TSTP Solution File: HAL003+3 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : HAL003+3 : 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 3.78s 1.16s
% Output : CNFRefutation 3.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 17
% Syntax : Number of formulae : 109 ( 21 unt; 0 def)
% Number of atoms : 368 ( 95 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 404 ( 145 ~; 145 |; 85 &)
% ( 0 <=>; 29 =>; 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 : 18 ( 18 usr; 7 con; 0-3 aty)
% Number of variables : 238 ( 7 sgn; 153 !; 32 ?)
% 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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',properties_for_injection) ).
fof(f4,axiom,
! [X0,X1,X2] :
( ( morphism(X0,X1,X2)
& surjection(X0) )
=> ! [X6] :
( element(X6,X2)
=> ? [X7] :
( apply(X0,X7) = X6
& element(X7,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',surjection_properties) ).
fof(f5,axiom,
! [X0,X1,X2] :
( ( ! [X6] :
( element(X6,X2)
=> ? [X7] :
( apply(X0,X7) = X6
& element(X7,X1) ) )
& morphism(X0,X1,X2) )
=> surjection(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',properties_for_surjection) ).
fof(f10,axiom,
! [X1,X4,X5] :
( ( element(X5,X1)
& element(X4,X1) )
=> element(subtract(X1,X4,X5),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subtract_in_domain) ).
fof(f17,axiom,
morphism(delta,e,r),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',delta_morphism) ).
fof(f19,axiom,
morphism(g,b,e),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',g_morphism) ).
fof(f24,axiom,
surjection(delta),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',delta_surjection) ).
fof(f31,axiom,
! [X18] :
( element(X18,e)
=> ? [X19,X20] :
( apply(delta,apply(g,X20)) = X19
& apply(h,apply(beta,X20)) = X19
& element(X20,b)
& apply(delta,X18) = X19
& element(X19,r) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma3) ).
fof(f33,axiom,
! [X18] :
( element(X18,e)
=> ? [X20,X23] :
( apply(g,subtract(b,X20,X23)) = X18
& element(X23,b)
& element(X20,b) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma12) ).
fof(f34,conjecture,
surjection(g),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',g_surjection) ).
fof(f35,negated_conjecture,
~ surjection(g),
inference(negated_conjecture,[],[f34]) ).
fof(f36,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(f37,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(f38,plain,
! [X0,X1,X2] :
( ( morphism(X0,X1,X2)
& surjection(X0) )
=> ! [X3] :
( element(X3,X2)
=> ? [X4] :
( apply(X0,X4) = X3
& element(X4,X1) ) ) ),
inference(rectify,[],[f4]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( element(X3,X2)
=> ? [X4] :
( apply(X0,X4) = X3
& element(X4,X1) ) )
& morphism(X0,X1,X2) )
=> surjection(X0) ),
inference(rectify,[],[f5]) ).
fof(f44,plain,
! [X0,X1,X2] :
( ( element(X2,X0)
& element(X1,X0) )
=> element(subtract(X0,X1,X2),X0) ),
inference(rectify,[],[f10]) ).
fof(f48,plain,
! [X0] :
( element(X0,e)
=> ? [X1,X2] :
( apply(delta,apply(g,X2)) = X1
& apply(h,apply(beta,X2)) = X1
& element(X2,b)
& apply(delta,X0) = X1
& element(X1,r) ) ),
inference(rectify,[],[f31]) ).
fof(f50,plain,
! [X0] :
( element(X0,e)
=> ? [X1,X2] :
( apply(g,subtract(b,X1,X2)) = X0
& element(X2,b)
& element(X1,b) ) ),
inference(rectify,[],[f33]) ).
fof(f51,plain,
~ surjection(g),
inference(flattening,[],[f35]) ).
fof(f52,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(f53,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,[],[f36]) ).
fof(f54,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,[],[f53]) ).
fof(f55,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,[],[f37]) ).
fof(f56,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,[],[f55]) ).
