TSTP Solution File: HAL002+1 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : HAL002+1 : TPTP v8.1.2. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 01:53:41 EDT 2023
% Result : Theorem 151.12s 20.83s
% Output : CNFRefutation 151.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 49
% Number of leaves : 17
% Syntax : Number of formulae : 279 ( 46 unt; 0 def)
% Number of atoms : 774 ( 279 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 832 ( 337 ~; 416 |; 50 &)
% ( 2 <=>; 26 =>; 0 <=; 1 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 6 ( 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 : 427 ( 25 sgn; 177 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] :
( morphism(X0,X1,X2)
=> ( apply(X0,zero(X1)) = zero(X2)
& ! [X3] :
( element(X3,X1)
=> element(apply(X0,X3),X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',morphism) ).
fof(f2,axiom,
! [X0,X1,X2] :
( ( morphism(X0,X1,X2)
& injection(X0) )
=> ! [X4,X5] :
( ( apply(X0,X4) = apply(X0,X5)
& element(X5,X1)
& element(X4,X1) )
=> X4 = X5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',injection_properties) ).
fof(f3,axiom,
! [X0,X1,X2] :
( ( ! [X4,X5] :
( ( apply(X0,X4) = apply(X0,X5)
& element(X5,X1)
& element(X4,X1) )
=> X4 = X5 )
& morphism(X0,X1,X2) )
=> injection(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',properties_for_injection) ).
fof(f10,axiom,
! [X1,X4,X5] :
( ( element(X5,X1)
& element(X4,X1) )
=> element(subtract(X1,X4,X5),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subtract_in_domain) ).
fof(f11,axiom,
! [X1,X3] :
( element(X3,X1)
=> zero(X1) = subtract(X1,X3,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subtract_to_0) ).
fof(f12,axiom,
! [X1,X4,X5] :
( ( element(X5,X1)
& element(X4,X1) )
=> subtract(X1,X4,subtract(X1,X4,X5)) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subtract_cancellation) ).
fof(f13,axiom,
! [X0,X1,X2] :
( morphism(X0,X1,X2)
=> ! [X4,X5] :
( ( element(X5,X1)
& element(X4,X1) )
=> apply(X0,subtract(X1,X4,X5)) = subtract(X2,apply(X0,X4),apply(X0,X5)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subtract_distribution) ).
fof(f14,axiom,
! [X0,X1,X2] :
( ( morphism(X0,X1,X2)
& injection_2(X0) )
=> ! [X3] :
( ( apply(X0,X3) = zero(X2)
& element(X3,X1) )
=> zero(X1) = X3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',injection_properties_2) ).
fof(f15,axiom,
! [X0,X1,X2] :
( ( ! [X3] :
( ( apply(X0,X3) = zero(X2)
& element(X3,X1) )
=> zero(X1) = X3 )
& morphism(X0,X1,X2) )
=> injection_2(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',properties_for_injection_2) ).
fof(f16,axiom,
morphism(x,any1,any2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_morphism) ).
fof(f17,conjecture,
( injection(x)
<=> injection_2(x) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',my) ).
fof(f18,negated_conjecture,
~ ( injection(x)
<=> injection_2(x) ),
inference(negated_conjecture,[],[f17]) ).
fof(f19,plain,
! [X0,X1,X2] :
( ( morphism(X0,X1,X2)
& injection(X0) )
=> ! [X3,X4] :
( ( apply(X0,X3) = apply(X0,X4)
& element(X4,X1)
& element(X3,X1) )
=> X3 = X4 ) ),
inference(rectify,[],[f2]) ).
fof(f20,plain,
! [X0,X1,X2] :
( ( ! [X3,X4] :
( ( apply(X0,X3) = apply(X0,X4)
& element(X4,X1)
& element(X3,X1) )
=> X3 = X4 )
& morphism(X0,X1,X2) )
=> injection(X0) ),
inference(rectify,[],[f3]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ( element(X2,X0)
& element(X1,X0) )
=> element(subtract(X0,X1,X2),X0) ),
inference(rectify,[],[f10]) ).
fof(f28,plain,
! [X0,X1] :
( element(X1,X0)
=> zero(X0) = subtract(X0,X1,X1) ),
inference(rectify,[],[f11]) ).
fof(f29,plain,
! [X0,X1,X2] :
( ( element(X2,X0)
& element(X1,X0) )
=> subtract(X0,X1,subtract(X0,X1,X2)) = X2 ),
inference(rectify,[],[f12]) ).
fof(f30,plain,
! [X0,X1,X2] :
( morphism(X0,X1,X2)
=> ! [X3,X4] :
( ( element(X4,X1)
& element(X3,X1) )
=> apply(X0,subtract(X1,X3,X4)) = subtract(X2,apply(X0,X3),apply(X0,X4)) ) ),
inference(rectify,[],[f13]) ).
fof(f31,plain,
! [X0,X1,X2] :
( ( apply(X0,zero(X1)) = zero(X2)
& ! [X3] :
( element(apply(X0,X3),X2)
| ~ element(X3,X1) ) )
| ~ morphism(X0,X1,X2) ),
inference(ennf_transformation,[],[f1]) ).
fof(f32,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( X3 = X4
| apply(X0,X3) != apply(X0,X4)
| ~ element(X4,X1)
| ~ element(X3,X1) )
| ~ morphism(X0,X1,X2)
| ~ injection(X0) ),
inference(ennf_transformation,[],[f19]) ).
fof(f33,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( X3 = X4
| apply(X0,X3) != apply(X0,X4)
| ~ element(X4,X1)
| ~ element(X3,X1) )
| ~ morphism(X0,X1,X2)
| ~ injection(X0) ),
inference(flattening,[],[f32]) ).
fof(f34,plain,
! [X0,X1,X2] :
( injection(X0)
| ? [X3,X4] :
( X3 != X4
& apply(X0,X3) = apply(X0,X4)
& element(X4,X1)
& element(X3,X1) )
| ~ morphism(X0,X1,X2) ),
inference(ennf_transformation,[],[f20]) ).
fof(f35,plain,
! [X0,X1,X2] :
( injection(X0)
| ? [X3,X4] :
( X3 != X4
& apply(X0,X3) = apply(X0,X4)
& element(X4,X1)
& element(X3,X1) )
| ~ morphism(X0,X1,X2) ),
inference(flattening,[],[f34]) ).
fof(f48,plain,
! [X0,X1,X2] :
( element(subtract(X0,X1,X2),X0)
| ~ element(X2,X0)
| ~ element(X1,X0) ),
inference(ennf_transformation,[],[f27]) ).
fof(f49,plain,
! [X0,X1,X2] :
( element(subtract(X0,X1,X2),X0)
| ~ element(X2,X0)
| ~ element(X1,X0) ),
inference(flattening,[],[f48]) ).
fof(f50,plain,
! [X0,X1] :
( zero(X0) = subtract(X0,X1,X1)
| ~ element(X1,X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f51,plain,
! [X0,X1,X2] :
( subtract(X0,X1,subtract(X0,X1,X2)) = X2
| ~ element(X2,X0)
| ~ element(X1,X0) ),
inference(ennf_transformation,[],[f29]) ).
fof(f52,plain,
! [X0,X1,X2] :
( subtract(X0,X1,subtract(X0,X1,X2)) = X2
| ~ element(X2,X0)
| ~ element(X1,X0) ),
inference(flattening,[],[f51]) ).
fof(f53,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( apply(X0,subtract(X1,X3,X4)) = subtract(X2,apply(X0,X3),apply(X0,X4))
| ~ element(X4,X1)
| ~ element(X3,X1) )
| ~ morphism(X0,X1,X2) ),
inference(ennf_transformation,[],[f30]) ).
fof(f54,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( apply(X0,subtract(X1,X3,X4)) = subtract(X2,apply(X0,X3),apply(X0,X4))
| ~ element(X4,X1)
| ~ element(X3,X1) )
| ~ morphism(X0,X1,X2) ),
inference(flattening,[],[f53]) ).
fof(f55,plain,
! [X0,X1,X2] :
( ! [X3] :
( zero(X1) = X3
| apply(X0,X3) != zero(X2)
| ~ element(X3,X1) )
| ~ morphism(X0,X1,X2)
| ~ injection_2(X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f56,plain,
! [X0,X1,X2] :
( ! [X3] :
( zero(X1) = X3
| apply(X0,X3) != zero(X2)
| ~ element(X3,X1) )
| ~ morphism(X0,X1,X2)
| ~ injection_2(X0) ),
inference(flattening,[],[f55]) ).
fof(f57,plain,
! [X0,X1,X2] :
( injection_2(X0)
| ? [X3] :
( zero(X1) != X3
& apply(X0,X3) = zero(X2)
& element(X3,X1) )
| ~ morphism(X0,X1,X2) ),
inference(ennf_transformation,[],[f15]) ).
fof(f58,plain,
! [X0,X1,X2] :
( injection_2(X0)
| ? [X3] :
( zero(X1) != X3
& apply(X0,X3) = zero(X2)
& element(X3,X1) )
| ~ morphism(X0,X1,X2) ),
inference(flattening,[],[f57]) ).
fof(f59,plain,
( injection(x)
<~> injection_2(x) ),
inference(ennf_transformation,[],[f18]) ).
fof(f60,plain,
! [X0,X1] :
( ? [X3,X4] :
( X3 != X4
& apply(X0,X3) = apply(X0,X4)
& element(X4,X1)
& element(X3,X1) )
=> ( sK0(X0,X1) != sK1(X0,X1)
& apply(X0,sK0(X0,X1)) = apply(X0,sK1(X0,X1))
& element(sK1(X0,X1),X1)
& element(sK0(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f61,plain,
! [X0,X1,X2] :
( injection(X0)
| ( sK0(X0,X1) != sK1(X0,X1)
& apply(X0,sK0(X0,X1)) = apply(X0,sK1(X0,X1))
& element(sK1(X0,X1),X1)
& element(sK0(X0,X1),X1) )
| ~ morphism(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f35,f60]) ).
