%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE029+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n020.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 01:52:13 PM UTC 2026
% Result : Theorem 2.95s 1.09s
% Output : CNFRefutation 2.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 7
% Syntax : Number of formulae : 102 ( 29 unt; 0 def)
% Number of atoms : 341 ( 24 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 389 ( 150 ~; 178 |; 51 &)
% ( 8 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 207 ( 0 sgn 195 !; 12 ?; 81 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
fof(f2,axiom,
! [X0,X1,X2] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_associativity) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
fof(f12,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',order) ).
fof(f13,axiom,
! [X0,X1,X2] :
( ismeet(X2,X0,X1)
<=> ( ! [X3] :
( ( leq(X3,X1)
& leq(X3,X0) )
=> leq(X3,X2) )
& leq(X2,X1)
& leq(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+3.ax',ismeet) ).
fof(f14,axiom,
! [X0,X1,X2] :
( ismeetu(X2,X0,X1)
<=> ! [X3] :
( ( leq(X3,X1)
& leq(X3,X0) )
<=> leq(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+3.ax',ismeetu) ).
fof(f15,conjecture,
! [X0,X1,X2] :
( ismeet(X0,X1,X2)
<=> ismeetu(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f16,negated_conjecture,
~ ! [X0,X1,X2] :
( ismeet(X0,X1,X2)
<=> ismeetu(X0,X1,X2) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
fof(f17,plain,
! [X0,X1,X2] :
( ismeet(X2,X0,X1)
<=> ( ! [X3] :
( ~ leq(X3,X1)
| ~ leq(X3,X0)
| leq(X3,X2) )
& leq(X2,X1)
& leq(X2,X0) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f18,plain,
! [X0,X1,X2] :
( ismeet(X2,X0,X1)
<=> ( ! [X3] :
( ~ leq(X3,X1)
| ~ leq(X3,X0)
| leq(X3,X2) )
& leq(X2,X1)
& leq(X2,X0) ) ),
inference(flattening,[],[f17]) ).
fof(f19,plain,
? [X0,X1,X2] :
( ismeet(X0,X1,X2)
<~> ismeetu(X0,X1,X2) ),
inference(ennf_transformation,[],[f16]) ).
fof(f20,plain,
! [X0,X1] :
( ( ~ leq(X0,X1)
| addition(X0,X1) = X1 )
& ( addition(X0,X1) != X1
| leq(X0,X1) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ( ~ ismeet(X2,X0,X1)
| ( ! [X3] :
( ~ leq(X3,X1)
| ~ leq(X3,X0)
| leq(X3,X2) )
& leq(X2,X1)
& leq(X2,X0) ) )
& ( ? [X3] :
( leq(X3,X1)
& leq(X3,X0)
& ~ leq(X3,X2) )
| ~ leq(X2,X1)
| ~ leq(X2,X0)
| ismeet(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f18]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ( ~ ismeet(X2,X0,X1)
| ( ! [X3] :
( ~ leq(X3,X1)
| ~ leq(X3,X0)
| leq(X3,X2) )
& leq(X2,X1)
& leq(X2,X0) ) )
& ( ? [X3] :
( leq(X3,X1)
& leq(X3,X0)
& ~ leq(X3,X2) )
| ~ leq(X2,X1)
| ~ leq(X2,X0)
| ismeet(X2,X0,X1) ) ),
inference(flattening,[],[f21]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ( ~ ismeet(X2,X0,X1)
| ( ! [X4] :
( ~ leq(X4,X1)
| ~ leq(X4,X0)
| leq(X4,X2) )
& leq(X2,X1)