fof(f57,plain,
! [X0,X1,X2] :
( ! [X3] :
( ? [X4] :
( apply(X0,X4) = X3
& element(X4,X1) )
| ~ element(X3,X2) )
| ~ morphism(X0,X1,X2)
| ~ surjection(X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f58,plain,
! [X0,X1,X2] :
( ! [X3] :
( ? [X4] :
( apply(X0,X4) = X3
& element(X4,X1) )
| ~ element(X3,X2) )
| ~ morphism(X0,X1,X2)
| ~ surjection(X0) ),
inference(flattening,[],[f57]) ).
fof(f59,plain,
! [X0,X1,X2] :
( surjection(X0)
| ? [X3] :
( ! [X4] :
( apply(X0,X4) != X3
| ~ element(X4,X1) )
& element(X3,X2) )
| ~ morphism(X0,X1,X2) ),
inference(ennf_transformation,[],[f39]) ).
fof(f60,plain,
! [X0,X1,X2] :
( surjection(X0)
| ? [X3] :
( ! [X4] :
( apply(X0,X4) != X3
| ~ element(X4,X1) )
& element(X3,X2) )
| ~ morphism(X0,X1,X2) ),
inference(flattening,[],[f59]) ).
fof(f69,plain,
! [X0,X1,X2] :
( element(subtract(X0,X1,X2),X0)
| ~ element(X2,X0)
| ~ element(X1,X0) ),
inference(ennf_transformation,[],[f44]) ).
fof(f70,plain,
! [X0,X1,X2] :
( element(subtract(X0,X1,X2),X0)
| ~ element(X2,X0)
| ~ element(X1,X0) ),
inference(flattening,[],[f69]) ).
fof(f76,plain,
! [X0] :
( ? [X1,X2] :
( apply(delta,apply(g,X2)) = X1
& apply(h,apply(beta,X2)) = X1
& element(X2,b)
& apply(delta,X0) = X1
& element(X1,r) )
| ~ element(X0,e) ),
inference(ennf_transformation,[],[f48]) ).
fof(f78,plain,
! [X0] :
( ? [X1,X2] :
( apply(g,subtract(b,X1,X2)) = X0
& element(X2,b)
& element(X1,b) )
| ~ element(X0,e) ),
inference(ennf_transformation,[],[f50]) ).
fof(f79,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(f80,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])],[f56,f79]) ).
fof(f81,plain,
! [X0,X1,X3] :
( ? [X4] :
( apply(X0,X4) = X3
& element(X4,X1) )
=> ( apply(X0,sK2(X0,X1,X3)) = X3
& element(sK2(X0,X1,X3),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f82,plain,
! [X0,X1,X2] :
( ! [X3] :
( ( apply(X0,sK2(X0,X1,X3)) = X3
& element(sK2(X0,X1,X3),X1) )
| ~ element(X3,X2) )
| ~ morphism(X0,X1,X2)
| ~ surjection(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f58,f81]) ).
fof(f83,plain,
! [X0,X1,X2] :
( ? [X3] :
( ! [X4] :
( apply(X0,X4) != X3
| ~ element(X4,X1) )
& element(X3,X2) )
=> ( ! [X4] :
( apply(X0,X4) != sK3(X0,X1,X2)
| ~ element(X4,X1) )
& element(sK3(X0,X1,X2),X2) ) ),
introduced(choice_axiom,[]) ).
fof(f84,plain,
! [X0,X1,X2] :
( surjection(X0)
| ( ! [X4] :
( apply(X0,X4) != sK3(X0,X1,X2)
| ~ element(X4,X1) )
& element(sK3(X0,X1,X2),X2) )
| ~ morphism(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f60,f83]) ).
fof(f98,plain,
! [X0] :
( ? [X1,X2] :
( apply(delta,apply(g,X2)) = X1
& apply(h,apply(beta,X2)) = X1
& element(X2,b)
& apply(delta,X0) = X1
& element(X1,r) )
=> ( sK8(X0) = apply(delta,apply(g,sK9(X0)))
& sK8(X0) = apply(h,apply(beta,sK9(X0)))
& element(sK9(X0),b)
& apply(delta,X0) = sK8(X0)
& element(sK8(X0),r) ) ),
introduced(choice_axiom,[]) ).
fof(f99,plain,
! [X0] :
( ( sK8(X0) = apply(delta,apply(g,sK9(X0)))
& sK8(X0) = apply(h,apply(beta,sK9(X0)))
& element(sK9(X0),b)
& apply(delta,X0) = sK8(X0)
& element(sK8(X0),r) )
| ~ element(X0,e) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9])],[f76,f98]) ).