fof(f79,plain,
! [X0,X1,X2] :
( ? [X3] :
( zero(X1) != X3
& apply(X0,X3) = zero(X2)
& element(X3,X1) )
=> ( zero(X1) != sK8(X0,X1,X2)
& zero(X2) = apply(X0,sK8(X0,X1,X2))
& element(sK8(X0,X1,X2),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f80,plain,
! [X0,X1,X2] :
( injection_2(X0)
| ( zero(X1) != sK8(X0,X1,X2)
& zero(X2) = apply(X0,sK8(X0,X1,X2))
& element(sK8(X0,X1,X2),X1) )
| ~ morphism(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f58,f79]) ).
fof(f81,plain,
( ( ~ injection_2(x)
| ~ injection(x) )
& ( injection_2(x)
| injection(x) ) ),
inference(nnf_transformation,[],[f59]) ).
fof(f82,plain,
! [X2,X3,X0,X1] :
( element(apply(X0,X3),X2)
| ~ element(X3,X1)
| ~ morphism(X0,X1,X2) ),
inference(cnf_transformation,[],[f31]) ).
fof(f83,plain,
! [X2,X0,X1] :
( apply(X0,zero(X1)) = zero(X2)
| ~ morphism(X0,X1,X2) ),
inference(cnf_transformation,[],[f31]) ).
fof(f84,plain,
! [X2,X3,X0,X1,X4] :
( X3 = X4
| apply(X0,X3) != apply(X0,X4)
| ~ element(X4,X1)
| ~ element(X3,X1)
| ~ morphism(X0,X1,X2)
| ~ injection(X0) ),
inference(cnf_transformation,[],[f33]) ).
fof(f85,plain,
! [X2,X0,X1] :
( injection(X0)
| element(sK0(X0,X1),X1)
| ~ morphism(X0,X1,X2) ),
inference(cnf_transformation,[],[f61]) ).
fof(f86,plain,
! [X2,X0,X1] :
( injection(X0)
| element(sK1(X0,X1),X1)
| ~ morphism(X0,X1,X2) ),
inference(cnf_transformation,[],[f61]) ).
fof(f87,plain,
! [X2,X0,X1] :
( injection(X0)
| apply(X0,sK0(X0,X1)) = apply(X0,sK1(X0,X1))
| ~ morphism(X0,X1,X2) ),
inference(cnf_transformation,[],[f61]) ).
fof(f88,plain,
! [X2,X0,X1] :
( injection(X0)
| sK0(X0,X1) != sK1(X0,X1)
| ~ morphism(X0,X1,X2) ),
inference(cnf_transformation,[],[f61]) ).
fof(f105,plain,
! [X2,X0,X1] :
( element(subtract(X0,X1,X2),X0)
| ~ element(X2,X0)
| ~ element(X1,X0) ),
inference(cnf_transformation,[],[f49]) ).
fof(f106,plain,
! [X0,X1] :
( zero(X0) = subtract(X0,X1,X1)
| ~ element(X1,X0) ),
inference(cnf_transformation,[],[f50]) ).
fof(f107,plain,
! [X2,X0,X1] :
( subtract(X0,X1,subtract(X0,X1,X2)) = X2
| ~ element(X2,X0)
| ~ element(X1,X0) ),
inference(cnf_transformation,[],[f52]) ).
fof(f108,plain,
! [X2,X3,X0,X1,X4] :
( apply(X0,subtract(X1,X3,X4)) = subtract(X2,apply(X0,X3),apply(X0,X4))
| ~ element(X4,X1)
| ~ element(X3,X1)
| ~ morphism(X0,X1,X2) ),
inference(cnf_transformation,[],[f54]) ).
fof(f109,plain,
! [X2,X3,X0,X1] :
( zero(X1) = X3
| apply(X0,X3) != zero(X2)
| ~ element(X3,X1)
| ~ morphism(X0,X1,X2)
| ~ injection_2(X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f110,plain,
! [X2,X0,X1] :
( injection_2(X0)
| element(sK8(X0,X1,X2),X1)
| ~ morphism(X0,X1,X2) ),
inference(cnf_transformation,[],[f80]) ).
fof(f111,plain,
! [X2,X0,X1] :
( injection_2(X0)
| zero(X2) = apply(X0,sK8(X0,X1,X2))
| ~ morphism(X0,X1,X2) ),
inference(cnf_transformation,[],[f80]) ).
fof(f112,plain,
! [X2,X0,X1] :
( injection_2(X0)
| zero(X1) != sK8(X0,X1,X2)
| ~ morphism(X0,X1,X2) ),
inference(cnf_transformation,[],[f80]) ).
fof(f113,plain,
morphism(x,any1,any2),
inference(cnf_transformation,[],[f16]) ).
fof(f114,plain,
( injection_2(x)
| injection(x) ),
inference(cnf_transformation,[],[f81]) ).
fof(f115,plain,
( ~ injection_2(x)
| ~ injection(x) ),
inference(cnf_transformation,[],[f81]) ).
cnf(c_49,plain,
( ~ morphism(X0,X1,X2)
| apply(X0,zero(X1)) = zero(X2) ),
inference(cnf_transformation,[],[f83]) ).
cnf(c_50,plain,
( ~ morphism(X0,X1,X2)
| ~ element(X3,X1)
| element(apply(X0,X3),X2) ),
inference(cnf_transformation,[],[f82]) ).
cnf(c_51,plain,
( apply(X0,X1) != apply(X0,X2)
| ~ morphism(X0,X3,X4)
| ~ element(X1,X3)
| ~ element(X2,X3)
| ~ injection(X0)
| X1 = X2 ),
inference(cnf_transformation,[],[f84]) ).
cnf(c_52,plain,
( sK0(X0,X1) != sK1(X0,X1)
| ~ morphism(X0,X1,X2)
| injection(X0) ),
inference(cnf_transformation,[],[f88]) ).
cnf(c_53,plain,
( ~ morphism(X0,X1,X2)
| apply(X0,sK0(X0,X1)) = apply(X0,sK1(X0,X1))
| injection(X0) ),
inference(cnf_transformation,[],[f87]) ).
cnf(c_54,plain,
( ~ morphism(X0,X1,X2)
| element(sK1(X0,X1),X1)
| injection(X0) ),
inference(cnf_transformation,[],[f86]) ).
cnf(c_55,plain,
( ~ morphism(X0,X1,X2)
| element(sK0(X0,X1),X1)
| injection(X0) ),
inference(cnf_transformation,[],[f85]) ).
cnf(c_72,plain,
( ~ element(X0,X1)
| ~ element(X2,X1)
| element(subtract(X1,X0,X2),X1) ),
inference(cnf_transformation,[],[f105]) ).
cnf(c_73,plain,
( ~ element(X0,X1)
| subtract(X1,X0,X0) = zero(X1) ),
inference(cnf_transformation,[],[f106]) ).
cnf(c_74,plain,
( ~ element(X0,X1)
| ~ element(X2,X1)
| subtract(X1,X0,subtract(X1,X0,X2)) = X2 ),
inference(cnf_transformation,[],[f107]) ).
cnf(c_75,plain,
( ~ morphism(X0,X1,X2)
| ~ element(X3,X1)
| ~ element(X4,X1)
| subtract(X2,apply(X0,X3),apply(X0,X4)) = apply(X0,subtract(X1,X3,X4)) ),
inference(cnf_transformation,[],[f108]) ).
cnf(c_76,plain,
( apply(X0,X1) != zero(X2)
| ~ morphism(X0,X3,X2)
| ~ element(X1,X3)
| ~ injection_2(X0)
| zero(X3) = X1 ),
inference(cnf_transformation,[],[f109]) ).
cnf(c_77,plain,
( sK8(X0,X1,X2) != zero(X1)
| ~ morphism(X0,X1,X2)
| injection_2(X0) ),
inference(cnf_transformation,[],[f112]) ).
cnf(c_78,plain,
( ~ morphism(X0,X1,X2)
| apply(X0,sK8(X0,X1,X2)) = zero(X2)
| injection_2(X0) ),
inference(cnf_transformation,[],[f111]) ).
cnf(c_79,plain,
( ~ morphism(X0,X1,X2)
| element(sK8(X0,X1,X2),X1)
| injection_2(X0) ),
inference(cnf_transformation,[],[f110]) ).
cnf(c_80,plain,
morphism(x,any1,any2),
inference(cnf_transformation,[],[f113]) ).
cnf(c_81,negated_conjecture,
( ~ injection(x)
| ~ injection_2(x) ),
inference(cnf_transformation,[],[f115]) ).
cnf(c_82,negated_conjecture,
( injection(x)
| injection_2(x) ),
inference(cnf_transformation,[],[f114]) ).
cnf(c_3012,negated_conjecture,
( ~ injection(x)
| ~ injection_2(x) ),
inference(subtyping,[status(esa)],[c_81]) ).
cnf(c_3013,plain,
morphism(x,any1,any2),
inference(subtyping,[status(esa)],[c_80]) ).
cnf(c_3014,plain,
( ~ morphism(X0_13,X0_14,X1_14)
| element(sK8(X0_13,X0_14,X1_14),X0_14)
| injection_2(X0_13) ),
inference(subtyping,[status(esa)],[c_79]) ).
cnf(c_3015,plain,
( ~ morphism(X0_13,X0_14,X1_14)
| apply(X0_13,sK8(X0_13,X0_14,X1_14)) = zero(X1_14)
| injection_2(X0_13) ),
inference(subtyping,[status(esa)],[c_78]) ).
cnf(c_3016,plain,
( sK8(X0_13,X0_14,X1_14) != zero(X0_14)
| ~ morphism(X0_13,X0_14,X1_14)
| injection_2(X0_13) ),
inference(subtyping,[status(esa)],[c_77]) ).
cnf(c_3017,plain,
( apply(X0_13,X0_15) != zero(X0_14)
| ~ morphism(X0_13,X1_14,X0_14)
| ~ element(X0_15,X1_14)
| ~ injection_2(X0_13)
| zero(X1_14) = X0_15 ),
inference(subtyping,[status(esa)],[c_76]) ).
cnf(c_3018,plain,
( ~ morphism(X0_13,X0_14,X1_14)
| ~ element(X0_15,X0_14)
| ~ element(X1_15,X0_14)
| subtract(X1_14,apply(X0_13,X0_15),apply(X0_13,X1_15)) = apply(X0_13,subtract(X0_14,X0_15,X1_15)) ),
inference(subtyping,[status(esa)],[c_75]) ).
