%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : HAL003+3 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:36:53 PM UTC 2026
% Result : Theorem 6.43s 1.89s
% Output : CNFRefutation 6.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 12
% Syntax : Number of formulae : 100 ( 21 unt; 0 def)
% Number of atoms : 305 ( 69 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 347 ( 142 ~; 146 |; 46 &)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% 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 : 191 ( 0 sgn 173 !; 18 ?; 54 :)
% 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/Axioms/HAL001+0.ax',morphism) ).
fof(f2,axiom,
! [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 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HAL001+0.ax',injection_properties) ).
fof(f3,axiom,
! [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) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HAL001+0.ax',properties_for_injection) ).
fof(f4,axiom,
! [X0,X1,X2] :
( ( morphism(X0,X1,X2)
& surjection(X0) )
=> ! [X3] :
( element(X3,X2)
=> ? [X4] :
( apply(X0,X4) = X3
& element(X4,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HAL001+0.ax',surjection_properties) ).
fof(f5,axiom,
! [X0,X1,X2] :
( ( ! [X3] :
( element(X3,X2)
=> ? [X4] :
( apply(X0,X4) = X3
& element(X4,X1) ) )
& morphism(X0,X1,X2) )
=> surjection(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HAL001+0.ax',properties_for_surjection) ).
fof(f10,axiom,
! [X0,X1,X2] :
( ( element(X2,X0)
& element(X1,X0) )
=> element(subtract(X0,X1,X2),X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HAL001+0.ax',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,
! [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) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma3) ).
fof(f33,axiom,
! [X0] :
( element(X0,e)
=> ? [X1,X2] :
( apply(g,subtract(b,X1,X2)) = X0
& element(X2,b)
& element(X1,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,[status(cth)],[f34]) ).
fof(f36,plain,
~ surjection(g),
inference(flattening,[],[f35]) ).
fof(f37,plain,
! [X0,X1,X2] :
( ? [X3] :
( element(X3,X2)
& ! [X4] :
( apply(X0,X4) != X3
| ~ element(X4,X1) ) )
| ~ morphism(X0,X1,X2)
| surjection(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f38,plain,
! [X0,X1,X2] :
( ? [X3] :
( element(X3,X2)
& ! [X4] :
( apply(X0,X4) != X3
| ~ element(X4,X1) ) )
| ~ morphism(X0,X1,X2)
| surjection(X0) ),
inference(flattening,[],[f37]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ~ morphism(X0,X1,X2)
| ~ surjection(X0)
| ! [X3] :
( ~ element(X3,X2)
| ? [X4] :
( apply(X0,X4) = X3
& element(X4,X1) ) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f40,plain,
! [X0,X1,X2] :
( ~ morphism(X0,X1,X2)
| ~ surjection(X0)
| ! [X3] :
( ~ element(X3,X2)
| ? [X4] :
( apply(X0,X4) = X3
& element(X4,X1) ) ) ),
inference(flattening,[],[f39]) ).
fof(f42,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(ennf_transformation,[],[f31]) ).
fof(f43,plain,
! [X0] :
( ~ element(X0,e)
| ? [X1,X2] :
( apply(g,subtract(b,X1,X2)) = X0
& element(X2,b)
& element(X1,b) ) ),
inference(ennf_transformation,[],[f33]) ).
fof(f49,plain,
! [X0,X1,X2] :
( ~ element(X2,X0)
| ~ element(X1,X0)
| element(subtract(X0,X1,X2),X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f50,plain,
! [X0,X1,X2] :
( ~ element(X2,X0)
| ~ element(X1,X0)
| element(subtract(X0,X1,X2),X0) ),
inference(flattening,[],[f49]) ).
fof(f59,plain,
! [X0,X1,X2] :
( ~ morphism(X0,X1,X2)
| ( apply(X0,zero(X1)) = zero(X2)
& ! [X3] :
( ~ element(X3,X1)
| element(apply(X0,X3),X2) ) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f60,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(ennf_transformation,[],[f3]) ).
fof(f61,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(flattening,[],[f60]) ).
fof(f62,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(ennf_transformation,[],[f2]) ).
fof(f63,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(flattening,[],[f62]) ).
fof(f64,plain,
! [X0,X1,X2] :
( ( element(sK0(X0,X1,X2),X2)
& ! [X4] :
( apply(X0,X4) != sK0(X0,X1,X2)
| ~ element(X4,X1) ) )
| ~ morphism(X0,X1,X2)
| surjection(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1,X2))],[f38]) ).