fof(f102,plain,
! [X0] :
( ? [X1,X2] :
( apply(g,subtract(b,X1,X2)) = X0
& element(X2,b)
& element(X1,b) )
=> ( apply(g,subtract(b,sK13(X0),sK14(X0))) = X0
& element(sK14(X0),b)
& element(sK13(X0),b) ) ),
introduced(choice_axiom,[]) ).
fof(f103,plain,
! [X0] :
( ( apply(g,subtract(b,sK13(X0),sK14(X0))) = X0
& element(sK14(X0),b)
& element(sK13(X0),b) )
| ~ element(X0,e) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13,sK14])],[f78,f102]) ).
fof(f104,plain,
! [X2,X3,X0,X1] :
( element(apply(X0,X3),X2)
| ~ element(X3,X1)
| ~ morphism(X0,X1,X2) ),
inference(cnf_transformation,[],[f52]) ).
fof(f106,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,[],[f54]) ).
fof(f107,plain,
! [X2,X0,X1] :
( injection(X0)
| element(sK0(X0,X1),X1)
| ~ morphism(X0,X1,X2) ),
inference(cnf_transformation,[],[f80]) ).
fof(f111,plain,
! [X2,X3,X0,X1] :
( element(sK2(X0,X1,X3),X1)
| ~ element(X3,X2)
| ~ morphism(X0,X1,X2)
| ~ surjection(X0) ),
inference(cnf_transformation,[],[f82]) ).
fof(f112,plain,
! [X2,X3,X0,X1] :
( apply(X0,sK2(X0,X1,X3)) = X3
| ~ element(X3,X2)
| ~ morphism(X0,X1,X2)
| ~ surjection(X0) ),
inference(cnf_transformation,[],[f82]) ).
fof(f113,plain,
! [X2,X0,X1] :
( surjection(X0)
| element(sK3(X0,X1,X2),X2)
| ~ morphism(X0,X1,X2) ),
inference(cnf_transformation,[],[f84]) ).
fof(f114,plain,
! [X2,X0,X1,X4] :
( surjection(X0)
| apply(X0,X4) != sK3(X0,X1,X2)
| ~ element(X4,X1)
| ~ morphism(X0,X1,X2) ),
inference(cnf_transformation,[],[f84]) ).
fof(f127,plain,
! [X2,X0,X1] :
( element(subtract(X0,X1,X2),X0)
| ~ element(X2,X0)
| ~ element(X1,X0) ),
inference(cnf_transformation,[],[f70]) ).
fof(f134,plain,
morphism(delta,e,r),
inference(cnf_transformation,[],[f17]) ).
fof(f136,plain,
morphism(g,b,e),
inference(cnf_transformation,[],[f19]) ).
fof(f141,plain,
surjection(delta),
inference(cnf_transformation,[],[f24]) ).
fof(f149,plain,
! [X0] :
( apply(delta,X0) = sK8(X0)
| ~ element(X0,e) ),
inference(cnf_transformation,[],[f99]) ).
fof(f159,plain,
! [X0] :
( element(sK13(X0),b)
| ~ element(X0,e) ),
inference(cnf_transformation,[],[f103]) ).
fof(f160,plain,
! [X0] :
( element(sK14(X0),b)
| ~ element(X0,e) ),
inference(cnf_transformation,[],[f103]) ).
fof(f161,plain,
! [X0] :
( apply(g,subtract(b,sK13(X0),sK14(X0))) = X0
| ~ element(X0,e) ),
inference(cnf_transformation,[],[f103]) ).
fof(f162,plain,
~ surjection(g),
inference(cnf_transformation,[],[f51]) ).
cnf(c_50,plain,
( ~ morphism(X0,X1,X2)
| ~ element(X3,X1)
| element(apply(X0,X3),X2) ),
inference(cnf_transformation,[],[f104]) ).