cnf(c_3019,plain,
( ~ element(X0_15,X0_14)
| ~ element(X1_15,X0_14)
| subtract(X0_14,X0_15,subtract(X0_14,X0_15,X1_15)) = X1_15 ),
inference(subtyping,[status(esa)],[c_74]) ).
cnf(c_3020,plain,
( ~ element(X0_15,X0_14)
| subtract(X0_14,X0_15,X0_15) = zero(X0_14) ),
inference(subtyping,[status(esa)],[c_73]) ).
cnf(c_3021,plain,
( ~ element(X0_15,X0_14)
| ~ element(X1_15,X0_14)
| element(subtract(X0_14,X0_15,X1_15),X0_14) ),
inference(subtyping,[status(esa)],[c_72]) ).
cnf(c_3037,plain,
( ~ morphism(X0_13,X0_14,X1_14)
| element(sK0(X0_13,X0_14),X0_14)
| injection(X0_13) ),
inference(subtyping,[status(esa)],[c_55]) ).
cnf(c_3038,plain,
( ~ morphism(X0_13,X0_14,X1_14)
| element(sK1(X0_13,X0_14),X0_14)
| injection(X0_13) ),
inference(subtyping,[status(esa)],[c_54]) ).
cnf(c_3039,plain,
( ~ morphism(X0_13,X0_14,X1_14)
| apply(X0_13,sK0(X0_13,X0_14)) = apply(X0_13,sK1(X0_13,X0_14))
| injection(X0_13) ),
inference(subtyping,[status(esa)],[c_53]) ).
cnf(c_3040,plain,
( sK0(X0_13,X0_14) != sK1(X0_13,X0_14)
| ~ morphism(X0_13,X0_14,X1_14)
| injection(X0_13) ),
inference(subtyping,[status(esa)],[c_52]) ).
cnf(c_3041,plain,
( apply(X0_13,X0_15) != apply(X0_13,X1_15)
| ~ morphism(X0_13,X0_14,X1_14)
| ~ element(X0_15,X0_14)
| ~ element(X1_15,X0_14)
| ~ injection(X0_13)
| X0_15 = X1_15 ),
inference(subtyping,[status(esa)],[c_51]) ).
cnf(c_3042,plain,
( ~ morphism(X0_13,X0_14,X1_14)
| ~ element(X0_15,X0_14)
| element(apply(X0_13,X0_15),X1_14) ),
inference(subtyping,[status(esa)],[c_50]) ).
cnf(c_3043,plain,
( ~ morphism(X0_13,X0_14,X1_14)
| apply(X0_13,zero(X0_14)) = zero(X1_14) ),
inference(subtyping,[status(esa)],[c_49]) ).
cnf(c_3045,plain,
X0_15 = X0_15,
theory(equality) ).
cnf(c_3046,plain,
( X0_15 != X1_15
| X2_15 != X1_15
| X2_15 = X0_15 ),
theory(equality) ).
cnf(c_3047,plain,
( X0_15 != X1_15
| apply(X0_13,X0_15) = apply(X0_13,X1_15) ),
theory(equality) ).
cnf(c_3048,plain,
( X0_15 != X1_15
| ~ element(X1_15,X0_14)
| element(X0_15,X0_14) ),
theory(equality) ).
cnf(c_3844,plain,
apply(x,zero(any1)) = zero(any2),
inference(superposition,[status(thm)],[c_3013,c_3043]) ).
cnf(c_3886,plain,
( element(sK0(x,any1),any1)
| injection(x) ),
inference(superposition,[status(thm)],[c_3013,c_3037]) ).
cnf(c_3887,plain,
( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1)
| injection(x) ),
inference(superposition,[status(thm)],[c_3886,c_3020]) ).
cnf(c_3888,plain,
( element(sK1(x,any1),any1)
| injection(x) ),
inference(superposition,[status(thm)],[c_3013,c_3038]) ).
cnf(c_3889,plain,
( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1)
| injection(x) ),
inference(superposition,[status(thm)],[c_3888,c_3020]) ).
cnf(c_3890,plain,
( ~ morphism(X0_13,X0_14,X1_14)
| subtract(X0_14,sK8(X0_13,X0_14,X1_14),sK8(X0_13,X0_14,X1_14)) = zero(X0_14)
| injection_2(X0_13) ),
inference(superposition,[status(thm)],[c_3014,c_3020]) ).
cnf(c_3894,plain,
apply(x,zero(any1)) = zero(any2),
inference(superposition,[status(thm)],[c_3013,c_3043]) ).
cnf(c_3895,plain,
( ~ element(X0_15,X0_14)
| ~ element(X1_15,X0_14)
| subtract(X0_14,subtract(X0_14,X0_15,X1_15),subtract(X0_14,X0_15,X1_15)) = zero(X0_14) ),
inference(superposition,[status(thm)],[c_3021,c_3020]) ).
cnf(c_3897,plain,
( ~ element(X0_15,any1)
| element(apply(x,X0_15),any2) ),
inference(superposition,[status(thm)],[c_3013,c_3042]) ).
cnf(c_3899,plain,
( ~ element(X0_15,any1)
| subtract(any2,apply(x,X0_15),apply(x,X0_15)) = zero(any2) ),
inference(superposition,[status(thm)],[c_3897,c_3020]) ).
cnf(c_3905,plain,
( subtract(any2,apply(x,sK1(x,any1)),apply(x,sK1(x,any1))) = zero(any2)
| injection(x) ),
inference(superposition,[status(thm)],[c_3888,c_3899]) ).
cnf(c_3909,plain,
( apply(x,sK8(x,any1,any2)) = zero(any2)
| injection_2(x) ),
inference(superposition,[status(thm)],[c_3013,c_3015]) ).
cnf(c_3910,plain,
( ~ injection(x)
| apply(x,sK8(x,any1,any2)) = zero(any2) ),
inference(superposition,[status(thm)],[c_3909,c_3012]) ).
cnf(c_3912,plain,
( subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1)
| apply(x,sK8(x,any1,any2)) = zero(any2) ),
inference(superposition,[status(thm)],[c_3887,c_3910]) ).
cnf(c_3914,plain,
( ~ element(X0_15,X0_14)
| ~ element(X1_15,X0_14)
| ~ element(X2_15,X0_14)
| subtract(X0_14,subtract(X0_14,X0_15,X1_15),subtract(X0_14,subtract(X0_14,X0_15,X1_15),X2_15)) = X2_15 ),
inference(superposition,[status(thm)],[c_3021,c_3019]) ).
cnf(c_3917,plain,
( ~ element(X0_15,any1)
| subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),X0_15)) = X0_15
| injection(x) ),
inference(superposition,[status(thm)],[c_3888,c_3019]) ).
cnf(c_3918,plain,
( ~ element(X0_15,any1)
| ~ element(X1_15,any2)
| subtract(any2,apply(x,X0_15),subtract(any2,apply(x,X0_15),X1_15)) = X1_15 ),
inference(superposition,[status(thm)],[c_3897,c_3019]) ).
cnf(c_3933,plain,
( apply(x,sK0(x,any1)) = apply(x,sK1(x,any1))
| injection(x) ),
inference(superposition,[status(thm)],[c_3013,c_3039]) ).
cnf(c_3948,plain,
( apply(x,sK8(x,any1,any2)) = zero(any2)
| apply(x,sK0(x,any1)) = apply(x,sK1(x,any1)) ),
inference(superposition,[status(thm)],[c_3933,c_3910]) ).
cnf(c_3950,plain,
( ~ element(sK0(X0_13,X0_14),X0_14)
| ~ element(X0_15,X0_14)
| element(subtract(X0_14,X0_15,sK0(X0_13,X0_14)),X0_14) ),
inference(instantiation,[status(thm)],[c_3021]) ).
cnf(c_3952,plain,
( ~ element(sK1(X0_13,X0_14),X0_14)
| ~ element(X0_15,X0_14)
| element(subtract(X0_14,X0_15,sK1(X0_13,X0_14)),X0_14) ),
inference(instantiation,[status(thm)],[c_3021]) ).
cnf(c_3958,plain,
( ~ morphism(x,any1,any2)
| ~ element(X0_15,any1)
| element(apply(x,X0_15),any2) ),
inference(instantiation,[status(thm)],[c_3042]) ).
cnf(c_3991,plain,
( zero(X0_14) != zero(any2)
| ~ element(sK8(x,any1,any2),X1_14)
| ~ morphism(x,X1_14,X0_14)
| ~ injection_2(x)
| apply(x,sK0(x,any1)) = apply(x,sK1(x,any1))
| sK8(x,any1,any2) = zero(X1_14) ),
inference(superposition,[status(thm)],[c_3948,c_3017]) ).
cnf(c_4000,plain,
( ~ element(X0_15,any1)
| ~ element(X1_15,any1)
| subtract(any2,apply(x,X0_15),apply(x,X1_15)) = apply(x,subtract(any1,X0_15,X1_15)) ),
inference(superposition,[status(thm)],[c_3013,c_3018]) ).
cnf(c_4007,plain,
( ~ element(sK0(X0_13,any1),any1)
| ~ morphism(x,any1,any2)
| element(apply(x,sK0(X0_13,any1)),any2) ),
inference(instantiation,[status(thm)],[c_3958]) ).
cnf(c_4009,plain,
( ~ element(sK0(x,any1),any1)
| ~ morphism(x,any1,any2)
| element(apply(x,sK0(x,any1)),any2) ),
inference(instantiation,[status(thm)],[c_4007]) ).
cnf(c_4026,plain,
( zero(X0_14) != X0_15
| X1_15 != X0_15
| zero(X0_14) = X1_15 ),
inference(instantiation,[status(thm)],[c_3046]) ).
cnf(c_4050,plain,
( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK0(x,any1))) = sK0(x,any1)
| injection(x) ),
inference(superposition,[status(thm)],[c_3886,c_3917]) ).