fof(f65,plain,
! [X0,X1,X2] :
( ~ morphism(X0,X1,X2)
| ~ surjection(X0)
| ! [X3] :
( ~ element(X3,X2)
| ( apply(X0,sK1(X0,X1,X3)) = X3
& element(sK1(X0,X1,X3),X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X4,sK1(X0,X1,X3))],[f40]) ).
fof(f67,plain,
! [X0] :
( ~ element(X0,e)
| ( sK5(X0) = apply(delta,apply(g,sK6(X0)))
& sK5(X0) = apply(h,apply(beta,sK6(X0)))
& element(sK6(X0),b)
& apply(delta,X0) = sK5(X0)
& element(sK5(X0),r) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6]),skolemize(X1,sK5(X0)),skolemize(X2,sK6(X0))],[f42]) ).
fof(f68,plain,
! [X0] :
( ~ element(X0,e)
| ( apply(g,subtract(b,sK7(X0),sK8(X0))) = X0
& element(sK8(X0),b)
& element(sK7(X0),b) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8]),skolemize(X1,sK7(X0)),skolemize(X2,sK8(X0))],[f43]) ).
fof(f78,plain,
! [X0,X1,X2] :
( ( apply(X0,sK13(X0,X1)) = apply(X0,sK14(X0,X1))
& element(sK14(X0,X1),X1)
& element(sK13(X0,X1),X1)
& sK13(X0,X1) != sK14(X0,X1) )
| ~ morphism(X0,X1,X2)
| injection(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14]),skolemize(X3,sK13(X0,X1)),skolemize(X4,sK14(X0,X1))],[f61]) ).
fof(f81,plain,
~ surjection(g),
inference(cnf_transformation,[],[f36]) ).
fof(f82,plain,
surjection(delta),
inference(cnf_transformation,[],[f24]) ).
fof(f84,plain,
! [X2,X0,X1] :
( element(sK0(X0,X1,X2),X2)
| ~ morphism(X0,X1,X2)
| surjection(X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f85,plain,
! [X2,X0,X1,X4] :
( apply(X0,X4) != sK0(X0,X1,X2)
| ~ element(X4,X1)
| ~ morphism(X0,X1,X2)
| surjection(X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f86,plain,
! [X2,X3,X0,X1] :
( ~ morphism(X0,X1,X2)
| ~ surjection(X0)
| ~ element(X3,X2)
| apply(X0,sK1(X0,X1,X3)) = X3 ),
inference(cnf_transformation,[],[f65]) ).
fof(f87,plain,
! [X2,X3,X0,X1] :
( ~ morphism(X0,X1,X2)
| ~ surjection(X0)
| ~ element(X3,X2)
| element(sK1(X0,X1,X3),X1) ),
inference(cnf_transformation,[],[f65]) ).
fof(f98,plain,
! [X0] :
( ~ element(X0,e)
| apply(delta,X0) = sK5(X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f99,plain,
! [X0] :
( ~ element(X0,e)
| element(sK5(X0),r) ),
inference(cnf_transformation,[],[f67]) ).
fof(f101,plain,
! [X0] :
( ~ element(X0,e)
| apply(g,subtract(b,sK7(X0),sK8(X0))) = X0 ),
inference(cnf_transformation,[],[f68]) ).
fof(f102,plain,
! [X0] :
( ~ element(X0,e)
| element(sK8(X0),b) ),
inference(cnf_transformation,[],[f68]) ).
fof(f103,plain,
! [X0] :
( ~ element(X0,e)
| element(sK7(X0),b) ),
inference(cnf_transformation,[],[f68]) ).
fof(f104,plain,
morphism(g,b,e),
inference(cnf_transformation,[],[f19]) ).
fof(f109,plain,
! [X2,X0,X1] :
( ~ element(X2,X0)
| ~ element(X1,X0)
| element(subtract(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f50]) ).
fof(f118,plain,
morphism(delta,e,r),
inference(cnf_transformation,[],[f17]) ).
fof(f129,plain,
! [X2,X3,X0,X1] :
( ~ morphism(X0,X1,X2)
| ~ element(X3,X1)
| element(apply(X0,X3),X2) ),
inference(cnf_transformation,[],[f59]) ).
fof(f131,plain,
! [X2,X0,X1] :
( element(sK14(X0,X1),X1)
| ~ morphism(X0,X1,X2)
| injection(X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f134,plain,
! [X2,X3,X0,X1,X4] :
( ~ morphism(X0,X1,X2)
| ~ injection(X0)
| apply(X0,X3) != apply(X0,X4)
| ~ element(X4,X1)
| ~ element(X3,X1)
| X3 = X4 ),
inference(cnf_transformation,[],[f63]) ).