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,[],[f106]) ).
cnf(c_55,plain,
( ~ morphism(X0,X1,X2)
| element(sK0(X0,X1),X1)
| injection(X0) ),
inference(cnf_transformation,[],[f107]) ).
cnf(c_56,plain,
( ~ morphism(X0,X1,X2)
| ~ element(X3,X2)
| ~ surjection(X0)
| apply(X0,sK2(X0,X1,X3)) = X3 ),
inference(cnf_transformation,[],[f112]) ).
cnf(c_57,plain,
( ~ morphism(X0,X1,X2)
| ~ element(X3,X2)
| ~ surjection(X0)
| element(sK2(X0,X1,X3),X1) ),
inference(cnf_transformation,[],[f111]) ).
cnf(c_58,plain,
( sK3(X0,X1,X2) != apply(X0,X3)
| ~ morphism(X0,X1,X2)
| ~ element(X3,X1)
| surjection(X0) ),
inference(cnf_transformation,[],[f114]) ).
cnf(c_59,plain,
( ~ morphism(X0,X1,X2)
| element(sK3(X0,X1,X2),X2)
| surjection(X0) ),
inference(cnf_transformation,[],[f113]) ).
cnf(c_72,plain,
( ~ element(X0,X1)
| ~ element(X2,X1)
| element(subtract(X1,X0,X2),X1) ),
inference(cnf_transformation,[],[f127]) ).
cnf(c_79,plain,
morphism(delta,e,r),
inference(cnf_transformation,[],[f134]) ).
cnf(c_81,plain,
morphism(g,b,e),
inference(cnf_transformation,[],[f136]) ).
cnf(c_86,plain,
surjection(delta),
inference(cnf_transformation,[],[f141]) ).
cnf(c_96,plain,
( ~ element(X0,e)
| apply(delta,X0) = sK8(X0) ),
inference(cnf_transformation,[],[f149]) ).
cnf(c_104,plain,
( ~ element(X0,e)
| apply(g,subtract(b,sK13(X0),sK14(X0))) = X0 ),
inference(cnf_transformation,[],[f161]) ).
cnf(c_105,plain,
( ~ element(X0,e)
| element(sK14(X0),b) ),
inference(cnf_transformation,[],[f160]) ).
cnf(c_106,plain,
( ~ element(X0,e)
| element(sK13(X0),b) ),
inference(cnf_transformation,[],[f159]) ).
cnf(c_107,negated_conjecture,
~ surjection(g),
inference(cnf_transformation,[],[f162]) ).
cnf(c_4655,plain,
( ~ element(X0,r)
| ~ surjection(delta)
| apply(delta,sK2(delta,e,X0)) = X0 ),
inference(superposition,[status(thm)],[c_79,c_56]) ).
cnf(c_4656,plain,
( ~ element(X0,r)
| apply(delta,sK2(delta,e,X0)) = X0 ),
inference(forward_subsumption_resolution,[status(thm)],[c_4655,c_86]) ).
cnf(c_4706,plain,
( ~ element(X0,r)
| ~ surjection(delta)
| element(sK2(delta,e,X0),e) ),
inference(superposition,[status(thm)],[c_79,c_57]) ).
cnf(c_4716,plain,
( ~ element(X0,r)
| element(sK2(delta,e,X0),e) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4706,c_86]) ).
cnf(c_4778,plain,
( element(sK0(delta,e),e)
| injection(delta) ),
inference(superposition,[status(thm)],[c_79,c_55]) ).
cnf(c_4823,plain,
( apply(delta,sK0(delta,e)) = sK8(sK0(delta,e))
| injection(delta) ),
inference(superposition,[status(thm)],[c_4778,c_96]) ).
cnf(c_4942,plain,
( ~ morphism(X0,X1,e)
| apply(delta,sK3(X0,X1,e)) = sK8(sK3(X0,X1,e))
| surjection(X0) ),
inference(superposition,[status(thm)],[c_59,c_96]) ).
cnf(c_4960,plain,
( ~ element(X0,e)
| element(apply(delta,X0),r) ),
inference(superposition,[status(thm)],[c_79,c_50]) ).
cnf(c_5030,plain,
( ~ morphism(g,b,e)
| element(sK3(g,b,e),e)
| surjection(g) ),
inference(instantiation,[status(thm)],[c_59]) ).