& leq(X2,X0) ) )
& ( ? [X3] :
( leq(X3,X1)
& leq(X3,X0)
& ~ leq(X3,X2) )
| ~ leq(X2,X1)
| ~ leq(X2,X0)
| ismeet(X2,X0,X1) ) ),
inference(rectify,[],[f22]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ( ~ ismeet(X2,X0,X1)
| ( ! [X4] :
( ~ leq(X4,X1)
| ~ leq(X4,X0)
| leq(X4,X2) )
& leq(X2,X1)
& leq(X2,X0) ) )
& ( ( leq(sK0(X0,X1,X2),X1)
& leq(sK0(X0,X1,X2),X0)
& ~ leq(sK0(X0,X1,X2),X2) )
| ~ leq(X2,X1)
| ~ leq(X2,X0)
| ismeet(X2,X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1,X2))],[f23]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ( ~ ismeetu(X2,X0,X1)
| ! [X3] :
( ( ~ leq(X3,X1)
| ~ leq(X3,X0)
| leq(X3,X2) )
& ( ~ leq(X3,X2)
| ( leq(X3,X1)
& leq(X3,X0) ) ) ) )
& ( ? [X3] :
( ( ( leq(X3,X1)
& leq(X3,X0) )
| leq(X3,X2) )
& ( ~ leq(X3,X1)
| ~ leq(X3,X0)
| ~ leq(X3,X2) ) )
| ismeetu(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f26,plain,
! [X0,X1,X2] :
( ( ~ ismeetu(X2,X0,X1)
| ! [X3] :
( ( ~ leq(X3,X1)
| ~ leq(X3,X0)
| leq(X3,X2) )
& ( ~ leq(X3,X2)
| ( leq(X3,X1)
& leq(X3,X0) ) ) ) )
& ( ? [X3] :
( ( ( leq(X3,X1)
& leq(X3,X0) )
| leq(X3,X2) )
& ( ~ leq(X3,X1)
| ~ leq(X3,X0)
| ~ leq(X3,X2) ) )
| ismeetu(X2,X0,X1) ) ),
inference(flattening,[],[f25]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ( ~ ismeetu(X2,X0,X1)
| ! [X4] :
( ( ~ leq(X4,X1)
| ~ leq(X4,X0)
| leq(X4,X2) )
& ( ~ leq(X4,X2)
| ( leq(X4,X1)
& leq(X4,X0) ) ) ) )
& ( ? [X3] :
( ( ( leq(X3,X1)
& leq(X3,X0) )
| leq(X3,X2) )
& ( ~ leq(X3,X1)
| ~ leq(X3,X0)
| ~ leq(X3,X2) ) )
| ismeetu(X2,X0,X1) ) ),
inference(rectify,[],[f26]) ).
fof(f28,plain,
! [X0,X1,X2] :
( ( ~ ismeetu(X2,X0,X1)
| ! [X4] :
( ( ~ leq(X4,X1)
| ~ leq(X4,X0)
| leq(X4,X2) )
& ( ~ leq(X4,X2)
| ( leq(X4,X1)
& leq(X4,X0) ) ) ) )
& ( ( ( ( leq(sK1(X0,X1,X2),X1)
& leq(sK1(X0,X1,X2),X0) )
| leq(sK1(X0,X1,X2),X2) )
& ( ~ leq(sK1(X0,X1,X2),X1)
| ~ leq(sK1(X0,X1,X2),X0)
| ~ leq(sK1(X0,X1,X2),X2) ) )
| ismeetu(X2,X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1,X2))],[f27]) ).
fof(f29,plain,
? [X0,X1,X2] :
( ( ismeet(X0,X1,X2)
| ismeetu(X0,X1,X2) )
& ( ~ ismeet(X0,X1,X2)
| ~ ismeetu(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f19]) ).
fof(f30,plain,
( ( ismeet(sK2,sK3,sK4)
| ismeetu(sK2,sK3,sK4) )
& ( ~ ismeet(sK2,sK3,sK4)
| ~ ismeetu(sK2,sK3,sK4) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f29]) ).
fof(f31,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f32,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f34,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f42,plain,
! [X0,X1] :
( ~ leq(X0,X1)
| addition(X0,X1) = X1 ),
inference(cnf_transformation,[],[f20]) ).
fof(f43,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f44,plain,
! [X2,X0,X1,X4] :
( ~ ismeet(X2,X0,X1)
| ~ leq(X4,X1)
| ~ leq(X4,X0)
| leq(X4,X2) ),
inference(cnf_transformation,[],[f24]) ).