tcf(c_51,negated_conjecture,
~ surjection(g),
inference(cnf_transformation,[],[f81]) ).
tcf(c_52,plain,
surjection(delta),
inference(cnf_transformation,[],[f82]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( surjection(X0)
| ~ element(X3,X1)
| ~ morphism(X0,X1,X2)
| ( sK0(X0,X1,X2) != apply(X0,X3) ) ),
inference(cnf_transformation,[],[f85]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( surjection(X0)
| element(sK0(X0,X1,X2),X2)
| ~ morphism(X0,X1,X2) ),
inference(cnf_transformation,[],[f84]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(sK1(X0,X1,X3),X1)
| ~ surjection(X0)
| ~ element(X3,X2)
| ~ morphism(X0,X1,X2) ),
inference(cnf_transformation,[],[f87]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( apply(X0,sK1(X0,X1,X3)) = X3 )
| ~ surjection(X0)
| ~ element(X3,X2)
| ~ morphism(X0,X1,X2) ),
inference(cnf_transformation,[],[f86]) ).
tcf(c_65,plain,
! [X0: $i] :
( element(sK5(X0),r)
| ~ element(X0,e) ),
inference(cnf_transformation,[],[f99]) ).
tcf(c_66,plain,
! [X0: $i] :
( ( apply(delta,X0) = sK5(X0) )
| ~ element(X0,e) ),
inference(cnf_transformation,[],[f98]) ).
tcf(c_71,plain,
! [X0: $i] :
( element(sK7(X0),b)
| ~ element(X0,e) ),
inference(cnf_transformation,[],[f103]) ).
tcf(c_72,plain,
! [X0: $i] :
( element(sK8(X0),b)
| ~ element(X0,e) ),
inference(cnf_transformation,[],[f102]) ).
tcf(c_73,plain,
! [X0: $i] :
( ( apply(g,subtract(b,sK7(X0),sK8(X0))) = X0 )
| ~ element(X0,e) ),
inference(cnf_transformation,[],[f101]) ).
tcf(c_74,plain,
morphism(g,b,e),
inference(cnf_transformation,[],[f104]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(subtract(X1,X0,X2),X1)
| ~ element(X2,X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f109]) ).
tcf(c_88,plain,
morphism(delta,e,r),
inference(cnf_transformation,[],[f118]) ).
tcf(c_98,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( element(apply(X0,X3),X2)
| ~ element(X3,X1)
| ~ morphism(X0,X1,X2) ),
inference(cnf_transformation,[],[f129]) ).
tcf(c_102,plain,
! [X0: $i,X1: $i,X2: $i] :
( injection(X0)
| element(sK14(X0,X1),X1)
| ~ morphism(X0,X1,X2) ),
inference(cnf_transformation,[],[f131]) ).
tcf(c_104,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X1 = X2 )
| ~ injection(X0)
| ~ element(X2,X3)
| ~ element(X1,X3)
| ~ morphism(X0,X3,X4)
| ( apply(X0,X1) != apply(X0,X2) ) ),
inference(cnf_transformation,[],[f134]) ).
tcf(c_4542,plain,
! [X0: $i,X1: $i] :
( surjection(X0)
| ( apply(delta,sK0(X0,X1,e)) = sK5(sK0(X0,X1,e)) )
| ~ morphism(X0,X1,e) ),
inference(superposition,[status(thm)],[c_55,c_66]) ).
tcf(c_4621,plain,
( injection(delta)
| element(sK14(delta,e),e) ),
inference(superposition,[status(thm)],[c_88,c_102]) ).
tcf(c_4697,plain,
( injection(delta)
| ( apply(delta,sK14(delta,e)) = sK5(sK14(delta,e)) ) ),
inference(superposition,[status(thm)],[c_4621,c_66]) ).
tcf(c_4873,plain,
( surjection(g)
| element(sK0(g,b,e),e)
| ~ morphism(g,b,e) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_4888,plain,
! [X0: $i] :
( element(apply(delta,X0),r)
| ~ element(X0,e) ),
inference(superposition,[status(thm)],[c_88,c_98]) ).
tcf(c_4984,plain,
! [X0: $i] :
( element(sK1(delta,e,X0),e)
| ~ surjection(delta)
| ~ element(X0,r) ),
inference(superposition,[status(thm)],[c_88,c_56]) ).
tcf(c_4993,plain,
! [X0: $i] :
( element(sK1(delta,e,X0),e)
| ~ element(X0,r) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4984,c_52]) ).
tcf(c_5407,plain,
! [X0: $i] :
( ( apply(delta,sK1(delta,e,X0)) = X0 )
| ~ surjection(delta)
| ~ element(X0,r) ),
inference(superposition,[status(thm)],[c_88,c_57]) ).
