TSTP Solution File: HAL004+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : HAL004+1 : TPTP v5.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art04.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 2018MB
% OS : Linux 2.6.26.8-57.fc8
% CPULimit : 300s
% DateTime : Sat Dec 25 11:35:57 EST 2010
% Result : Theorem 5.76s
% Output : CNFRefutation 5.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 15
% Syntax : Number of formulae : 141 ( 25 unt; 0 def)
% Number of atoms : 448 ( 101 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 580 ( 273 ~; 263 |; 31 &)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-4 aty)
% Number of functors : 13 ( 13 usr; 9 con; 0-4 aty)
% Number of variables : 286 ( 8 sgn 134 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,axiom,
! [X6,X7,X8,X9,X2,X10,X11,X3] :
( ( commute(X6,X7,X8,X9)
& morphism(X6,X2,X10)
& morphism(X7,X10,X3)
& morphism(X8,X2,X11)
& morphism(X9,X11,X3) )
=> ! [X12] :
( element(X12,X2)
=> apply(X7,apply(X6,X12)) = apply(X9,apply(X8,X12)) ) ),
file('/tmp/tmpnPBfN8/sel_HAL004+1.p_1',commute_properties) ).
fof(5,axiom,
! [X2,X4,X5] :
( ( element(X4,X2)
& element(X5,X2) )
=> subtract(X2,X4,subtract(X2,X4,X5)) = X5 ),
file('/tmp/tmpnPBfN8/sel_HAL004+1.p_1',subtract_cancellation) ).
fof(7,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/tmpnPBfN8/sel_HAL004+1.p_1',subtract_distribution) ).
fof(8,axiom,
! [X2,X4,X5] :
( ( element(X4,X2)
& element(X5,X2) )
=> element(subtract(X2,X4,X5),X2) ),
file('/tmp/tmpnPBfN8/sel_HAL004+1.p_1',subtract_in_domain) ).
fof(10,axiom,
! [X2,X17] :
( element(X17,X2)
=> subtract(X2,X17,X17) = zero(X2) ),
file('/tmp/tmpnPBfN8/sel_HAL004+1.p_1',subtract_to_0) ).
fof(11,axiom,
! [X1,X2,X3] :
( ( surjection(X1)
& morphism(X1,X2,X3) )
=> ! [X18] :
( element(X18,X3)
=> ? [X12] :
( element(X12,X2)
& apply(X1,X12) = X18 ) ) ),
file('/tmp/tmpnPBfN8/sel_HAL004+1.p_1',surjection_properties) ).
fof(13,axiom,
! [X1,X2,X3] :
( morphism(X1,X2,X3)
=> ( ! [X17] :
( element(X17,X2)
=> element(apply(X1,X17),X3) )
& apply(X1,zero(X2)) = zero(X3) ) ),
file('/tmp/tmpnPBfN8/sel_HAL004+1.p_1',morphism) ).
fof(14,axiom,
morphism(delta,e,r),
file('/tmp/tmpnPBfN8/sel_HAL004+1.p_1',delta_morphism) ).
fof(15,axiom,
surjection(beta),
file('/tmp/tmpnPBfN8/sel_HAL004+1.p_1',beta_surjection) ).
fof(17,axiom,
surjection(h),
file('/tmp/tmpnPBfN8/sel_HAL004+1.p_1',h_surjection) ).
fof(19,axiom,
morphism(g,b,e),
file('/tmp/tmpnPBfN8/sel_HAL004+1.p_1',g_morphism) ).
fof(20,conjecture,
! [X19] :
( element(X19,e)
=> ? [X20,X21] :
( element(X20,r)
& apply(delta,X19) = X20
& element(X21,b)
& apply(h,apply(beta,X21)) = X20
& apply(delta,apply(g,X21)) = X20 ) ),
file('/tmp/tmpnPBfN8/sel_HAL004+1.p_1',lemma3) ).
fof(22,axiom,
morphism(beta,b,c),
file('/tmp/tmpnPBfN8/sel_HAL004+1.p_1',beta_morphism) ).
fof(24,axiom,
commute(beta,h,g,delta),
file('/tmp/tmpnPBfN8/sel_HAL004+1.p_1',beta_h_g_delta_commute) ).
fof(25,axiom,
morphism(h,c,r),
file('/tmp/tmpnPBfN8/sel_HAL004+1.p_1',h_morphism) ).