cnf(c_5308,plain,
( apply(delta,sK3(g,b,e)) = sK8(sK3(g,b,e))
| surjection(g) ),
inference(superposition,[status(thm)],[c_81,c_4942]) ).
cnf(c_5309,plain,
apply(delta,sK3(g,b,e)) = sK8(sK3(g,b,e)),
inference(forward_subsumption_resolution,[status(thm)],[c_5308,c_107]) ).
cnf(c_5472,plain,
( ~ element(sK3(g,b,e),e)
| element(sK8(sK3(g,b,e)),r) ),
inference(superposition,[status(thm)],[c_5309,c_4960]) ).
cnf(c_5475,plain,
element(sK8(sK3(g,b,e)),r),
inference(global_subsumption_just,[status(thm)],[c_5472,c_107,c_81,c_5030,c_5472]) ).
cnf(c_5864,plain,
( sK8(sK3(g,b,e)) != apply(delta,X0)
| ~ element(sK3(g,b,e),X1)
| ~ morphism(delta,X1,X2)
| ~ element(X0,X1)
| ~ injection(delta)
| sK3(g,b,e) = X0 ),
inference(superposition,[status(thm)],[c_5309,c_51]) ).
cnf(c_6106,plain,
( ~ element(sK3(g,b,e),e)
| element(sK13(sK3(g,b,e)),b) ),
inference(instantiation,[status(thm)],[c_106]) ).
cnf(c_6107,plain,
( ~ element(sK3(g,b,e),e)
| element(sK14(sK3(g,b,e)),b) ),
inference(instantiation,[status(thm)],[c_105]) ).
cnf(c_7049,plain,
apply(delta,sK2(delta,e,sK8(sK3(g,b,e)))) = sK8(sK3(g,b,e)),
inference(superposition,[status(thm)],[c_5475,c_4656]) ).
cnf(c_7148,plain,
( ~ element(sK2(delta,e,sK8(sK3(g,b,e))),X0)
| ~ element(sK3(g,b,e),X0)
| ~ morphism(delta,X0,X1)
| ~ injection(delta)
| sK2(delta,e,sK8(sK3(g,b,e))) = sK3(g,b,e) ),
inference(superposition,[status(thm)],[c_7049,c_5864]) ).
cnf(c_7180,plain,
( ~ element(sK8(sK3(g,b,e)),r)
| ~ element(sK3(g,b,e),e)
| ~ morphism(delta,e,X0)
| ~ injection(delta)
| sK2(delta,e,sK8(sK3(g,b,e))) = sK3(g,b,e) ),
inference(superposition,[status(thm)],[c_4716,c_7148]) ).
cnf(c_7181,plain,
( ~ element(sK3(g,b,e),e)
| ~ morphism(delta,e,X0)
| ~ injection(delta)
| sK2(delta,e,sK8(sK3(g,b,e))) = sK3(g,b,e) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7180,c_5475]) ).
cnf(c_7192,plain,
( ~ morphism(delta,e,X0)
| ~ injection(delta)
| sK2(delta,e,sK8(sK3(g,b,e))) = sK3(g,b,e) ),
inference(global_subsumption_just,[status(thm)],[c_7181,c_107,c_81,c_5030,c_7181]) ).
cnf(c_7201,plain,
( ~ injection(delta)
| sK2(delta,e,sK8(sK3(g,b,e))) = sK3(g,b,e) ),
inference(superposition,[status(thm)],[c_79,c_7192]) ).
cnf(c_8416,plain,
( sK2(delta,e,sK8(sK3(g,b,e))) = sK3(g,b,e)
| apply(delta,sK0(delta,e)) = sK8(sK0(delta,e)) ),
inference(superposition,[status(thm)],[c_4823,c_7201]) ).
cnf(c_8998,plain,
( ~ element(sK8(sK3(g,b,e)),r)
| apply(delta,sK0(delta,e)) = sK8(sK0(delta,e))
| element(sK3(g,b,e),e) ),
inference(superposition,[status(thm)],[c_8416,c_4716]) ).
cnf(c_9000,plain,
( apply(delta,sK0(delta,e)) = sK8(sK0(delta,e))
| element(sK3(g,b,e),e) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8998,c_5475]) ).