cnf(c_4057,plain,
( ~ element(sK0(X0_13,X0_14),X0_14)
| ~ element(sK0(X1_13,X0_14),X0_14)
| element(subtract(X0_14,sK0(X1_13,X0_14),sK0(X0_13,X0_14)),X0_14) ),
inference(instantiation,[status(thm)],[c_3950]) ).
cnf(c_4058,plain,
( ~ element(sK0(x,any1),any1)
| element(subtract(any1,sK0(x,any1),sK0(x,any1)),any1) ),
inference(instantiation,[status(thm)],[c_4057]) ).
cnf(c_4061,plain,
( ~ element(sK0(X0_13,X0_14),X0_14)
| ~ element(sK1(X1_13,X0_14),X0_14)
| element(subtract(X0_14,sK0(X0_13,X0_14),sK1(X1_13,X0_14)),X0_14) ),
inference(instantiation,[status(thm)],[c_3952]) ).
cnf(c_4062,plain,
( ~ element(sK0(x,any1),any1)
| ~ element(sK1(x,any1),any1)
| element(subtract(any1,sK0(x,any1),sK1(x,any1)),any1) ),
inference(instantiation,[status(thm)],[c_4061]) ).
cnf(c_4063,plain,
( ~ element(sK1(X0_13,X0_14),X0_14)
| ~ element(sK1(X1_13,X0_14),X0_14)
| element(subtract(X0_14,sK1(X1_13,X0_14),sK1(X0_13,X0_14)),X0_14) ),
inference(instantiation,[status(thm)],[c_3952]) ).
cnf(c_4064,plain,
( ~ element(sK1(x,any1),any1)
| element(subtract(any1,sK1(x,any1),sK1(x,any1)),any1) ),
inference(instantiation,[status(thm)],[c_4063]) ).
cnf(c_4076,plain,
( apply(x,sK0(x,any1)) = apply(x,sK1(x,any1))
| ~ injection_2(x) ),
inference(global_subsumption_just,[status(thm)],[c_3991,c_81,c_3933]) ).
cnf(c_4077,plain,
( ~ injection_2(x)
| apply(x,sK0(x,any1)) = apply(x,sK1(x,any1)) ),
inference(renaming,[status(thm)],[c_4076]) ).
cnf(c_4105,plain,
( zero(X0_14) != zero(X0_14)
| X0_15 != zero(X0_14)
| zero(X0_14) = X0_15 ),
inference(instantiation,[status(thm)],[c_4026]) ).
cnf(c_4106,plain,
zero(X0_14) = zero(X0_14),
inference(instantiation,[status(thm)],[c_3045]) ).
cnf(c_4108,plain,
zero(any1) = zero(any1),
inference(instantiation,[status(thm)],[c_4106]) ).
cnf(c_4119,plain,
( ~ morphism(x,any1,any2)
| element(sK8(x,any1,any2),any1)
| injection_2(x) ),
inference(instantiation,[status(thm)],[c_3014]) ).
cnf(c_4148,plain,
( sK8(x,any1,any2) != zero(any1)
| ~ morphism(x,any1,any2)
| injection_2(x) ),
inference(instantiation,[status(thm)],[c_3016]) ).
cnf(c_4162,plain,
( subtract(X0_14,sK1(X0_13,X0_14),sK1(X0_13,X0_14)) != zero(X0_14)
| zero(X0_14) != zero(X0_14)
| zero(X0_14) = subtract(X0_14,sK1(X0_13,X0_14),sK1(X0_13,X0_14)) ),
inference(instantiation,[status(thm)],[c_4105]) ).
cnf(c_4163,plain,
( subtract(any1,sK1(x,any1),sK1(x,any1)) != zero(any1)
| zero(any1) != zero(any1)
| zero(any1) = subtract(any1,sK1(x,any1),sK1(x,any1)) ),
inference(instantiation,[status(thm)],[c_4162]) ).
cnf(c_4184,plain,
( ~ element(sK8(x,any1,any2),any1)
| ~ element(X0_15,any1)
| element(subtract(any1,X0_15,sK8(x,any1,any2)),any1) ),
inference(instantiation,[status(thm)],[c_3021]) ).
cnf(c_4195,plain,
( apply(x,X0_15) != zero(any2)
| ~ morphism(x,X0_14,X1_14)
| ~ element(zero(any1),X0_14)
| ~ element(X0_15,X0_14)
| ~ injection(x)
| zero(any1) = X0_15 ),
inference(superposition,[status(thm)],[c_3894,c_3041]) ).
cnf(c_4196,plain,
( apply(x,X0_15) != zero(any2)
| ~ element(sK8(x,any1,any2),X0_14)
| ~ morphism(x,X0_14,X1_14)
| ~ element(X0_15,X0_14)
| ~ injection(x)
| apply(x,sK0(x,any1)) = apply(x,sK1(x,any1))
| sK8(x,any1,any2) = X0_15 ),
inference(superposition,[status(thm)],[c_3948,c_3041]) ).
cnf(c_4270,plain,
( ~ element(X0_15,X0_14)
| ~ morphism(x,X0_14,X1_14)
| ~ element(sK8(x,any1,any2),X0_14)
| apply(x,X0_15) != zero(any2)
| apply(x,sK0(x,any1)) = apply(x,sK1(x,any1))
| sK8(x,any1,any2) = X0_15 ),
inference(global_subsumption_just,[status(thm)],[c_4196,c_3933,c_4196]) ).
cnf(c_4271,plain,
( apply(x,X0_15) != zero(any2)
| ~ element(sK8(x,any1,any2),X0_14)
| ~ morphism(x,X0_14,X1_14)
| ~ element(X0_15,X0_14)
| apply(x,sK0(x,any1)) = apply(x,sK1(x,any1))
| sK8(x,any1,any2) = X0_15 ),
inference(renaming,[status(thm)],[c_4270]) ).
cnf(c_4273,plain,
( ~ element(sK8(x,any1,any2),X0_14)
| ~ morphism(x,X0_14,X1_14)
| ~ element(zero(any1),X0_14)
| apply(x,sK0(x,any1)) = apply(x,sK1(x,any1))
| sK8(x,any1,any2) = zero(any1) ),
inference(superposition,[status(thm)],[c_3894,c_4271]) ).
cnf(c_4290,plain,
( element(sK0(x,any1),any1)
| injection(x) ),
inference(resolution,[status(thm)],[c_3037,c_3013]) ).
cnf(c_4304,plain,
( subtract(any1,sK8(x,any1,any2),sK8(x,any1,any2)) != zero(any1)
| zero(any1) != zero(any1)
| zero(any1) = subtract(any1,sK8(x,any1,any2),sK8(x,any1,any2)) ),
inference(instantiation,[status(thm)],[c_4105]) ).
cnf(c_4384,plain,
( apply(x,sK0(x,any1)) = apply(x,sK1(x,any1))
| injection(x) ),
inference(resolution,[status(thm)],[c_3039,c_3013]) ).
cnf(c_4465,plain,
( ~ element(apply(x,sK1(x,any1)),X0_14)
| element(apply(x,sK0(x,any1)),X0_14)
| injection(x) ),
inference(resolution,[status(thm)],[c_3048,c_4384]) ).
cnf(c_4474,plain,
( X0_15 != X1_15
| ~ element(apply(X0_13,X1_15),X0_14)
| element(apply(X0_13,X0_15),X0_14) ),
inference(resolution,[status(thm)],[c_3047,c_3048]) ).
cnf(c_4476,plain,
( subtract(any1,sK8(x,any1,any2),sK8(x,any1,any2)) = zero(any1)
| injection_2(x) ),
inference(superposition,[status(thm)],[c_3013,c_3890]) ).
cnf(c_4477,plain,
( subtract(any1,sK8(x,any1,any2),sK8(x,any1,any2)) = zero(any1)
| apply(x,sK0(x,any1)) = apply(x,sK1(x,any1)) ),
inference(superposition,[status(thm)],[c_4476,c_4077]) ).
cnf(c_4478,plain,
( ~ injection(x)
| subtract(any1,sK8(x,any1,any2),sK8(x,any1,any2)) = zero(any1) ),
inference(superposition,[status(thm)],[c_4476,c_3012]) ).
cnf(c_4489,plain,
( X0_15 != X1_15
| X1_15 = X0_15 ),
inference(resolution,[status(thm)],[c_3046,c_3045]) ).
cnf(c_4493,plain,
( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK0(x,any1))) = sK0(x,any1)
| subtract(any1,sK8(x,any1,any2),sK8(x,any1,any2)) = zero(any1) ),
inference(superposition,[status(thm)],[c_4050,c_4478]) ).
cnf(c_4499,plain,
( subtract(any1,sK8(x,any1,any2),sK8(x,any1,any2)) = zero(any1)
| subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1) ),
inference(superposition,[status(thm)],[c_3889,c_4478]) ).
cnf(c_4523,plain,
( ~ element(sK8(x,any1,any2),any1)
| subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1)
| element(zero(any1),any1) ),
inference(superposition,[status(thm)],[c_4499,c_3021]) ).
cnf(c_4595,plain,
( ~ morphism(X0_13,X0_14,X1_14)
| ~ element(X0_15,X0_14)
| subtract(X0_14,subtract(X0_14,sK8(X0_13,X0_14,X1_14),X0_15),subtract(X0_14,sK8(X0_13,X0_14,X1_14),X0_15)) = zero(X0_14)
| injection_2(X0_13) ),
inference(superposition,[status(thm)],[c_3014,c_3895]) ).
cnf(c_4602,plain,
( ~ element(X0_15,any1)
| subtract(any1,subtract(any1,sK0(x,any1),X0_15),subtract(any1,sK0(x,any1),X0_15)) = zero(any1)
| injection(x) ),
inference(superposition,[status(thm)],[c_3886,c_3895]) ).
cnf(c_4700,plain,
( ~ element(X0_15,any2)
| subtract(any2,apply(x,sK0(x,any1)),subtract(any2,apply(x,sK0(x,any1)),X0_15)) = X0_15
| injection(x) ),
inference(superposition,[status(thm)],[c_3886,c_3918]) ).
cnf(c_4793,plain,
( ~ element(subtract(any1,sK1(x,any1),sK0(x,any1)),any1)
| ~ element(sK1(x,any1),any1)
| subtract(any1,sK8(x,any1,any2),sK8(x,any1,any2)) = zero(any1)
| element(sK0(x,any1),any1) ),
inference(superposition,[status(thm)],[c_4493,c_3021]) ).