fof(32,negated_conjecture,
~ ! [X19] :
( element(X19,e)
=> ? [X20,X21] :
( element(X20,r)
& apply(delta,X19) = X20
& element(X21,b)
& apply(h,apply(beta,X21)) = X20
& apply(delta,apply(g,X21)) = X20 ) ),
inference(assume_negation,[status(cth)],[20]) ).
fof(37,plain,
! [X6,X7,X8,X9,X2,X10,X11,X3] :
( ~ commute(X6,X7,X8,X9)
| ~ morphism(X6,X2,X10)
| ~ morphism(X7,X10,X3)
| ~ morphism(X8,X2,X11)
| ~ morphism(X9,X11,X3)
| ! [X12] :
( ~ element(X12,X2)
| apply(X7,apply(X6,X12)) = apply(X9,apply(X8,X12)) ) ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(38,plain,
! [X13,X14,X15,X16,X17,X18,X19,X20] :
( ~ commute(X13,X14,X15,X16)
| ~ morphism(X13,X17,X18)
| ~ morphism(X14,X18,X20)
| ~ morphism(X15,X17,X19)
| ~ morphism(X16,X19,X20)
| ! [X21] :
( ~ element(X21,X17)
| apply(X14,apply(X13,X21)) = apply(X16,apply(X15,X21)) ) ),
inference(variable_rename,[status(thm)],[37]) ).
fof(39,plain,
! [X13,X14,X15,X16,X17,X18,X19,X20,X21] :
( ~ element(X21,X17)
| apply(X14,apply(X13,X21)) = apply(X16,apply(X15,X21))
| ~ commute(X13,X14,X15,X16)
| ~ morphism(X13,X17,X18)
| ~ morphism(X14,X18,X20)
| ~ morphism(X15,X17,X19)
| ~ morphism(X16,X19,X20) ),
inference(shift_quantors,[status(thm)],[38]) ).
cnf(40,plain,
( apply(X6,apply(X8,X9)) = apply(X1,apply(X4,X9))
| ~ morphism(X1,X2,X3)
| ~ morphism(X4,X5,X2)
| ~ morphism(X6,X7,X3)
| ~ morphism(X8,X5,X7)
| ~ commute(X8,X6,X4,X1)
| ~ element(X9,X5) ),
inference(split_conjunct,[status(thm)],[39]) ).
fof(56,plain,
! [X2,X4,X5] :
( ~ element(X4,X2)
| ~ element(X5,X2)
| subtract(X2,X4,subtract(X2,X4,X5)) = X5 ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(57,plain,
! [X6,X7,X8] :
( ~ element(X7,X6)
| ~ element(X8,X6)
| subtract(X6,X7,subtract(X6,X7,X8)) = X8 ),
inference(variable_rename,[status(thm)],[56]) ).
cnf(58,plain,
( subtract(X1,X2,subtract(X1,X2,X3)) = X3
| ~ element(X3,X1)
| ~ element(X2,X1) ),
inference(split_conjunct,[status(thm)],[57]) ).
fof(67,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)],[7]) ).
fof(68,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)],[67]) ).
fof(69,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)],[68]) ).
cnf(70,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)],[69]) ).
fof(71,plain,
! [X2,X4,X5] :
( ~ element(X4,X2)
| ~ element(X5,X2)
| element(subtract(X2,X4,X5),X2) ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(72,plain,
! [X6,X7,X8] :
( ~ element(X7,X6)
| ~ element(X8,X6)
| element(subtract(X6,X7,X8),X6) ),
inference(variable_rename,[status(thm)],[71]) ).
cnf(73,plain,
( element(subtract(X1,X2,X3),X1)
| ~ element(X3,X1)
| ~ element(X2,X1) ),
inference(split_conjunct,[status(thm)],[72]) ).
fof(84,plain,
! [X2,X17] :
( ~ element(X17,X2)
| subtract(X2,X17,X17) = zero(X2) ),
inference(fof_nnf,[status(thm)],[10]) ).
fof(85,plain,
! [X18,X19] :
( ~ element(X19,X18)
| subtract(X18,X19,X19) = zero(X18) ),
inference(variable_rename,[status(thm)],[84]) ).
cnf(86,plain,
( subtract(X1,X2,X2) = zero(X1)
| ~ element(X2,X1) ),
inference(split_conjunct,[status(thm)],[85]) ).