cnf(c_9255,plain,
element(sK3(g,b,e),e),
inference(global_subsumption_just,[status(thm)],[c_9000,c_107,c_81,c_5030]) ).
cnf(c_9268,plain,
apply(g,subtract(b,sK13(sK3(g,b,e)),sK14(sK3(g,b,e)))) = sK3(g,b,e),
inference(superposition,[status(thm)],[c_9255,c_104]) ).
cnf(c_10675,plain,
( sK3(g,X0,X1) != sK3(g,b,e)
| ~ element(subtract(b,sK13(sK3(g,b,e)),sK14(sK3(g,b,e))),X0)
| ~ morphism(g,X0,X1)
| surjection(g) ),
inference(superposition,[status(thm)],[c_9268,c_58]) ).
cnf(c_10681,plain,
( sK3(g,X0,X1) != sK3(g,b,e)
| ~ element(subtract(b,sK13(sK3(g,b,e)),sK14(sK3(g,b,e))),X0)
| ~ morphism(g,X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_10675,c_107]) ).
cnf(c_11176,plain,
( ~ element(subtract(b,sK13(sK3(g,b,e)),sK14(sK3(g,b,e))),b)
| ~ morphism(g,b,e) ),
inference(equality_resolution,[status(thm)],[c_10681]) ).
cnf(c_11177,plain,
~ element(subtract(b,sK13(sK3(g,b,e)),sK14(sK3(g,b,e))),b),
inference(forward_subsumption_resolution,[status(thm)],[c_11176,c_81]) ).
cnf(c_11180,plain,
( ~ element(sK13(sK3(g,b,e)),b)
| ~ element(sK14(sK3(g,b,e)),b) ),
inference(superposition,[status(thm)],[c_72,c_11177]) ).
cnf(c_11183,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_11180,c_6106,c_6107,c_5030,c_81,c_107]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : HAL003+3 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.14 % Command : run_iprover %s %d THM
% 0.13/0.35 % Computer : n001.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Aug 28 03:07:49 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.19/0.47 Running first-order theorem proving
% 0.19/0.47 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.78/1.16 % SZS status Started for theBenchmark.p
% 3.78/1.16 % SZS status Theorem for theBenchmark.p
% 3.78/1.16
% 3.78/1.16 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 3.78/1.16
% 3.78/1.16 ------ iProver source info
% 3.78/1.16
% 3.78/1.16 git: date: 2023-05-31 18:12:56 +0000
% 3.78/1.16 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 3.78/1.16 git: non_committed_changes: false
% 3.78/1.16 git: last_make_outside_of_git: false
% 3.78/1.16
% 3.78/1.16 ------ Parsing...
% 3.78/1.16 ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.78/1.16
% 3.78/1.16 ------ 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
% 3.78/1.16
% 3.78/1.16 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.78/1.16
% 3.78/1.16 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.78/1.16 ------ Proving...
% 3.78/1.16 ------ Problem Properties
% 3.78/1.16
% 3.78/1.16
% 3.78/1.16 clauses 58
% 3.78/1.16 conjectures 1
% 3.78/1.16 EPR 18
% 3.78/1.16 Horn 49
% 3.78/1.16 unary 18
% 3.78/1.16 binary 16
% 3.78/1.16 lits 159
% 3.78/1.16 lits eq 29
% 3.78/1.16 fd_pure 0
% 3.78/1.16 fd_pseudo 0
% 3.78/1.16 fd_cond 0
% 3.78/1.16 fd_pseudo_cond 1
% 3.78/1.16 AC symbols 0
% 3.78/1.16
% 3.78/1.16 ------ Schedule dynamic 5 is on
% 3.78/1.16
% 3.78/1.16 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.78/1.16
% 3.78/1.16
% 3.78/1.16 ------
% 3.78/1.16 Current options:
% 3.78/1.16 ------
% 3.78/1.16
% 3.78/1.16
% 3.78/1.16
% 3.78/1.16
% 3.78/1.16 ------ Proving...
% 3.78/1.16
% 3.78/1.16
% 3.78/1.16 % SZS status Theorem for theBenchmark.p
% 3.78/1.16
% 3.78/1.16 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.78/1.16
% 3.78/1.17
%------------------------------------------------------------------------------