tcf(c_5416,plain,
! [X0: $i] :
( ( apply(delta,sK1(delta,e,X0)) = X0 )
| ~ element(X0,r) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5407,c_52]) ).
tcf(c_5945,plain,
( element(sK8(sK0(g,b,e)),b)
| ~ element(sK0(g,b,e),e) ),
inference(instantiation,[status(thm)],[c_72]) ).
tcf(c_5946,plain,
( element(sK7(sK0(g,b,e)),b)
| ~ element(sK0(g,b,e),e) ),
inference(instantiation,[status(thm)],[c_71]) ).
tcf(c_5948,plain,
( element(sK5(sK0(g,b,e)),r)
| ~ element(sK0(g,b,e),e) ),
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_6355,plain,
( surjection(g)
| ( apply(delta,sK0(g,b,e)) = sK5(sK0(g,b,e)) ) ),
inference(superposition,[status(thm)],[c_74,c_4542]) ).
tcf(c_6359,plain,
apply(delta,sK0(g,b,e)) = sK5(sK0(g,b,e)),
inference(forward_subsumption_resolution,[status(thm)],[c_6355,c_51]) ).
tcf(c_6781,plain,
( element(sK5(sK0(g,b,e)),r)
| ~ element(sK0(g,b,e),e) ),
inference(superposition,[status(thm)],[c_6359,c_4888]) ).
tcf(c_6783,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK0(g,b,e) = X0 )
| ~ injection(delta)
| ~ element(X0,X1)
| ~ morphism(delta,X1,X2)
| ~ element(sK0(g,b,e),X1)
| ( sK5(sK0(g,b,e)) != apply(delta,X0) ) ),
inference(superposition,[status(thm)],[c_6359,c_104]) ).
tcf(c_7049,plain,
element(sK5(sK0(g,b,e)),r),
inference(global_subsumption_just,[status(thm)],[c_6781,c_51,c_74,c_4873,c_5948]) ).
tcf(c_7054,plain,
apply(delta,sK1(delta,e,sK5(sK0(g,b,e)))) = sK5(sK0(g,b,e)),
inference(superposition,[status(thm)],[c_7049,c_5416]) ).
tcf(c_7141,plain,
! [X0: $i,X1: $i] :
( ( sK1(delta,e,sK5(sK0(g,b,e))) = sK0(g,b,e) )
| ~ injection(delta)
| ~ morphism(delta,X0,X1)
| ~ element(sK0(g,b,e),X0)
| ~ element(sK1(delta,e,sK5(sK0(g,b,e))),X0) ),
inference(superposition,[status(thm)],[c_7054,c_6783]) ).
tcf(c_7894,plain,
! [X0: $i] :
( ( sK1(delta,e,sK5(sK0(g,b,e))) = sK0(g,b,e) )
| ~ injection(delta)
| ~ morphism(delta,e,X0)
| ~ element(sK0(g,b,e),e)
| ~ element(sK5(sK0(g,b,e)),r) ),
inference(superposition,[status(thm)],[c_4993,c_7141]) ).
tcf(c_7895,plain,
! [X0: $i] :
( ( sK1(delta,e,sK5(sK0(g,b,e))) = sK0(g,b,e) )
| ~ injection(delta)
| ~ morphism(delta,e,X0)
| ~ element(sK0(g,b,e),e) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7894,c_7049]) ).
tcf(c_7901,plain,
! [X0: $i] :
( ( sK1(delta,e,sK5(sK0(g,b,e))) = sK0(g,b,e) )
| ~ injection(delta)
| ~ morphism(delta,e,X0) ),
inference(global_subsumption_just,[status(thm)],[c_7895,c_51,c_74,c_4873,c_7895]) ).
tcf(c_7910,plain,
( ( sK1(delta,e,sK5(sK0(g,b,e))) = sK0(g,b,e) )
| ~ injection(delta) ),
inference(superposition,[status(thm)],[c_88,c_7901]) ).
tcf(c_8000,plain,
( ( apply(delta,sK14(delta,e)) = sK5(sK14(delta,e)) )
| ( sK1(delta,e,sK5(sK0(g,b,e))) = sK0(g,b,e) ) ),
inference(superposition,[status(thm)],[c_4697,c_7910]) ).
tcf(c_8010,plain,
( element(sK0(g,b,e),e)
| ( apply(delta,sK14(delta,e)) = sK5(sK14(delta,e)) )
| ~ element(sK5(sK0(g,b,e)),r) ),
inference(superposition,[status(thm)],[c_8000,c_4993]) ).