fof(87,plain,
! [X1,X2,X3] :
( ~ surjection(X1)
| ~ morphism(X1,X2,X3)
| ! [X18] :
( ~ element(X18,X3)
| ? [X12] :
( element(X12,X2)
& apply(X1,X12) = X18 ) ) ),
inference(fof_nnf,[status(thm)],[11]) ).
fof(88,plain,
! [X19,X20,X21] :
( ~ surjection(X19)
| ~ morphism(X19,X20,X21)
| ! [X22] :
( ~ element(X22,X21)
| ? [X23] :
( element(X23,X20)
& apply(X19,X23) = X22 ) ) ),
inference(variable_rename,[status(thm)],[87]) ).
fof(89,plain,
! [X19,X20,X21] :
( ~ surjection(X19)
| ~ morphism(X19,X20,X21)
| ! [X22] :
( ~ element(X22,X21)
| ( element(esk7_4(X19,X20,X21,X22),X20)
& apply(X19,esk7_4(X19,X20,X21,X22)) = X22 ) ) ),
inference(skolemize,[status(esa)],[88]) ).
fof(90,plain,
! [X19,X20,X21,X22] :
( ~ element(X22,X21)
| ( element(esk7_4(X19,X20,X21,X22),X20)
& apply(X19,esk7_4(X19,X20,X21,X22)) = X22 )
| ~ surjection(X19)
| ~ morphism(X19,X20,X21) ),
inference(shift_quantors,[status(thm)],[89]) ).
fof(91,plain,
! [X19,X20,X21,X22] :
( ( element(esk7_4(X19,X20,X21,X22),X20)
| ~ element(X22,X21)
| ~ surjection(X19)
| ~ morphism(X19,X20,X21) )
& ( apply(X19,esk7_4(X19,X20,X21,X22)) = X22
| ~ element(X22,X21)
| ~ surjection(X19)
| ~ morphism(X19,X20,X21) ) ),
inference(distribute,[status(thm)],[90]) ).
cnf(92,plain,
( apply(X1,esk7_4(X1,X2,X3,X4)) = X4
| ~ morphism(X1,X2,X3)
| ~ surjection(X1)
| ~ element(X4,X3) ),
inference(split_conjunct,[status(thm)],[91]) ).
cnf(93,plain,
( element(esk7_4(X1,X2,X3,X4),X2)
| ~ morphism(X1,X2,X3)
| ~ surjection(X1)
| ~ element(X4,X3) ),
inference(split_conjunct,[status(thm)],[91]) ).
fof(101,plain,
! [X1,X2,X3] :
( ~ morphism(X1,X2,X3)
| ( ! [X17] :
( ~ element(X17,X2)
| element(apply(X1,X17),X3) )
& apply(X1,zero(X2)) = zero(X3) ) ),
inference(fof_nnf,[status(thm)],[13]) ).
fof(102,plain,
! [X18,X19,X20] :
( ~ morphism(X18,X19,X20)
| ( ! [X21] :
( ~ element(X21,X19)
| element(apply(X18,X21),X20) )
& apply(X18,zero(X19)) = zero(X20) ) ),
inference(variable_rename,[status(thm)],[101]) ).
fof(103,plain,
! [X18,X19,X20,X21] :
( ( ( ~ element(X21,X19)
| element(apply(X18,X21),X20) )
& apply(X18,zero(X19)) = zero(X20) )
| ~ morphism(X18,X19,X20) ),
inference(shift_quantors,[status(thm)],[102]) ).
fof(104,plain,
! [X18,X19,X20,X21] :
( ( ~ element(X21,X19)
| element(apply(X18,X21),X20)
| ~ morphism(X18,X19,X20) )
& ( apply(X18,zero(X19)) = zero(X20)
| ~ morphism(X18,X19,X20) ) ),
inference(distribute,[status(thm)],[103]) ).
cnf(105,plain,
( apply(X1,zero(X2)) = zero(X3)
| ~ morphism(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[104]) ).
cnf(106,plain,
( element(apply(X1,X4),X3)
| ~ morphism(X1,X2,X3)
| ~ element(X4,X2) ),
inference(split_conjunct,[status(thm)],[104]) ).
cnf(107,plain,
morphism(delta,e,r),
inference(split_conjunct,[status(thm)],[14]) ).
cnf(108,plain,
surjection(beta),
inference(split_conjunct,[status(thm)],[15]) ).