cnf(c_4798,plain,
( subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1)
| element(zero(any1),any1) ),
inference(global_subsumption_just,[status(thm)],[c_4523,c_80,c_81,c_3889,c_4119,c_4523]) ).
cnf(c_4853,plain,
( ~ element(sK8(x,any1,any2),any1)
| element(subtract(any1,sK8(x,any1,any2),sK8(x,any1,any2)),any1) ),
inference(instantiation,[status(thm)],[c_4184]) ).
cnf(c_4979,plain,
( X0_15 != subtract(any1,sK8(x,any1,any2),sK8(x,any1,any2))
| ~ element(subtract(any1,sK8(x,any1,any2),sK8(x,any1,any2)),any1)
| element(X0_15,any1) ),
inference(instantiation,[status(thm)],[c_3048]) ).
cnf(c_5029,plain,
( subtract(any1,sK8(x,any1,any2),sK8(x,any1,any2)) = zero(any1)
| element(sK0(x,any1),any1) ),
inference(global_subsumption_just,[status(thm)],[c_4793,c_3886,c_4478]) ).
cnf(c_5048,plain,
( ~ element(X0_15,X0_14)
| zero(X0_14) = subtract(X0_14,X0_15,X0_15) ),
inference(resolution,[status(thm)],[c_3020,c_4489]) ).
cnf(c_5163,plain,
( ~ element(sK8(x,any1,any2),any1)
| apply(x,sK0(x,any1)) = apply(x,sK1(x,any1))
| element(zero(any1),any1) ),
inference(superposition,[status(thm)],[c_4477,c_3021]) ).
cnf(c_5192,plain,
( apply(x,sK0(x,any1)) = apply(x,sK1(x,any1))
| element(zero(any1),any1) ),
inference(global_subsumption_just,[status(thm)],[c_5163,c_80,c_4077,c_4119,c_5163]) ).
cnf(c_5218,plain,
( ~ element(X0_15,any1)
| subtract(any2,apply(x,sK0(x,any1)),apply(x,X0_15)) = apply(x,subtract(any1,sK0(x,any1),X0_15))
| injection(x) ),
inference(superposition,[status(thm)],[c_3886,c_4000]) ).
cnf(c_5221,plain,
( ~ element(X0_15,any1)
| subtract(any2,apply(x,sK1(x,any1)),apply(x,X0_15)) = apply(x,subtract(any1,sK1(x,any1),X0_15))
| injection(x) ),
inference(superposition,[status(thm)],[c_3888,c_4000]) ).
cnf(c_5607,plain,
( subtract(any1,subtract(any1,sK0(x,any1),sK0(x,any1)),subtract(any1,sK0(x,any1),sK0(x,any1))) = zero(any1)
| injection(x) ),
inference(superposition,[status(thm)],[c_3886,c_4602]) ).
cnf(c_5781,plain,
( ~ element(X0_15,any1)
| element(apply(x,X0_15),any2) ),
inference(resolution,[status(thm)],[c_3042,c_3013]) ).
cnf(c_5910,plain,
( subtract(any1,subtract(any1,sK0(x,any1),sK0(x,any1)),subtract(any1,sK0(x,any1),sK0(x,any1))) = zero(any1)
| subtract(any1,sK8(x,any1,any2),sK8(x,any1,any2)) = zero(any1) ),
inference(superposition,[status(thm)],[c_5607,c_4478]) ).
cnf(c_5921,plain,
( ~ element(subtract(any1,sK0(x,any1),sK0(x,any1)),any1)
| subtract(any1,sK8(x,any1,any2),sK8(x,any1,any2)) = zero(any1)
| element(zero(any1),any1) ),
inference(superposition,[status(thm)],[c_5910,c_3021]) ).
cnf(c_5959,plain,
( X0_15 != subtract(X0_14,sK1(X0_13,X0_14),sK1(X1_13,X0_14))
| ~ element(subtract(X0_14,sK1(X0_13,X0_14),sK1(X1_13,X0_14)),X0_14)
| element(X0_15,X0_14) ),
inference(instantiation,[status(thm)],[c_3048]) ).
cnf(c_6001,plain,
( subtract(any1,sK8(x,any1,any2),sK8(x,any1,any2)) = zero(any1)
| element(zero(any1),any1) ),
inference(global_subsumption_just,[status(thm)],[c_5921,c_4058,c_5029,c_5921]) ).
cnf(c_6147,plain,
( ~ element(sK1(x,any1),any1)
| element(apply(x,sK0(x,any1)),any2)
| injection(x) ),
inference(resolution,[status(thm)],[c_4465,c_5781]) ).
cnf(c_6148,plain,
( element(apply(x,sK0(x,any1)),any2)
| injection(x) ),
inference(global_subsumption_just,[status(thm)],[c_6147,c_80,c_3886,c_4009]) ).
cnf(c_6390,plain,
( X0_15 != X1_15
| ~ element(X1_15,any1)
| element(apply(x,X0_15),any2) ),
inference(resolution,[status(thm)],[c_4474,c_5781]) ).
cnf(c_6506,plain,
( apply(x,zero(any1)) != X0_15
| X1_15 != X0_15
| X1_15 = apply(x,zero(any1)) ),
inference(instantiation,[status(thm)],[c_3046]) ).
cnf(c_8281,plain,
( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))) = apply(x,subtract(any1,sK0(x,any1),sK0(x,any1)))
| injection(x) ),
inference(superposition,[status(thm)],[c_3886,c_5218]) ).
cnf(c_8284,plain,
( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK1(x,any1))) = apply(x,subtract(any1,sK0(x,any1),sK1(x,any1)))
| injection(x) ),
inference(superposition,[status(thm)],[c_3888,c_5218]) ).
cnf(c_8586,plain,
( ~ element(subtract(X0_14,X0_15,X0_15),any1)
| ~ element(X0_15,X0_14)
| element(apply(x,zero(X0_14)),any2) ),
inference(resolution,[status(thm)],[c_5048,c_6390]) ).
cnf(c_9179,plain,
( ~ element(X0_15,any1)
| element(apply(x,zero(any1)),any2) ),
inference(resolution,[status(thm)],[c_8586,c_3021]) ).
cnf(c_9185,plain,
( ~ morphism(X0_13,any1,X0_14)
| element(apply(x,zero(any1)),any2)
| injection_2(X0_13) ),
inference(resolution,[status(thm)],[c_9179,c_3014]) ).
cnf(c_9195,plain,
( element(apply(x,zero(any1)),any2)
| injection(x) ),
inference(resolution,[status(thm)],[c_9179,c_4290]) ).
cnf(c_9358,plain,
( element(apply(x,zero(any1)),any2)
| injection_2(x) ),
inference(resolution,[status(thm)],[c_9185,c_3013]) ).
cnf(c_9359,plain,
element(apply(x,zero(any1)),any2),
inference(global_subsumption_just,[status(thm)],[c_9358,c_81,c_9195,c_9358]) ).
cnf(c_9559,plain,
( apply(x,zero(any1)) != zero(any2)
| X0_15 != zero(any2)
| X0_15 = apply(x,zero(any1)) ),
inference(instantiation,[status(thm)],[c_6506]) ).
cnf(c_9770,plain,
( subtract(any2,apply(x,sK0(x,any1)),apply(x,sK0(x,any1))) = apply(x,subtract(any1,sK0(x,any1),sK0(x,any1)))
| apply(x,sK8(x,any1,any2)) = zero(any2) ),
inference(superposition,[status(thm)],[c_8281,c_3910]) ).
cnf(c_9787,plain,
( ~ element(apply(x,sK0(x,any1)),any2)
| apply(x,sK8(x,any1,any2)) = zero(any2)
| element(apply(x,subtract(any1,sK0(x,any1),sK0(x,any1))),any2) ),
inference(superposition,[status(thm)],[c_9770,c_3021]) ).
cnf(c_9847,plain,
( ~ element(sK8(x,any1,any2),X0_14)
| ~ morphism(x,X0_14,X1_14)
| ~ element(zero(any1),X0_14)
| ~ injection(x)
| apply(x,sK0(x,any1)) = apply(x,sK1(x,any1))
| sK8(x,any1,any2) = zero(any1) ),
inference(superposition,[status(thm)],[c_3948,c_4195]) ).
cnf(c_10131,plain,
( apply(x,sK8(x,any1,any2)) = zero(any2)
| element(apply(x,subtract(any1,sK0(x,any1),sK0(x,any1))),any2) ),
inference(global_subsumption_just,[status(thm)],[c_9787,c_3910,c_6148,c_9787]) ).
cnf(c_10135,plain,
( apply(x,sK8(x,any1,any2)) = zero(any2)
| element(apply(x,zero(any1)),any2) ),
inference(superposition,[status(thm)],[c_3912,c_10131]) ).
cnf(c_10271,plain,
element(apply(x,zero(any1)),any2),
inference(global_subsumption_just,[status(thm)],[c_10135,c_9359]) ).
cnf(c_10273,plain,
element(zero(any2),any2),
inference(superposition,[status(thm)],[c_3894,c_10271]) ).
cnf(c_10303,plain,
( ~ element(X0_15,any2)
| ~ element(X1_15,any2)
| subtract(any2,subtract(any2,zero(any2),X0_15),subtract(any2,subtract(any2,zero(any2),X0_15),X1_15)) = X1_15 ),
inference(superposition,[status(thm)],[c_10273,c_3914]) ).
cnf(c_10323,plain,
( subtract(any2,apply(x,sK0(x,any1)),subtract(any2,apply(x,sK0(x,any1)),zero(any2))) = zero(any2)
| injection(x) ),
inference(superposition,[status(thm)],[c_10273,c_4700]) ).
cnf(c_11052,plain,
( apply(x,sK0(x,any1)) = apply(x,sK1(x,any1))
| ~ element(sK8(x,any1,any2),X0_14)
| ~ morphism(x,X0_14,X1_14)
| ~ element(zero(any1),X0_14) ),
inference(global_subsumption_just,[status(thm)],[c_9847,c_80,c_4077,c_4148,c_4273]) ).