tcf(c_8012,plain,
( element(sK0(g,b,e),e)
| ( apply(delta,sK14(delta,e)) = sK5(sK14(delta,e)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8010,c_7049]) ).
tcf(c_8180,plain,
element(sK0(g,b,e),e),
inference(global_subsumption_just,[status(thm)],[c_8012,c_51,c_74,c_4873]) ).
tcf(c_8189,plain,
apply(g,subtract(b,sK7(sK0(g,b,e)),sK8(sK0(g,b,e)))) = sK0(g,b,e),
inference(superposition,[status(thm)],[c_8180,c_73]) ).
tcf(c_8874,plain,
! [X0: $i,X1: $i] :
( surjection(g)
| ~ morphism(g,X0,X1)
| ~ element(subtract(b,sK7(sK0(g,b,e)),sK8(sK0(g,b,e))),X0)
| ( sK0(g,X0,X1) != sK0(g,b,e) ) ),
inference(superposition,[status(thm)],[c_8189,c_54]) ).
tcf(c_8880,plain,
! [X0: $i,X1: $i] :
( ~ morphism(g,X0,X1)
| ~ element(subtract(b,sK7(sK0(g,b,e)),sK8(sK0(g,b,e))),X0)
| ( sK0(g,X0,X1) != sK0(g,b,e) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8874,c_51]) ).
tcf(c_8936,plain,
( ~ morphism(g,b,e)
| ~ element(subtract(b,sK7(sK0(g,b,e)),sK8(sK0(g,b,e))),b) ),
inference(equality_resolution,[status(thm)],[c_8880]) ).
tcf(c_8937,plain,
~ element(subtract(b,sK7(sK0(g,b,e)),sK8(sK0(g,b,e))),b),
inference(forward_subsumption_resolution,[status(thm)],[c_8936,c_74]) ).
tcf(c_8938,plain,
( ~ element(sK8(sK0(g,b,e)),b)
| ~ element(sK7(sK0(g,b,e)),b) ),
inference(superposition,[status(thm)],[c_79,c_8937]) ).
tcf(c_8941,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_8938,c_5945,c_5946,c_4873,c_74,c_51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HAL003+3 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.38 % Computer : n010.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Wed Sep 23 16:07:57 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.42 Running first-order theorem proving
% 0.13/0.42 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.44
% 0.13/0.44 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.44
% 0.13/0.44 % Detected problem language: tptp
% 0.13/0.46 % Proving...
% 6.43/1.89 % SZS status Started for theBenchmark.p
% 6.43/1.89 % SZS status Theorem for theBenchmark.p
% 6.43/1.89
% 6.43/1.89 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 6.43/1.89
% 6.43/1.89 % ------ iProver source info
% 6.43/1.89
% 6.43/1.89 % git: date: 2026-07-19 20:42:38 +0200
% 6.43/1.89 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 6.43/1.89 % git: non_committed_changes: false
% 6.43/1.89
% 6.43/1.89 % ------ Parsing...
% 6.43/1.89 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 6.43/1.89
% 6.43/1.89 % ------ 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 %
% 6.43/1.89
% 6.43/1.89 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 6.43/1.89
% 6.43/1.89 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 6.43/1.89 % ------ Proving...
% 6.43/1.89 % ------ Problem Properties
% 6.43/1.89
% 6.43/1.89 %
% 6.43/1.89 % clauses 57
% 6.43/1.89 % conjectures 1
% 6.43/1.89 % EPR 17
% 6.43/1.89 % Horn 48
% 6.43/1.89 % unary 17
% 6.43/1.89 % binary 16
% 6.43/1.89 % lits 158
% 6.43/1.89 % lits eq 29
% 6.43/1.89 % fd_pure 0
% 6.43/1.89 % fd_pseudo 0
% 6.43/1.89 % fd_cond 0
% 6.43/1.89 % fd_pseudo_cond 1
% 6.43/1.89 % AC symbols 0
% 6.43/1.89
% 6.43/1.89 % ------ Schedule dynamic 5 is on
% 6.43/1.89
% 6.43/1.89 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 6.43/1.89
% 6.43/1.89
% 6.43/1.89 % ------
% 6.43/1.89 % Current options:
% 6.43/1.89 % ------
% 6.43/1.89
% 6.43/1.89
% 6.43/1.89 %
% 6.43/1.89
% 6.43/1.89 % ------ Proving...
% 6.43/1.89 %
% 6.43/1.89
% 6.43/1.89 % SZS status Theorem for theBenchmark.p
% 6.43/1.89
% 6.43/1.89 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 6.43/1.89
% 6.43/1.89
%------------------------------------------------------------------------------