cnf(110,plain,
surjection(h),
inference(split_conjunct,[status(thm)],[17]) ).
cnf(112,plain,
morphism(g,b,e),
inference(split_conjunct,[status(thm)],[19]) ).
fof(113,negated_conjecture,
? [X19] :
( element(X19,e)
& ! [X20,X21] :
( ~ element(X20,r)
| apply(delta,X19) != X20
| ~ element(X21,b)
| apply(h,apply(beta,X21)) != X20
| apply(delta,apply(g,X21)) != X20 ) ),
inference(fof_nnf,[status(thm)],[32]) ).
fof(114,negated_conjecture,
? [X22] :
( element(X22,e)
& ! [X23,X24] :
( ~ element(X23,r)
| apply(delta,X22) != X23
| ~ element(X24,b)
| apply(h,apply(beta,X24)) != X23
| apply(delta,apply(g,X24)) != X23 ) ),
inference(variable_rename,[status(thm)],[113]) ).
fof(115,negated_conjecture,
( element(esk9_0,e)
& ! [X23,X24] :
( ~ element(X23,r)
| apply(delta,esk9_0) != X23
| ~ element(X24,b)
| apply(h,apply(beta,X24)) != X23
| apply(delta,apply(g,X24)) != X23 ) ),
inference(skolemize,[status(esa)],[114]) ).
fof(116,negated_conjecture,
! [X23,X24] :
( ( ~ element(X23,r)
| apply(delta,esk9_0) != X23
| ~ element(X24,b)
| apply(h,apply(beta,X24)) != X23
| apply(delta,apply(g,X24)) != X23 )
& element(esk9_0,e) ),
inference(shift_quantors,[status(thm)],[115]) ).
cnf(117,negated_conjecture,
element(esk9_0,e),
inference(split_conjunct,[status(thm)],[116]) ).
cnf(118,negated_conjecture,
( apply(delta,apply(g,X1)) != X2
| apply(h,apply(beta,X1)) != X2
| ~ element(X1,b)
| apply(delta,esk9_0) != X2
| ~ element(X2,r) ),
inference(split_conjunct,[status(thm)],[116]) ).
cnf(120,plain,
morphism(beta,b,c),
inference(split_conjunct,[status(thm)],[22]) ).
cnf(122,plain,
commute(beta,h,g,delta),
inference(split_conjunct,[status(thm)],[24]) ).
cnf(123,plain,
morphism(h,c,r),
inference(split_conjunct,[status(thm)],[25]) ).
cnf(130,plain,
( element(zero(X1),X1)
| ~ element(X2,X1) ),
inference(spm,[status(thm)],[73,86,theory(equality)]) ).
cnf(131,plain,
( element(apply(delta,X1),r)
| ~ element(X1,e) ),
inference(spm,[status(thm)],[106,107,theory(equality)]) ).
cnf(132,plain,
( element(apply(g,X1),e)
| ~ element(X1,b) ),
inference(spm,[status(thm)],[106,112,theory(equality)]) ).
cnf(134,plain,
( element(apply(h,X1),r)
| ~ element(X1,c) ),
inference(spm,[status(thm)],[106,123,theory(equality)]) ).
cnf(138,plain,
apply(delta,zero(e)) = zero(r),
inference(spm,[status(thm)],[105,107,theory(equality)]) ).
cnf(139,plain,
apply(g,zero(b)) = zero(e),
inference(spm,[status(thm)],[105,112,theory(equality)]) ).
cnf(141,plain,
apply(h,zero(c)) = zero(r),
inference(spm,[status(thm)],[105,123,theory(equality)]) ).
cnf(147,negated_conjecture,
( apply(h,apply(beta,X1)) != apply(delta,apply(g,X1))
| apply(delta,esk9_0) != apply(delta,apply(g,X1))
| ~ element(apply(delta,apply(g,X1)),r)
| ~ element(X1,b) ),
inference(er,[status(thm)],[118,theory(equality)]) ).
cnf(181,plain,
( subtract(r,apply(delta,X1),apply(delta,X2)) = apply(delta,subtract(e,X1,X2))
| ~ element(X2,e)
| ~ element(X1,e) ),
inference(spm,[status(thm)],[70,107,theory(equality)]) ).
cnf(182,plain,
( subtract(e,apply(g,X1),apply(g,X2)) = apply(g,subtract(b,X1,X2))
| ~ element(X2,b)
| ~ element(X1,b) ),
inference(spm,[status(thm)],[70,112,theory(equality)]) ).
