subtract(any2,apply(x,X1),apply(x,X2)) != zero(any2)
| ~ element(subtract(any1,subtract(any1,X1,zero(any1)),X2),any1)
| ~ element(subtract(any1,X1,zero(any1)),any1)
| ~ element(X2,any1)
| ~ element(X1,any1) ),
inference(spm,[status(thm)],[84,160,theory(equality)]) ).
cnf(1386,plain,
( apply(x,esk3_3(x,X1,X2)) = subtract(any2,zero(X2),zero(any2))
| injection_2(x)
| ~ element(esk3_3(x,X1,X2),any1)
| ~ morphism(x,X1,X2) ),
inference(csr,[status(thm)],[203,63]) ).
cnf(2608,plain,
( apply(x,esk1_3(x,X1,X2)) = apply(x,subtract(any1,esk2_3(x,X1,X2),zero(any1)))
| injection(x)
| ~ element(esk2_3(x,X1,X2),any1)
| ~ morphism(x,X1,X2) ),
inference(spm,[status(thm)],[154,302,theory(equality)]) ).
cnf(3928,plain,
( subtract(any2,apply(x,esk2_3(x,X1,X2)),apply(x,esk1_3(x,X1,X2))) = zero(any2)
| injection(x)
| ~ element(esk2_3(x,X1,X2),any1)
| ~ morphism(x,X1,X2) ),
inference(spm,[status(thm)],[836,2608,theory(equality)]) ).
cnf(34300,plain,
( subtract(any1,subtract(any1,X1,zero(any1)),X2) = zero(any1)
| injection(x)
| subtract(any2,apply(x,X1),apply(x,X2)) != zero(any2)
| ~ element(subtract(any1,X1,zero(any1)),any1)
| ~ element(X2,any1)
| ~ element(X1,any1) ),
inference(csr,[status(thm)],[1079,26]) ).
cnf(34306,plain,
( subtract(any1,X1,X2) = zero(any1)
| injection(x)
| subtract(any2,apply(x,X1),apply(x,X2)) != zero(any2)
| ~ element(X1,any1)
| ~ element(X2,any1) ),
inference(spm,[status(thm)],[34300,64,theory(equality)]) ).
cnf(35443,plain,
( subtract(any1,esk2_3(x,X1,X2),esk1_3(x,X1,X2)) = zero(any1)
| injection(x)
| ~ element(esk2_3(x,X1,X2),any1)
| ~ element(esk1_3(x,X1,X2),any1)
| ~ morphism(x,X1,X2) ),
inference(spm,[status(thm)],[34306,3928,theory(equality)]) ).
cnf(111352,plain,
( subtract(any1,esk2_3(x,X1,X2),zero(any1)) = esk1_3(x,X1,X2)
| injection(x)
| ~ element(esk1_3(x,X1,X2),any1)
| ~ element(esk2_3(x,X1,X2),any1)
| ~ morphism(x,X1,X2) ),
inference(spm,[status(thm)],[19,35443,theory(equality)]) ).
cnf(111395,plain,
( esk1_3(x,X1,X2) = esk2_3(x,X1,X2)
| injection(x)
| ~ element(esk2_3(x,X1,X2),any1)
| ~ element(esk1_3(x,X1,X2),any1)
| ~ morphism(x,X1,X2) ),
inference(spm,[status(thm)],[64,111352,theory(equality)]) ).
cnf(111514,plain,
( injection(x)
| ~ element(esk2_3(x,X1,X2),any1)
| ~ element(esk1_3(x,X1,X2),any1)
| ~ morphism(x,X1,X2) ),
inference(csr,[status(thm)],[111395,34]) ).
cnf(111515,plain,
( injection(x)
| ~ element(esk1_3(x,any1,X1),any1)
| ~ morphism(x,any1,X1) ),
inference(spm,[status(thm)],[111514,36,theory(equality)]) ).
cnf(111516,plain,
( injection(x)
| ~ morphism(x,any1,X1) ),
inference(csr,[status(thm)],[111515,37]) ).
cnf(111517,plain,
injection(x),
inference(spm,[status(thm)],[111516,54,theory(equality)]) ).
cnf(111724,plain,
( X1 = X2
| apply(x,X1) != apply(x,X2)
| ~ element(X2,any1)
| ~ element(X1,any1)
| $false ),
inference(rw,[status(thm)],[66,111517,theory(equality)]) ).