cnf(c_11053,plain,
( ~ element(sK8(x,any1,any2),X0_14)
| ~ morphism(x,X0_14,X1_14)
| ~ element(zero(any1),X0_14)
| apply(x,sK0(x,any1)) = apply(x,sK1(x,any1)) ),
inference(renaming,[status(thm)],[c_11052]) ).
cnf(c_11055,plain,
( ~ morphism(x,any1,X0_14)
| ~ morphism(x,any1,any2)
| ~ element(zero(any1),any1)
| apply(x,sK0(x,any1)) = apply(x,sK1(x,any1))
| injection_2(x) ),
inference(superposition,[status(thm)],[c_3014,c_11053]) ).
cnf(c_11513,plain,
( apply(x,sK0(x,any1)) = apply(x,sK1(x,any1))
| ~ morphism(x,any1,X0_14) ),
inference(global_subsumption_just,[status(thm)],[c_11055,c_80,c_4077,c_5192,c_11055]) ).
cnf(c_11514,plain,
( ~ morphism(x,any1,X0_14)
| apply(x,sK0(x,any1)) = apply(x,sK1(x,any1)) ),
inference(renaming,[status(thm)],[c_11513]) ).
cnf(c_11516,plain,
apply(x,sK0(x,any1)) = apply(x,sK1(x,any1)),
inference(superposition,[status(thm)],[c_3013,c_11514]) ).
cnf(c_12295,plain,
( zero(any1) != subtract(any1,sK8(x,any1,any2),sK8(x,any1,any2))
| ~ element(subtract(any1,sK8(x,any1,any2),sK8(x,any1,any2)),any1)
| element(zero(any1),any1) ),
inference(instantiation,[status(thm)],[c_4979]) ).
cnf(c_12352,plain,
( ~ element(X0_15,any1)
| subtract(any1,subtract(any1,sK8(x,any1,any2),X0_15),subtract(any1,sK8(x,any1,any2),X0_15)) = zero(any1)
| injection_2(x) ),
inference(superposition,[status(thm)],[c_3013,c_4595]) ).
cnf(c_12364,plain,
( ~ morphism(X0_13,any1,X0_14)
| subtract(any1,subtract(any1,sK8(x,any1,any2),sK8(X0_13,any1,X0_14)),subtract(any1,sK8(x,any1,any2),sK8(X0_13,any1,X0_14))) = zero(any1)
| injection_2(X0_13)
| injection_2(x) ),
inference(superposition,[status(thm)],[c_3014,c_12352]) ).
cnf(c_14084,plain,
( apply(x,sK8(x,any1,any2)) != zero(any2)
| apply(x,zero(any1)) != zero(any2)
| apply(x,sK8(x,any1,any2)) = apply(x,zero(any1)) ),
inference(instantiation,[status(thm)],[c_9559]) ).
cnf(c_14123,plain,
( ~ element(X0_15,any2)
| subtract(any2,subtract(any2,zero(any2),X0_15),subtract(any2,subtract(any2,zero(any2),X0_15),zero(any2))) = zero(any2) ),
inference(superposition,[status(thm)],[c_10273,c_10303]) ).
cnf(c_14251,plain,
( ~ element(X0_15,any1)
| subtract(any2,subtract(any2,zero(any2),apply(x,X0_15)),subtract(any2,subtract(any2,zero(any2),apply(x,X0_15)),zero(any2))) = zero(any2) ),
inference(superposition,[status(thm)],[c_3897,c_14123]) ).
cnf(c_18318,plain,
( zero(X0_14) != subtract(X0_14,sK1(X0_13,X0_14),sK1(X0_13,X0_14))
| ~ element(subtract(X0_14,sK1(X0_13,X0_14),sK1(X0_13,X0_14)),X0_14)
| element(zero(X0_14),X0_14) ),
inference(instantiation,[status(thm)],[c_5959]) ).
cnf(c_18319,plain,
( zero(any1) != subtract(any1,sK1(x,any1),sK1(x,any1))
| ~ element(subtract(any1,sK1(x,any1),sK1(x,any1)),any1)
| element(zero(any1),any1) ),
inference(instantiation,[status(thm)],[c_18318]) ).
cnf(c_22631,plain,
( ~ morphism(X0_13,any1,X0_14)
| subtract(any2,subtract(any2,zero(any2),apply(x,sK8(X0_13,any1,X0_14))),subtract(any2,subtract(any2,zero(any2),apply(x,sK8(X0_13,any1,X0_14))),zero(any2))) = zero(any2)
| injection_2(X0_13) ),
inference(superposition,[status(thm)],[c_3014,c_14251]) ).
cnf(c_28158,plain,
( subtract(any1,subtract(any1,sK8(x,any1,any2),sK8(x,any1,any2)),subtract(any1,sK8(x,any1,any2),sK8(x,any1,any2))) = zero(any1)
| injection_2(x) ),
inference(superposition,[status(thm)],[c_3013,c_12364]) ).
cnf(c_28354,plain,
( ~ injection(x)
| subtract(any1,subtract(any1,sK8(x,any1,any2),sK8(x,any1,any2)),subtract(any1,sK8(x,any1,any2),sK8(x,any1,any2))) = zero(any1) ),
inference(superposition,[status(thm)],[c_28158,c_3012]) ).
cnf(c_28387,plain,
( subtract(any1,subtract(any1,sK8(x,any1,any2),sK8(x,any1,any2)),subtract(any1,sK8(x,any1,any2),sK8(x,any1,any2))) = zero(any1)
| subtract(any2,apply(x,sK1(x,any1)),apply(x,sK1(x,any1))) = zero(any2) ),
inference(superposition,[status(thm)],[c_3905,c_28354]) ).
cnf(c_28735,plain,
( ~ element(subtract(any1,sK8(x,any1,any2),sK8(x,any1,any2)),any1)
| subtract(any2,apply(x,sK1(x,any1)),apply(x,sK1(x,any1))) = zero(any2)
| element(zero(any1),any1) ),
inference(superposition,[status(thm)],[c_28387,c_3021]) ).
cnf(c_28821,plain,
element(zero(any1),any1),
inference(global_subsumption_just,[status(thm)],[c_28735,c_80,c_81,c_3888,c_4064,c_4108,c_4119,c_4163,c_4304,c_4798,c_4853,c_6001,c_12295,c_18319]) ).
cnf(c_28826,plain,
( ~ element(X0_15,any1)
| subtract(any1,zero(any1),subtract(any1,zero(any1),X0_15)) = X0_15 ),
inference(superposition,[status(thm)],[c_28821,c_3019]) ).
cnf(c_28871,plain,
( subtract(any2,apply(x,sK1(x,any1)),apply(x,zero(any1))) = apply(x,subtract(any1,sK1(x,any1),zero(any1)))
| injection(x) ),
inference(superposition,[status(thm)],[c_28821,c_5221]) ).
cnf(c_28872,plain,
( subtract(any2,apply(x,sK0(x,any1)),apply(x,zero(any1))) = apply(x,subtract(any1,sK0(x,any1),zero(any1)))
| injection(x) ),
inference(superposition,[status(thm)],[c_28821,c_5218]) ).
cnf(c_28916,plain,
( ~ element(X0_15,any1)
| ~ element(X1_15,any1)
| subtract(any1,zero(any1),subtract(any1,zero(any1),subtract(any1,X0_15,X1_15))) = subtract(any1,X0_15,X1_15) ),
inference(superposition,[status(thm)],[c_3021,c_28826]) ).
cnf(c_28924,plain,
( subtract(any1,zero(any1),subtract(any1,zero(any1),sK0(x,any1))) = sK0(x,any1)
| injection(x) ),
inference(superposition,[status(thm)],[c_3886,c_28826]) ).
cnf(c_28927,plain,
( subtract(any1,zero(any1),subtract(any1,zero(any1),sK1(x,any1))) = sK1(x,any1)
| injection(x) ),
inference(superposition,[status(thm)],[c_3888,c_28826]) ).
cnf(c_29072,plain,
( ~ element(X0_15,any1)
| subtract(any1,zero(any1),subtract(any1,zero(any1),subtract(any1,sK0(x,any1),X0_15))) = subtract(any1,sK0(x,any1),X0_15)
| injection(x) ),
inference(superposition,[status(thm)],[c_3886,c_28916]) ).
cnf(c_61104,plain,
( subtract(any1,zero(any1),subtract(any1,zero(any1),subtract(any1,sK0(x,any1),sK1(x,any1)))) = subtract(any1,sK0(x,any1),sK1(x,any1))
| injection(x) ),
inference(superposition,[status(thm)],[c_3888,c_29072]) ).
cnf(c_80459,plain,
( subtract(any2,subtract(any2,zero(any2),apply(x,sK8(x,any1,any2))),subtract(any2,subtract(any2,zero(any2),apply(x,sK8(x,any1,any2))),zero(any2))) = zero(any2)
| injection_2(x) ),
inference(superposition,[status(thm)],[c_3013,c_22631]) ).
cnf(c_80482,plain,
( ~ injection(x)
| subtract(any2,subtract(any2,zero(any2),apply(x,sK8(x,any1,any2))),subtract(any2,subtract(any2,zero(any2),apply(x,sK8(x,any1,any2))),zero(any2))) = zero(any2) ),
inference(superposition,[status(thm)],[c_80459,c_3012]) ).
cnf(c_80720,plain,
( subtract(any2,subtract(any2,zero(any2),apply(x,sK8(x,any1,any2))),subtract(any2,subtract(any2,zero(any2),apply(x,sK8(x,any1,any2))),zero(any2))) = zero(any2)
| subtract(any1,zero(any1),subtract(any1,zero(any1),sK1(x,any1))) = sK1(x,any1) ),
inference(superposition,[status(thm)],[c_28927,c_80482]) ).
cnf(c_80721,plain,
( subtract(any2,subtract(any2,zero(any2),apply(x,sK8(x,any1,any2))),subtract(any2,subtract(any2,zero(any2),apply(x,sK8(x,any1,any2))),zero(any2))) = zero(any2)
| subtract(any1,zero(any1),subtract(any1,zero(any1),sK0(x,any1))) = sK0(x,any1) ),
inference(superposition,[status(thm)],[c_28924,c_80482]) ).