cnf(184,plain,
( subtract(r,apply(h,X1),apply(h,X2)) = apply(h,subtract(c,X1,X2))
| ~ element(X2,c)
| ~ element(X1,c) ),
inference(spm,[status(thm)],[70,123,theory(equality)]) ).
cnf(204,plain,
( apply(delta,apply(g,X1)) = apply(h,apply(beta,X1))
| ~ element(X1,X2)
| ~ morphism(beta,X2,X3)
| ~ morphism(h,X3,X4)
| ~ morphism(g,X2,X5)
| ~ morphism(delta,X5,X4) ),
inference(spm,[status(thm)],[40,122,theory(equality)]) ).
cnf(232,negated_conjecture,
element(zero(e),e),
inference(spm,[status(thm)],[130,117,theory(equality)]) ).
cnf(237,plain,
( element(zero(X1),X1)
| ~ surjection(X2)
| ~ element(X4,X3)
| ~ morphism(X2,X1,X3) ),
inference(spm,[status(thm)],[130,93,theory(equality)]) ).
cnf(240,plain,
( element(zero(r),r)
| ~ element(zero(e),e) ),
inference(spm,[status(thm)],[131,138,theory(equality)]) ).
cnf(272,plain,
( element(zero(r),r)
| $false ),
inference(rw,[status(thm)],[240,232,theory(equality)]) ).
cnf(273,plain,
element(zero(r),r),
inference(cn,[status(thm)],[272,theory(equality)]) ).
cnf(614,plain,
( element(zero(b),b)
| ~ surjection(beta)
| ~ element(X1,c) ),
inference(spm,[status(thm)],[237,120,theory(equality)]) ).
cnf(615,plain,
( element(zero(c),c)
| ~ surjection(h)
| ~ element(X1,r) ),
inference(spm,[status(thm)],[237,123,theory(equality)]) ).
cnf(622,plain,
( element(zero(b),b)
| $false
| ~ element(X1,c) ),
inference(rw,[status(thm)],[614,108,theory(equality)]) ).
cnf(623,plain,
( element(zero(b),b)
| ~ element(X1,c) ),
inference(cn,[status(thm)],[622,theory(equality)]) ).
cnf(624,plain,
( element(zero(c),c)
| $false
| ~ element(X1,r) ),
inference(rw,[status(thm)],[615,110,theory(equality)]) ).
cnf(625,plain,
( element(zero(c),c)
| ~ element(X1,r) ),
inference(cn,[status(thm)],[624,theory(equality)]) ).
cnf(684,plain,
element(zero(c),c),
inference(spm,[status(thm)],[625,273,theory(equality)]) ).
cnf(696,plain,
element(zero(b),b),
inference(spm,[status(thm)],[623,684,theory(equality)]) ).
cnf(990,plain,
( subtract(r,zero(r),apply(delta,X1)) = apply(delta,subtract(e,zero(e),X1))
| ~ element(X1,e)
| ~ element(zero(e),e) ),
inference(spm,[status(thm)],[181,138,theory(equality)]) ).
cnf(1005,plain,
( subtract(r,zero(r),apply(delta,X1)) = apply(delta,subtract(e,zero(e),X1))
| ~ element(X1,e)
| $false ),
inference(rw,[status(thm)],[990,232,theory(equality)]) ).
cnf(1006,plain,
( subtract(r,zero(r),apply(delta,X1)) = apply(delta,subtract(e,zero(e),X1))
| ~ element(X1,e) ),
inference(cn,[status(thm)],[1005,theory(equality)]) ).
cnf(1041,plain,
( subtract(e,zero(e),apply(g,X1)) = apply(g,subtract(b,zero(b),X1))
| ~ element(X1,b)
| ~ element(zero(b),b) ),
inference(spm,[status(thm)],[182,139,theory(equality)]) ).
cnf(1055,plain,
( subtract(e,zero(e),apply(g,X1)) = apply(g,subtract(b,zero(b),X1))
| ~ element(X1,b)
| $false ),
inference(rw,[status(thm)],[1041,696,theory(equality)]) ).
cnf(1056,plain,
( subtract(e,zero(e),apply(g,X1)) = apply(g,subtract(b,zero(b),X1))
| ~ element(X1,b) ),
inference(cn,[status(thm)],[1055,theory(equality)]) ).