fof(f45,plain,
! [X2,X0,X1] :
( ~ ismeet(X2,X0,X1)
| leq(X2,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f46,plain,
! [X2,X0,X1] :
( ~ ismeet(X2,X0,X1)
| leq(X2,X0) ),
inference(cnf_transformation,[],[f24]) ).
fof(f47,plain,
! [X2,X0,X1] :
( leq(sK0(X0,X1,X2),X1)
| ~ leq(X2,X1)
| ~ leq(X2,X0)
| ismeet(X2,X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f48,plain,
! [X2,X0,X1] :
( leq(sK0(X0,X1,X2),X0)
| ~ leq(X2,X1)
| ~ leq(X2,X0)
| ismeet(X2,X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f49,plain,
! [X2,X0,X1] :
( ~ leq(sK0(X0,X1,X2),X2)
| ~ leq(X2,X1)
| ~ leq(X2,X0)
| ismeet(X2,X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f50,plain,
! [X2,X0,X1,X4] :
( ~ ismeetu(X2,X0,X1)
| ~ leq(X4,X1)
| ~ leq(X4,X0)
| leq(X4,X2) ),
inference(cnf_transformation,[],[f28]) ).
fof(f51,plain,
! [X2,X0,X1,X4] :
( ~ ismeetu(X2,X0,X1)
| ~ leq(X4,X2)
| leq(X4,X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f52,plain,
! [X2,X0,X1,X4] :
( ~ ismeetu(X2,X0,X1)
| ~ leq(X4,X2)
| leq(X4,X0) ),
inference(cnf_transformation,[],[f28]) ).
fof(f53,plain,
! [X2,X0,X1] :
( leq(sK1(X0,X1,X2),X1)
| leq(sK1(X0,X1,X2),X2)
| ismeetu(X2,X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f54,plain,
! [X2,X0,X1] :
( leq(sK1(X0,X1,X2),X0)
| leq(sK1(X0,X1,X2),X2)
| ismeetu(X2,X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f55,plain,
! [X2,X0,X1] :
( ~ leq(sK1(X0,X1,X2),X1)
| ~ leq(sK1(X0,X1,X2),X0)
| ~ leq(sK1(X0,X1,X2),X2)
| ismeetu(X2,X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f56,plain,
( ismeet(sK2,sK3,sK4)
| ismeetu(sK2,sK3,sK4) ),
inference(cnf_transformation,[],[f30]) ).
fof(f57,plain,
( ~ ismeet(sK2,sK3,sK4)
| ~ ismeetu(sK2,sK3,sK4) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f31]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] : addition(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f32]) ).
tcf(c_52,plain,
! [X0: $i] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f34]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( leq(X0,X1)
| ( addition(X0,X1) != X1 ) ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( ( addition(X0,X1) = X1 )
| ~ leq(X0,X1) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i] :
( ismeet(X2,X0,X1)
| ~ leq(X2,X1)
| ~ leq(X2,X0)
| ~ leq(sK0(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f49]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i] :
( ismeet(X0,X1,X2)
| leq(sK0(X1,X2,X0),X1)
| ~ leq(X0,X2)
| ~ leq(X0,X1) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i] :
( ismeet(X0,X1,X2)
| leq(sK0(X1,X2,X0),X2)
| ~ leq(X0,X2)
| ~ leq(X0,X1) ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i] :
( leq(X0,X1)
| ~ ismeet(X0,X1,X2) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i,X2: $i] :
( leq(X0,X2)
| ~ ismeet(X0,X1,X2) ),
inference(cnf_transformation,[],[f45]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( leq(X3,X0)
| ~ leq(X3,X2)
| ~ leq(X3,X1)
| ~ ismeet(X0,X1,X2) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i] :
( ismeetu(X2,X0,X1)
| ~ leq(sK1(X0,X1,X2),X2)
| ~ leq(sK1(X0,X1,X2),X1)
| ~ leq(sK1(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f55]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i] :
( ismeetu(X2,X0,X1)
| leq(sK1(X0,X1,X2),X2)
| leq(sK1(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i,X2: $i] :
( ismeetu(X2,X0,X1)
| leq(sK1(X0,X1,X2),X2)
| leq(sK1(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f53]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( leq(X3,X1)
| ~ leq(X3,X0)
| ~ ismeetu(X0,X1,X2) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( leq(X3,X2)
| ~ leq(X3,X0)
| ~ ismeetu(X0,X1,X2) ),
inference(cnf_transformation,[],[f51]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( leq(X3,X0)
| ~ leq(X3,X2)
| ~ leq(X3,X1)
| ~ ismeetu(X0,X1,X2) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_74,negated_conjecture,
( ~ ismeetu(sK2,sK3,sK4)
| ~ ismeet(sK2,sK3,sK4) ),
inference(cnf_transformation,[],[f57]) ).