cnf(c_224928,plain,
( apply(x,X0_15) != apply(x,X1_15)
| ~ morphism(x,any1,any2)
| ~ element(X0_15,any1)
| ~ element(X1_15,any1)
| ~ injection(x)
| X0_15 = X1_15 ),
inference(instantiation,[status(thm)],[c_3041]) ).
cnf(c_227657,plain,
( apply(x,sK8(x,any1,any2)) != apply(x,zero(any1))
| ~ element(sK8(x,any1,any2),any1)
| ~ morphism(x,any1,any2)
| ~ element(zero(any1),any1)
| ~ injection(x)
| sK8(x,any1,any2) = zero(any1) ),
inference(instantiation,[status(thm)],[c_224928]) ).
cnf(c_245009,plain,
subtract(any1,zero(any1),subtract(any1,zero(any1),sK1(x,any1))) = sK1(x,any1),
inference(global_subsumption_just,[status(thm)],[c_80720,c_82,c_80,c_81,c_3844,c_3888,c_3909,c_4064,c_4108,c_4119,c_4148,c_4163,c_4304,c_4798,c_4853,c_6001,c_12295,c_14084,c_18319,c_28927,c_227657]) ).
cnf(c_245011,plain,
( ~ element(subtract(any1,zero(any1),sK1(x,any1)),any1)
| ~ element(zero(any1),any1)
| element(sK1(x,any1),any1) ),
inference(superposition,[status(thm)],[c_245009,c_3021]) ).
cnf(c_245012,plain,
subtract(any1,zero(any1),subtract(any1,zero(any1),sK0(x,any1))) = sK0(x,any1),
inference(global_subsumption_just,[status(thm)],[c_80721,c_82,c_80,c_81,c_3844,c_3888,c_3909,c_4064,c_4108,c_4119,c_4148,c_4163,c_4304,c_4798,c_4853,c_6001,c_12295,c_14084,c_18319,c_28924,c_227657]) ).
cnf(c_245014,plain,
( ~ element(subtract(any1,zero(any1),sK0(x,any1)),any1)
| ~ element(zero(any1),any1)
| element(sK0(x,any1),any1) ),
inference(superposition,[status(thm)],[c_245012,c_3021]) ).
cnf(c_245056,plain,
element(sK1(x,any1),any1),
inference(global_subsumption_just,[status(thm)],[c_245011,c_82,c_80,c_81,c_3844,c_3888,c_3909,c_4064,c_4108,c_4119,c_4148,c_4163,c_4304,c_4798,c_4853,c_6001,c_12295,c_14084,c_18319,c_227657]) ).
cnf(c_245062,plain,
( ~ element(X0_15,any1)
| subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),X0_15)) = X0_15 ),
inference(superposition,[status(thm)],[c_245056,c_3019]) ).
cnf(c_245063,plain,
subtract(any1,sK1(x,any1),sK1(x,any1)) = zero(any1),
inference(superposition,[status(thm)],[c_245056,c_3020]) ).
cnf(c_245332,plain,
( ~ morphism(X0_13,any1,X0_14)
| subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK8(X0_13,any1,X0_14))) = sK8(X0_13,any1,X0_14)
| injection_2(X0_13) ),
inference(superposition,[status(thm)],[c_3014,c_245062]) ).
cnf(c_245344,plain,
subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK1(x,any1))) = sK1(x,any1),
inference(superposition,[status(thm)],[c_245056,c_245062]) ).
cnf(c_245374,plain,
element(sK0(x,any1),any1),
inference(global_subsumption_just,[status(thm)],[c_245014,c_82,c_80,c_81,c_3844,c_3886,c_3888,c_3909,c_4064,c_4108,c_4119,c_4148,c_4163,c_4304,c_4798,c_4853,c_6001,c_12295,c_14084,c_18319,c_227657]) ).
cnf(c_245380,plain,
( ~ element(X0_15,any1)
| subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),X0_15)) = X0_15 ),
inference(superposition,[status(thm)],[c_245374,c_3019]) ).
cnf(c_245381,plain,
subtract(any1,sK0(x,any1),sK0(x,any1)) = zero(any1),
inference(superposition,[status(thm)],[c_245374,c_3020]) ).
cnf(c_245625,plain,
subtract(any1,sK1(x,any1),zero(any1)) = sK1(x,any1),
inference(superposition,[status(thm)],[c_245063,c_245344]) ).
cnf(c_245701,plain,
subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK0(x,any1))) = sK0(x,any1),
inference(superposition,[status(thm)],[c_245374,c_245380]) ).
cnf(c_245704,plain,
subtract(any1,sK0(x,any1),subtract(any1,sK0(x,any1),sK1(x,any1))) = sK1(x,any1),
inference(superposition,[status(thm)],[c_245056,c_245380]) ).
cnf(c_245738,plain,
( subtract(any1,sK1(x,any1),subtract(any1,sK1(x,any1),sK8(x,any1,any2))) = sK8(x,any1,any2)
| injection_2(x) ),
inference(superposition,[status(thm)],[c_3013,c_245332]) ).
cnf(c_245739,plain,
injection_2(x),
inference(global_subsumption_just,[status(thm)],[c_245738,c_82,c_80,c_81,c_3844,c_3888,c_3909,c_4064,c_4108,c_4119,c_4148,c_4163,c_4304,c_4798,c_4853,c_6001,c_12295,c_14084,c_18319,c_227657]) ).
cnf(c_245742,plain,
~ injection(x),
inference(superposition,[status(thm)],[c_245739,c_3012]) ).
cnf(c_245776,plain,
subtract(any1,zero(any1),subtract(any1,zero(any1),subtract(any1,sK0(x,any1),sK1(x,any1)))) = subtract(any1,sK0(x,any1),sK1(x,any1)),
inference(superposition,[status(thm)],[c_61104,c_245742]) ).
cnf(c_245795,plain,
subtract(any2,apply(x,sK0(x,any1)),apply(x,zero(any1))) = apply(x,subtract(any1,sK0(x,any1),zero(any1))),
inference(superposition,[status(thm)],[c_28872,c_245742]) ).
cnf(c_245796,plain,
subtract(any2,apply(x,sK1(x,any1)),apply(x,zero(any1))) = apply(x,subtract(any1,sK1(x,any1),zero(any1))),
inference(superposition,[status(thm)],[c_28871,c_245742]) ).
cnf(c_245810,plain,
subtract(any2,apply(x,sK0(x,any1)),subtract(any2,apply(x,sK0(x,any1)),zero(any2))) = zero(any2),
inference(superposition,[status(thm)],[c_10323,c_245742]) ).
cnf(c_245813,plain,
subtract(any2,apply(x,sK0(x,any1)),apply(x,sK1(x,any1))) = apply(x,subtract(any1,sK0(x,any1),sK1(x,any1))),
inference(superposition,[status(thm)],[c_8284,c_245742]) ).
cnf(c_245820,plain,
subtract(any1,sK0(x,any1),zero(any1)) = sK0(x,any1),
inference(superposition,[status(thm)],[c_245381,c_245701]) ).
cnf(c_245841,plain,
apply(x,subtract(any1,sK0(x,any1),zero(any1))) = subtract(any2,apply(x,sK0(x,any1)),zero(any2)),
inference(superposition,[status(thm)],[c_3894,c_245795]) ).
cnf(c_245846,plain,
apply(x,subtract(any1,sK1(x,any1),zero(any1))) = subtract(any2,apply(x,sK1(x,any1)),zero(any2)),
inference(superposition,[status(thm)],[c_3894,c_245796]) ).
cnf(c_247934,plain,
subtract(any2,apply(x,sK0(x,any1)),apply(x,subtract(any1,sK0(x,any1),zero(any1)))) = zero(any2),
inference(superposition,[status(thm)],[c_245841,c_245810]) ).
cnf(c_247943,plain,
apply(x,subtract(any1,sK1(x,any1),zero(any1))) = subtract(any2,apply(x,sK0(x,any1)),zero(any2)),
inference(superposition,[status(thm)],[c_11516,c_245846]) ).
cnf(c_247962,plain,
( ~ element(subtract(any1,zero(any1),subtract(any1,sK0(x,any1),sK1(x,any1))),any1)
| ~ element(zero(any1),any1)
| element(subtract(any1,sK0(x,any1),sK1(x,any1)),any1) ),
inference(superposition,[status(thm)],[c_245776,c_3021]) ).
cnf(c_248316,plain,
apply(x,subtract(any1,sK0(x,any1),zero(any1))) = apply(x,subtract(any1,sK1(x,any1),zero(any1))),
inference(superposition,[status(thm)],[c_247943,c_245841]) ).
cnf(c_248331,plain,
apply(x,subtract(any1,sK0(x,any1),zero(any1))) = apply(x,sK1(x,any1)),
inference(superposition,[status(thm)],[c_245625,c_248316]) ).
cnf(c_248366,plain,
subtract(any2,apply(x,sK0(x,any1)),apply(x,sK1(x,any1))) = zero(any2),
inference(superposition,[status(thm)],[c_248331,c_247934]) ).
cnf(c_248626,plain,
element(subtract(any1,sK0(x,any1),sK1(x,any1)),any1),
inference(global_subsumption_just,[status(thm)],[c_247962,c_4062,c_245056,c_245374]) ).
cnf(c_248821,plain,
apply(x,subtract(any1,sK0(x,any1),sK1(x,any1))) = zero(any2),
inference(superposition,[status(thm)],[c_248366,c_245813]) ).
cnf(c_248828,plain,
( zero(X0_14) != zero(any2)
| ~ element(subtract(any1,sK0(x,any1),sK1(x,any1)),X1_14)
| ~ morphism(x,X1_14,X0_14)
| ~ injection_2(x)
| subtract(any1,sK0(x,any1),sK1(x,any1)) = zero(X1_14) ),
inference(superposition,[status(thm)],[c_248821,c_3017]) ).