cnf(1174,plain,
( element(apply(delta,subtract(e,zero(e),X1)),r)
| ~ element(apply(delta,X1),r)
| ~ element(zero(r),r)
| ~ element(X1,e) ),
inference(spm,[status(thm)],[73,1006,theory(equality)]) ).
cnf(1186,plain,
( element(apply(delta,subtract(e,zero(e),X1)),r)
| ~ element(apply(delta,X1),r)
| $false
| ~ element(X1,e) ),
inference(rw,[status(thm)],[1174,273,theory(equality)]) ).
cnf(1187,plain,
( element(apply(delta,subtract(e,zero(e),X1)),r)
| ~ element(apply(delta,X1),r)
| ~ element(X1,e) ),
inference(cn,[status(thm)],[1186,theory(equality)]) ).
cnf(1196,plain,
( element(apply(delta,subtract(e,zero(e),X1)),r)
| ~ element(X1,e) ),
inference(csr,[status(thm)],[1187,131]) ).
cnf(1218,plain,
( subtract(r,apply(h,X1),zero(r)) = apply(h,subtract(c,X1,zero(c)))
| ~ element(zero(c),c)
| ~ element(X1,c) ),
inference(spm,[status(thm)],[184,141,theory(equality)]) ).
cnf(1221,plain,
( subtract(r,apply(h,X1),apply(h,subtract(c,X1,X2))) = apply(h,X2)
| ~ element(apply(h,X2),r)
| ~ element(apply(h,X1),r)
| ~ element(X2,c)
| ~ element(X1,c) ),
inference(spm,[status(thm)],[58,184,theory(equality)]) ).
cnf(1234,plain,
( subtract(r,apply(h,X1),zero(r)) = apply(h,subtract(c,X1,zero(c)))
| $false
| ~ element(X1,c) ),
inference(rw,[status(thm)],[1218,684,theory(equality)]) ).
cnf(1235,plain,
( subtract(r,apply(h,X1),zero(r)) = apply(h,subtract(c,X1,zero(c)))
| ~ element(X1,c) ),
inference(cn,[status(thm)],[1234,theory(equality)]) ).
cnf(1517,plain,
( element(apply(delta,apply(g,subtract(b,zero(b),X1))),r)
| ~ element(apply(g,X1),e)
| ~ element(X1,b) ),
inference(spm,[status(thm)],[1196,1056,theory(equality)]) ).
cnf(1723,plain,
( element(apply(delta,apply(g,subtract(b,zero(b),X1))),r)
| ~ element(X1,b) ),
inference(csr,[status(thm)],[1517,132]) ).
cnf(1726,plain,
( element(apply(delta,apply(g,X1)),r)
| ~ element(subtract(b,zero(b),X1),b)
| ~ element(X1,b)
| ~ element(zero(b),b) ),
inference(spm,[status(thm)],[1723,58,theory(equality)]) ).
cnf(1741,plain,
( element(apply(delta,apply(g,X1)),r)
| ~ element(subtract(b,zero(b),X1),b)
| ~ element(X1,b)
| $false ),
inference(rw,[status(thm)],[1726,696,theory(equality)]) ).
cnf(1742,plain,
( element(apply(delta,apply(g,X1)),r)
| ~ element(subtract(b,zero(b),X1),b)
| ~ element(X1,b) ),
inference(cn,[status(thm)],[1741,theory(equality)]) ).
cnf(1760,plain,
( element(apply(delta,apply(g,X1)),r)
| ~ element(X1,b)
| ~ element(zero(b),b) ),
inference(spm,[status(thm)],[1742,73,theory(equality)]) ).
cnf(1766,plain,
( element(apply(delta,apply(g,X1)),r)
| ~ element(X1,b)
| $false ),
inference(rw,[status(thm)],[1760,696,theory(equality)]) ).
cnf(1767,plain,
( element(apply(delta,apply(g,X1)),r)
| ~ element(X1,b) ),
inference(cn,[status(thm)],[1766,theory(equality)]) ).
cnf(1779,negated_conjecture,
( apply(delta,apply(g,X1)) != apply(h,apply(beta,X1))
| apply(delta,apply(g,X1)) != apply(delta,esk9_0)
| ~ element(X1,b) ),
inference(spm,[status(thm)],[147,1767,theory(equality)]) ).