tcf(c_75,negated_conjecture,
( ismeetu(sK2,sK3,sK4)
| ismeet(sK2,sK3,sK4) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_97,plain,
( ismeet(sK2,sK3,sK4)
| ismeetu(sK2,sK3,sK4) ),
inference(prop_impl_just,[status(thm)],[c_75]) ).
tcf(c_98,plain,
( ismeetu(sK2,sK3,sK4)
| ismeet(sK2,sK3,sK4) ),
inference(renaming,[status(thm)],[c_97]) ).
tcf(c_489,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( leq(X3,X0)
| ismeetu(sK2,sK3,sK4)
| ~ leq(X3,X2)
| ~ leq(X3,X1)
| ( X2 != sK4 )
| ( X1 != sK3 )
| ( X0 != sK2 ) ),
inference(resolution_lifted,[status(thm)],[c_67,c_98]) ).
tcf(c_490,plain,
! [X0: $i] :
( leq(X0,sK2)
| ismeetu(sK2,sK3,sK4)
| ~ leq(X0,sK4)
| ~ leq(X0,sK3) ),
inference(unflattening,[status(thm)],[c_489]) ).
tcf(c_500,plain,
! [X0: $i] :
( leq(X0,sK2)
| ~ leq(X0,sK4)
| ~ leq(X0,sK3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_490,c_73]) ).
tcf(c_836,negated_conjecture,
( ismeetu(sK2,sK3,sK4)
| ismeet(sK2,sK3,sK4) ),
inference(demodulation,[status(thm)],[c_75]) ).
tcf(c_837,negated_conjecture,
( ~ ismeetu(sK2,sK3,sK4)
| ~ ismeet(sK2,sK3,sK4) ),
inference(demodulation,[status(thm)],[c_74]) ).
tcf(c_1361,plain,
! [X0: $i] : leq(X0,X0),
inference(superposition,[status(thm)],[c_52,c_60]) ).
tcf(c_1395,plain,
! [X0: $i,X1: $i] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[c_52,c_50]) ).
tcf(c_1416,plain,
! [X0: $i,X1: $i] : leq(X0,addition(X0,X1)),
inference(superposition,[status(thm)],[c_1395,c_60]) ).
tcf(c_1427,plain,
! [X0: $i,X1: $i] : leq(X0,addition(X1,X0)),
inference(superposition,[status(thm)],[c_49,c_1416]) ).
tcf(c_1438,plain,
! [X0: $i,X1: $i,X2: $i] : leq(X0,addition(X1,addition(X2,X0))),
inference(superposition,[status(thm)],[c_50,c_1427]) ).
tcf(c_1496,plain,
! [X0: $i] :
( leq(X0,sK3)
| ismeet(sK2,sK3,sK4)
| ~ leq(X0,sK2) ),
inference(superposition,[status(thm)],[c_836,c_71]) ).
tcf(c_1506,plain,
! [X0: $i] :
( leq(X0,sK4)
| ismeet(sK2,sK3,sK4)
| ~ leq(X0,sK2) ),
inference(superposition,[status(thm)],[c_836,c_72]) ).
tcf(c_1691,plain,
! [X0: $i] :
( leq(sK2,sK3)
| leq(X0,sK3)
| ~ leq(X0,sK2) ),
inference(superposition,[status(thm)],[c_1496,c_65]) ).