cnf(c_251965,plain,
( ~ morphism(x,X1_14,X0_14)
| ~ element(subtract(any1,sK0(x,any1),sK1(x,any1)),X1_14)
| zero(X0_14) != zero(any2)
| subtract(any1,sK0(x,any1),sK1(x,any1)) = zero(X1_14) ),
inference(global_subsumption_just,[status(thm)],[c_248828,c_82,c_80,c_81,c_3844,c_3888,c_3909,c_4064,c_4108,c_4119,c_4148,c_4163,c_4304,c_4798,c_4853,c_6001,c_12295,c_14084,c_18319,c_227657,c_248828]) ).
cnf(c_251966,plain,
( zero(X0_14) != zero(any2)
| ~ element(subtract(any1,sK0(x,any1),sK1(x,any1)),X1_14)
| ~ morphism(x,X1_14,X0_14)
| subtract(any1,sK0(x,any1),sK1(x,any1)) = zero(X1_14) ),
inference(renaming,[status(thm)],[c_251965]) ).
cnf(c_251968,plain,
( ~ element(subtract(any1,sK0(x,any1),sK1(x,any1)),X0_14)
| ~ morphism(x,X0_14,any2)
| subtract(any1,sK0(x,any1),sK1(x,any1)) = zero(X0_14) ),
inference(equality_resolution,[status(thm)],[c_251966]) ).
cnf(c_251969,plain,
( ~ element(subtract(any1,sK0(x,any1),sK1(x,any1)),any1)
| ~ morphism(x,any1,any2)
| subtract(any1,sK0(x,any1),sK1(x,any1)) = zero(any1) ),
inference(instantiation,[status(thm)],[c_251968]) ).
cnf(c_256169,plain,
( ~ morphism(x,any1,any2)
| subtract(any1,sK0(x,any1),sK1(x,any1)) = zero(any1) ),
inference(superposition,[status(thm)],[c_248626,c_251968]) ).
cnf(c_256350,plain,
subtract(any1,sK0(x,any1),sK1(x,any1)) = zero(any1),
inference(global_subsumption_just,[status(thm)],[c_256169,c_80,c_4062,c_245056,c_245374,c_251969]) ).
cnf(c_256371,plain,
subtract(any1,sK0(x,any1),zero(any1)) = sK1(x,any1),
inference(superposition,[status(thm)],[c_256350,c_245704]) ).
cnf(c_256396,plain,
sK0(x,any1) = sK1(x,any1),
inference(superposition,[status(thm)],[c_256371,c_245820]) ).
cnf(c_256400,plain,
( ~ morphism(x,any1,X0_14)
| injection(x) ),
inference(superposition,[status(thm)],[c_256396,c_3040]) ).
cnf(c_256578,plain,
~ morphism(x,any1,X0_14),
inference(global_subsumption_just,[status(thm)],[c_256400,c_81,c_245739,c_256400]) ).
cnf(c_256581,plain,
$false,
inference(superposition,[status(thm)],[c_3013,c_256578]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : HAL002+1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n001.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 03:05:04 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.47 Running first-order theorem proving
% 0.20/0.47 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 46.14/7.25 % SZS status Started for theBenchmark.p
% 46.14/7.25 ERROR - "ProverProcess:heur/379306:2.0" ran with exit code 2 and error: iprover.ml: Unexpected exception: Z3.Error("Sort mismatch at argument #1 for function (declare-fun k!98 (|16777216| |16777216| |16777216|) Bool) supplied sort is |16777229|")
% 46.14/7.25 Fatal error: exception Z3.Error("Sort mismatch at argument #1 for function (declare-fun k!98 (|16777216| |16777216| |16777216|) Bool) supplied sort is |16777229|")
% 46.14/7.25 ERROR - cmd was: ulimit -v 4096000; ./res/iproveropt_static_z3 --abstr_ref "[]" --abstr_ref_under "[]" --comb_inst_mult 3 --comb_mode clause_based --comb_res_mult 1 --comb_sup_deep_mult 6 --comb_sup_mult 32 --conj_cone_tolerance 3. --demod_completeness_check fast --demod_use_ground false --eq_ax_congr_red true --extra_neg_conj none --inst_activity_threshold 500 --inst_dismatching true --inst_eager_unprocessed_to_passive true --inst_eq_res_simp false --inst_learning_factor 2 --inst_learning_loop_flag true --inst_learning_start 3000 --inst_lit_activity_flag true --inst_lit_sel "[+prop;+sign;+ground;-num_var;-num_symb]" --inst_lit_sel_side num_symb --inst_orphan_elimination true --inst_passive_queue_type priority_queues --inst_passive_queues "[[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]" --inst_passive_queues_freq "[25;2]" --inst_prop_sim_given true --inst_prop_sim_new false --inst_restr_to_given false --inst_sel_renew solver --inst_solver_calls_frac 1. --inst_solver_per_active 1400 --inst_sos_flag false --inst_start_prop_sim_after_learn 3 --inst_subs_given false --inst_subs_new false --instantiation_flag true --out_options none --pred_elim true --prep_def_merge true --prep_def_merge_mbd true --prep_def_merge_prop_impl false --prep_def_merge_tr_cl false --prep_def_merge_tr_red false --prep_gs_sim true --prep_res_sim true --prep_sem_filter exhaustive --prep_sup_sim_all true --prep_sup_sim_sup false --prep_unflatten true --prep_upred true --preprocessing_flag true --prolific_symb_bound 256 --prop_solver_per_cl 1024 --pure_diseq_elim true --res_backward_subs full --res_backward_subs_resolution true --res_forward_subs full --res_forward_subs_resolution true --res_lit_sel adaptive --res_lit_sel_side none --res_ordering kbo --res_passive_queue_type priority_queues --res_passive_queues "[[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]" --res_passive_queues_freq "[15;5]" --res_prop_simpl_given true --res_prop_simpl_new false --res_sim_input true --res_time_limit 300.00 --res_to_prop_solver active --resolution_flag true --schedule none --share_sel_clauses true --smt_ac_axioms fast --smt_preprocessing true --splitting_cvd false --splitting_cvd_svl false --splitting_grd true --splitting_mode input --splitting_nvd 32 --stats_out none --sub_typing true --subs_bck_mult 8 --sup_full_bw "[]" --sup_full_fw "[]" --sup_full_triv "[PropSubs;Unflattening]" --sup_fun_splitting false --sup_immed_bw_immed "[]" --sup_immed_bw_main "[]" --sup_immed_fw_immed "[Subsumption;SubsumptionRes;UnitSubsAndRes;DemodLoopTriv;ACNormalisation]" --sup_immed_fw_main "[Subsumption;UnitSubsAndRes;Demod;LightNorm;ACNormalisation]" --sup_immed_triv "[PropSubs]" --sup_indices_passive "[]" --sup_input_bw "[SubsumptionRes]" --sup_input_fw "[SMTSubs;]" --sup_input_triv "[]" --sup_iter_deepening 1 --sup_passive_queue_type priority_queues --sup_passive_queues "[[+min_def_symb;-score;+epr];[-next_state;-conj_dist;+conj_symb]]" --sup_passive_queues_freq "[3;512]" --sup_prop_simpl_given false --sup_prop_simpl_new true --sup_restarts_mult 16 --sup_score sim_d_gen --sup_share_max_num_cl 320 --sup_share_score_frac 0.2 --sup_smt_interval 10000 --sup_symb_ordering arity_rev --sup_to_prop_solver none --superposition_flag true --time_out_prep_mult 0.1 --proof_out true --sat_out_model small --clausifier res/vclausify_rel --clausifier_options "--mode clausify -t 2.00" --time_out_real 2.00 /export/starexec/sandbox/benchmark/theBenchmark.p 1>> /export/starexec/sandbox/tmp/iprover_out_rq4fovul/k99_15c3 2>> /export/starexec/sandbox/tmp/iprover_out_rq4fovul/k99_15c3_error
% 151.12/20.83 % SZS status Theorem for theBenchmark.p
% 151.12/20.83
% 151.12/20.83 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 151.12/20.83
% 151.12/20.83 ------ iProver source info
% 151.12/20.83
% 151.12/20.83 git: date: 2023-05-31 18:12:56 +0000
% 151.12/20.83 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 151.12/20.83 git: non_committed_changes: false
% 151.12/20.83 git: last_make_outside_of_git: false
% 151.12/20.83
% 151.12/20.83 ------ Parsing...
% 151.12/20.83 ------ Clausification by vclausify_rel & Parsing by iProver...
% 151.12/20.83
% 151.12/20.83 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 151.12/20.83
% 151.12/20.83 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 151.12/20.83
% 151.12/20.83 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 151.12/20.83 ------ Proving...
% 151.12/20.83 ------ Problem Properties
% 151.12/20.83
% 151.12/20.83
% 151.12/20.83 clauses 33
% 151.12/20.83 conjectures 2
% 151.12/20.83 EPR 3
% 151.12/20.83 Horn 21
% 151.12/20.83 unary 1
% 151.12/20.83 binary 4
% 151.12/20.83 lits 132
% 151.12/20.83 lits eq 26
% 151.12/20.83 fd_pure 0
% 151.12/20.83 fd_pseudo 0
% 151.12/20.83 fd_cond 0
% 151.12/20.83 fd_pseudo_cond 2
% 151.12/20.83 AC symbols 0
% 151.12/20.83
% 151.12/20.83 ------ Input Options Time Limit: Unbounded
% 151.12/20.83
% 151.12/20.83
% 151.12/20.83 ------
% 151.12/20.83 Current options:
% 151.12/20.83 ------
% 151.12/20.83
% 151.12/20.83
% 151.12/20.83
% 151.12/20.83
% 151.12/20.83 ------ Proving...
% 151.12/20.83
% 151.12/20.83
% 151.12/20.83 ------ Proving...
% 151.12/20.83
% 151.12/20.83
% 151.12/20.83 ------ Proving...
% 151.12/20.83
% 151.12/20.83
% 151.12/20.83 ------ Proving...
% 151.12/20.83
% 151.12/20.83
% 151.12/20.83 ------ Proving...
% 151.12/20.83
% 151.12/20.83
% 151.12/20.83 % SZS status Theorem for theBenchmark.p
% 151.12/20.83
% 151.12/20.83 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 151.12/20.84
% 151.12/20.84
%------------------------------------------------------------------------------