cnf(2230,plain,
( apply(delta,apply(g,X1)) = apply(h,apply(beta,X1))
| ~ element(X1,b)
| ~ morphism(h,c,X2)
| ~ morphism(g,b,X3)
| ~ morphism(delta,X3,X2) ),
inference(spm,[status(thm)],[204,120,theory(equality)]) ).
cnf(12181,plain,
( subtract(r,apply(h,X1),apply(h,subtract(c,X1,X2))) = apply(h,X2)
| ~ element(apply(h,X2),r)
| ~ element(X2,c)
| ~ element(X1,c) ),
inference(csr,[status(thm)],[1221,134]) ).
cnf(12182,plain,
( subtract(r,apply(h,X1),apply(h,subtract(c,X1,X2))) = apply(h,X2)
| ~ element(X2,c)
| ~ element(X1,c) ),
inference(csr,[status(thm)],[12181,134]) ).
cnf(12184,plain,
( subtract(r,apply(h,X1),apply(h,zero(c))) = apply(h,X1)
| ~ element(X1,c) ),
inference(spm,[status(thm)],[12182,86,theory(equality)]) ).
cnf(12227,plain,
( subtract(r,apply(h,X1),zero(r)) = apply(h,X1)
| ~ element(X1,c) ),
inference(rw,[status(thm)],[12184,141,theory(equality)]) ).
cnf(15054,plain,
( apply(h,X1) = apply(h,subtract(c,X1,zero(c)))
| ~ element(X1,c) ),
inference(spm,[status(thm)],[1235,12227,theory(equality)]) ).
cnf(29720,plain,
( apply(delta,apply(g,X1)) = apply(h,apply(beta,X1))
| ~ element(X1,b)
| ~ morphism(h,c,r)
| ~ morphism(g,b,e) ),
inference(spm,[status(thm)],[2230,107,theory(equality)]) ).
cnf(29721,plain,
( apply(delta,apply(g,X1)) = apply(h,apply(beta,X1))
| ~ element(X1,b)
| $false
| ~ morphism(g,b,e) ),
inference(rw,[status(thm)],[29720,123,theory(equality)]) ).
cnf(29722,plain,
( apply(delta,apply(g,X1)) = apply(h,apply(beta,X1))
| ~ element(X1,b)
| $false
| $false ),
inference(rw,[status(thm)],[29721,112,theory(equality)]) ).
cnf(29723,plain,
( apply(delta,apply(g,X1)) = apply(h,apply(beta,X1))
| ~ element(X1,b) ),
inference(cn,[status(thm)],[29722,theory(equality)]) ).
cnf(29772,negated_conjecture,
( apply(h,apply(beta,X1)) != apply(delta,esk9_0)
| ~ element(X1,b) ),
inference(spm,[status(thm)],[1779,29723,theory(equality)]) ).
cnf(29981,negated_conjecture,
( apply(h,X3) != apply(delta,esk9_0)
| ~ element(esk7_4(beta,X1,X2,X3),b)
| ~ surjection(beta)
| ~ element(X3,X2)
| ~ morphism(beta,X1,X2) ),
inference(spm,[status(thm)],[29772,92,theory(equality)]) ).
cnf(30019,negated_conjecture,
( apply(h,X3) != apply(delta,esk9_0)
| ~ element(esk7_4(beta,X1,X2,X3),b)
| $false
| ~ element(X3,X2)
| ~ morphism(beta,X1,X2) ),
inference(rw,[status(thm)],[29981,108,theory(equality)]) ).
cnf(30020,negated_conjecture,
( apply(h,X3) != apply(delta,esk9_0)
| ~ element(esk7_4(beta,X1,X2,X3),b)
| ~ element(X3,X2)
| ~ morphism(beta,X1,X2) ),
inference(cn,[status(thm)],[30019,theory(equality)]) ).
cnf(34036,negated_conjecture,
( apply(h,X1) != apply(delta,esk9_0)
| ~ element(X1,X2)
| ~ morphism(beta,b,X2)
| ~ surjection(beta) ),
inference(spm,[status(thm)],[30020,93,theory(equality)]) ).
cnf(34037,negated_conjecture,
( apply(h,X1) != apply(delta,esk9_0)
| ~ element(X1,X2)
| ~ morphism(beta,b,X2)
| $false ),
inference(rw,[status(thm)],[34036,108,theory(equality)]) ).