cnf(111725,plain,
( X1 = X2
| apply(x,X1) != apply(x,X2)
| ~ element(X2,any1)
| ~ element(X1,any1) ),
inference(cn,[status(thm)],[111724,theory(equality)]) ).
cnf(111728,negated_conjecture,
( ~ injection_2(x)
| $false ),
inference(rw,[status(thm)],[53,111517,theory(equality)]) ).
cnf(111729,negated_conjecture,
~ injection_2(x),
inference(cn,[status(thm)],[111728,theory(equality)]) ).
cnf(111732,plain,
( zero(any1) = X1
| zero(any2) != apply(x,X1)
| ~ element(X1,any1)
| ~ element(zero(any1),any1) ),
inference(spm,[status(thm)],[111725,60,theory(equality)]) ).
cnf(112078,plain,
( zero(any1) = X1
| zero(any2) != apply(x,X1)
| ~ element(X1,any1) ),
inference(csr,[status(thm)],[111732,63]) ).
cnf(112252,plain,
element(zero(any1),any1),
inference(sr,[status(thm)],[88,111729,theory(equality)]) ).
cnf(112267,plain,
subtract(any2,zero(any2),zero(any2)) = zero(any2),
inference(spm,[status(thm)],[379,112252,theory(equality)]) ).
cnf(112302,plain,
( apply(x,esk3_3(x,X1,any2)) = zero(any2)
| injection_2(x)
| ~ element(esk3_3(x,X1,any2),any1)
| ~ morphism(x,X1,any2) ),
inference(spm,[status(thm)],[1386,112267,theory(equality)]) ).
cnf(112505,plain,
( apply(x,esk3_3(x,X1,any2)) = zero(any2)
| ~ element(esk3_3(x,X1,any2),any1)
| ~ morphism(x,X1,any2) ),
inference(sr,[status(thm)],[112302,111729,theory(equality)]) ).
cnf(113875,plain,
( zero(any1) = esk3_3(x,X1,any2)
| ~ element(esk3_3(x,X1,any2),any1)
| ~ morphism(x,X1,any2) ),
inference(spm,[status(thm)],[112078,112505,theory(equality)]) ).
cnf(114032,plain,
( esk3_3(x,any1,any2) = zero(any1)
| injection_2(x)
| ~ morphism(x,any1,any2) ),
inference(spm,[status(thm)],[113875,50,theory(equality)]) ).
cnf(114033,plain,
( esk3_3(x,any1,any2) = zero(any1)
| injection_2(x)
| $false ),
inference(rw,[status(thm)],[114032,54,theory(equality)]) ).
cnf(114034,plain,
( esk3_3(x,any1,any2) = zero(any1)
| injection_2(x) ),
inference(cn,[status(thm)],[114033,theory(equality)]) ).
cnf(114035,plain,
esk3_3(x,any1,any2) = zero(any1),
inference(sr,[status(thm)],[114034,111729,theory(equality)]) ).
cnf(114036,plain,
( injection_2(x)
| ~ morphism(x,any1,any2) ),
inference(spm,[status(thm)],[48,114035,theory(equality)]) ).
cnf(114174,plain,
( injection_2(x)
| $false ),
inference(rw,[status(thm)],[114036,54,theory(equality)]) ).
cnf(114175,plain,
injection_2(x),
inference(cn,[status(thm)],[114174,theory(equality)]) ).
cnf(114176,plain,
$false,
inference(sr,[status(thm)],[114175,111729,theory(equality)]) ).
cnf(114177,plain,
$false,
114176,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% /home/graph/tptp/Systems/SInE---0.4/Source/sine.py:10: DeprecationWarning: the sets module is deprecated
% from sets import Set
% % SZS status Started for /home/graph/tptp/TPTP/Problems/HAL/HAL002+1.p
% --creating new selector for [HAL001+0.ax]
% -running prover on /tmp/tmpbrbZqO/sel_HAL002+1.p_1 with time limit 29
% -prover status Theorem
% Problem HAL002+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/HAL/HAL002+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/HAL/HAL002+1.p
% Solved 1 out of 1.
% # Problem is unsatisfiable (or provable), constructing proof object
% # SZS status Theorem
% # SZS output start CNFRefutation.
% See solution above
% # SZS output end CNFRefutation
%
%------------------------------------------------------------------------------