tcf(c_1714,plain,
! [X0: $i] :
( leq(sK2,sK4)
| leq(X0,sK4)
| ~ leq(X0,sK2) ),
inference(superposition,[status(thm)],[c_1506,c_66]) ).
tcf(c_1753,plain,
leq(sK2,sK3),
inference(superposition,[status(thm)],[c_1361,c_1691]) ).
tcf(c_1761,plain,
leq(sK2,sK4),
inference(superposition,[status(thm)],[c_1361,c_1714]) ).
tcf(c_2004,plain,
! [X0: $i] :
( leq(X0,sK2)
| ismeet(sK2,sK3,sK4)
| ~ leq(X0,sK4)
| ~ leq(X0,sK3) ),
inference(superposition,[status(thm)],[c_836,c_73]) ).
tcf(c_2009,plain,
addition(sK2,sK3) = sK3,
inference(superposition,[status(thm)],[c_1753,c_61]) ).
tcf(c_2010,plain,
addition(sK2,sK4) = sK4,
inference(superposition,[status(thm)],[c_1761,c_61]) ).
tcf(c_2073,plain,
! [X0: $i] :
( leq(X0,sK2)
| ~ leq(X0,sK3)
| ~ leq(X0,sK4) ),
inference(global_subsumption_just,[status(thm)],[c_2004,c_500]) ).
tcf(c_2074,plain,
! [X0: $i] :
( leq(X0,sK2)
| ~ leq(X0,sK4)
| ~ leq(X0,sK3) ),
inference(renaming,[status(thm)],[c_2073]) ).
tcf(c_2083,plain,
! [X0: $i,X1: $i] :
( ismeetu(X1,sK3,X0)
| leq(sK1(sK3,X0,X1),sK2)
| leq(sK1(sK3,X0,X1),X1)
| ~ leq(sK1(sK3,X0,X1),sK4) ),
inference(superposition,[status(thm)],[c_69,c_2074]) ).
tcf(c_2185,plain,
! [X0: $i] :
( ismeetu(X0,sK3,sK4)
| leq(sK1(sK3,sK4,X0),sK2)
| leq(sK1(sK3,sK4,X0),X0) ),
inference(superposition,[status(thm)],[c_70,c_2083]) ).
tcf(c_2329,plain,
! [X0: $i,X1: $i] :
( ismeet(X1,sK3,X0)
| leq(sK0(sK3,X0,X1),sK2)
| ~ leq(X1,sK3)
| ~ leq(X1,X0)
| ~ leq(sK0(sK3,X0,X1),sK4) ),
inference(superposition,[status(thm)],[c_63,c_2074]) ).
tcf(c_2623,plain,
! [X0: $i] :
( ismeet(X0,sK3,sK4)
| leq(sK0(sK3,sK4,X0),sK2)
| ~ leq(X0,sK4)
| ~ leq(X0,sK3) ),
inference(superposition,[status(thm)],[c_64,c_2329]) ).
tcf(c_3087,plain,
( ismeetu(sK2,sK3,sK4)
| leq(sK1(sK3,sK4,sK2),sK2) ),
inference(equality_factoring,[status(thm)],[c_2185]) ).
tcf(c_3931,plain,
( ismeet(sK2,sK3,sK4)
| ~ leq(sK2,sK4)
| ~ leq(sK2,sK3) ),
inference(superposition,[status(thm)],[c_2623,c_62]) ).
tcf(c_3936,plain,
ismeet(sK2,sK3,sK4),
inference(forward_subsumption_resolution,[status(thm)],[c_3931,c_1761,c_1753]) ).
tcf(c_3942,plain,
~ ismeetu(sK2,sK3,sK4),
inference(backward_subsumption_resolution,[status(thm)],[c_837,c_3936]) ).
tcf(c_4915,plain,
leq(sK1(sK3,sK4,sK2),sK2),
inference(global_subsumption_just,[status(thm)],[c_3087,c_74,c_3087,c_3936]) ).