cnf(34038,negated_conjecture,
( apply(h,X1) != apply(delta,esk9_0)
| ~ element(X1,X2)
| ~ morphism(beta,b,X2) ),
inference(cn,[status(thm)],[34037,theory(equality)]) ).
cnf(34052,negated_conjecture,
( apply(h,subtract(X1,X2,X3)) != apply(delta,esk9_0)
| ~ morphism(beta,b,X1)
| ~ element(X3,X1)
| ~ element(X2,X1) ),
inference(spm,[status(thm)],[34038,73,theory(equality)]) ).
cnf(37120,negated_conjecture,
( apply(h,X1) != apply(delta,esk9_0)
| ~ element(zero(c),c)
| ~ element(X1,c)
| ~ morphism(beta,b,c) ),
inference(spm,[status(thm)],[34052,15054,theory(equality)]) ).
cnf(37251,negated_conjecture,
( apply(h,X1) != apply(delta,esk9_0)
| $false
| ~ element(X1,c)
| ~ morphism(beta,b,c) ),
inference(rw,[status(thm)],[37120,684,theory(equality)]) ).
cnf(37252,negated_conjecture,
( apply(h,X1) != apply(delta,esk9_0)
| $false
| ~ element(X1,c)
| $false ),
inference(rw,[status(thm)],[37251,120,theory(equality)]) ).
cnf(37253,negated_conjecture,
( apply(h,X1) != apply(delta,esk9_0)
| ~ element(X1,c) ),
inference(cn,[status(thm)],[37252,theory(equality)]) ).
cnf(37483,negated_conjecture,
( X3 != apply(delta,esk9_0)
| ~ element(esk7_4(h,X1,X2,X3),c)
| ~ surjection(h)
| ~ element(X3,X2)
| ~ morphism(h,X1,X2) ),
inference(spm,[status(thm)],[37253,92,theory(equality)]) ).
cnf(37523,negated_conjecture,
( X3 != apply(delta,esk9_0)
| ~ element(esk7_4(h,X1,X2,X3),c)
| $false
| ~ element(X3,X2)
| ~ morphism(h,X1,X2) ),
inference(rw,[status(thm)],[37483,110,theory(equality)]) ).
cnf(37524,negated_conjecture,
( X3 != apply(delta,esk9_0)
| ~ element(esk7_4(h,X1,X2,X3),c)
| ~ element(X3,X2)
| ~ morphism(h,X1,X2) ),
inference(cn,[status(thm)],[37523,theory(equality)]) ).
cnf(42957,negated_conjecture,
( X1 != apply(delta,esk9_0)
| ~ element(X1,X2)
| ~ morphism(h,c,X2)
| ~ surjection(h) ),
inference(spm,[status(thm)],[37524,93,theory(equality)]) ).
cnf(42958,negated_conjecture,
( X1 != apply(delta,esk9_0)
| ~ element(X1,X2)
| ~ morphism(h,c,X2)
| $false ),
inference(rw,[status(thm)],[42957,110,theory(equality)]) ).
cnf(42959,negated_conjecture,
( X1 != apply(delta,esk9_0)
| ~ element(X1,X2)
| ~ morphism(h,c,X2) ),
inference(cn,[status(thm)],[42958,theory(equality)]) ).
cnf(42964,negated_conjecture,
( ~ element(apply(delta,esk9_0),X1)
| ~ morphism(h,c,X1) ),
inference(er,[status(thm)],[42959,theory(equality)]) ).
cnf(42967,negated_conjecture,
( ~ morphism(h,c,r)
| ~ element(esk9_0,e) ),
inference(spm,[status(thm)],[42964,131,theory(equality)]) ).
cnf(42977,negated_conjecture,
( $false
| ~ element(esk9_0,e) ),
inference(rw,[status(thm)],[42967,123,theory(equality)]) ).
cnf(42978,negated_conjecture,
~ element(esk9_0,e),
inference(cn,[status(thm)],[42977,theory(equality)]) ).
cnf(42981,negated_conjecture,
$false,
inference(sr,[status(thm)],[117,42978,theory(equality)]) ).
cnf(42982,negated_conjecture,
$false,
42981,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/HAL/HAL004+1.p
% --creating new selector for [HAL001+0.ax]
% -running prover on /tmp/tmpnPBfN8/sel_HAL004+1.p_1 with time limit 29
% -prover status Theorem
% Problem HAL004+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/HAL/HAL004+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/HAL/HAL004+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
%
%------------------------------------------------------------------------------