tcf(c_4917,plain,
addition(sK1(sK3,sK4,sK2),sK2) = sK2,
inference(superposition,[status(thm)],[c_4915,c_61]) ).
tcf(c_4918,plain,
( ismeetu(sK2,sK3,sK4)
| ~ leq(sK1(sK3,sK4,sK2),sK4)
| ~ leq(sK1(sK3,sK4,sK2),sK3) ),
inference(superposition,[status(thm)],[c_4915,c_68]) ).
tcf(c_4919,plain,
addition(sK2,sK1(sK3,sK4,sK2)) = sK2,
inference(theory_normalisation,[status(thm)],[c_4917,c_50,c_49]) ).
tcf(c_4920,plain,
( ~ leq(sK1(sK3,sK4,sK2),sK4)
| ~ leq(sK1(sK3,sK4,sK2),sK3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4918,c_3942]) ).
tcf(c_5435,plain,
! [X0: $i] : leq(sK1(sK3,sK4,sK2),addition(X0,sK2)),
inference(superposition,[status(thm)],[c_4919,c_1438]) ).
tcf(c_5562,plain,
! [X0: $i] : leq(sK1(sK3,sK4,sK2),addition(sK2,X0)),
inference(superposition,[status(thm)],[c_49,c_5435]) ).
tcf(c_5601,plain,
leq(sK1(sK3,sK4,sK2),sK3),
inference(superposition,[status(thm)],[c_2009,c_5562]) ).
tcf(c_5602,plain,
leq(sK1(sK3,sK4,sK2),sK4),
inference(superposition,[status(thm)],[c_2010,c_5562]) ).
tcf(c_5610,plain,
~ leq(sK1(sK3,sK4,sK2),sK4),
inference(backward_subsumption_resolution,[status(thm)],[c_4920,c_5601]) ).
tcf(c_5611,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_5610,c_5602]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE029+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n020.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Wed Sep 23 18:43:03 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 2.95/1.09 % SZS status Started for theBenchmark.p
% 2.95/1.09 % SZS status Theorem for theBenchmark.p
% 2.95/1.09
% 2.95/1.09 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.95/1.09
% 2.95/1.09 % ------ iProver source info
% 2.95/1.09
% 2.95/1.09 % git: date: 2026-07-19 20:42:38 +0200
% 2.95/1.09 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.95/1.09 % git: non_committed_changes: false
% 2.95/1.09
% 2.95/1.09 % ------ Parsing...
% 2.95/1.09 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.95/1.09
% 2.95/1.09 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 2.95/1.09
% 2.95/1.09 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.95/1.09
% 2.95/1.09 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.95/1.09 % ------ Proving...
% 2.95/1.09 % ------ Problem Properties
% 2.95/1.09
% 2.95/1.09 %
% 2.95/1.09 % clauses 27
% 2.95/1.09 % conjectures 2
% 2.95/1.09 % EPR 8
% 2.95/1.09 % Horn 22
% 2.95/1.09 % unary 11
% 2.95/1.09 % binary 6
% 2.95/1.09 % lits 59
% 2.95/1.09 % lits eq 13
% 2.95/1.09 % fd_pure 0
% 2.95/1.09 % fd_pseudo 0
% 2.95/1.09 % fd_cond 0
% 2.95/1.09 % fd_pseudo_cond 0
% 2.95/1.09 % AC symbols 1
% 2.95/1.09
% 2.95/1.09 % ------ Schedule dynamic 5 is on
% 2.95/1.09
% 2.95/1.09 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.95/1.09
% 2.95/1.09
% 2.95/1.09 % ------
% 2.95/1.09 % Current options:
% 2.95/1.09 % ------
% 2.95/1.09
% 2.95/1.09
% 2.95/1.09 %
% 2.95/1.09
% 2.95/1.09 % ------ Proving...
% 2.95/1.09 %
% 2.95/1.09
% 2.95/1.09 % SZS status Theorem for theBenchmark.p
% 2.95/1.09
% 2.95/1.09 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.95/1.09
% 2.95/1.09
%------------------------------------------------------------------------------