%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE002+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n016.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 01:52:05 PM UTC 2026
% Result : Theorem 2.20s 1.31s
% Output : CNFRefutation 2.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 33 ( 18 unt; 0 def)
% Number of atoms : 52 ( 29 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 41 ( 22 ~; 13 |; 3 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 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 : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 55 ( 0 sgn 52 !; 3 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_associativity) ).
fof(f9,axiom,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',left_distributivity) ).
fof(f12,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',order) ).
fof(f13,conjecture,
! [X0,X1,X2] :
( leq(X0,X1)
=> leq(multiplication(X0,X2),multiplication(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f14,negated_conjecture,
~ ! [X0,X1,X2] :
( leq(X0,X1)
=> leq(multiplication(X0,X2),multiplication(X1,X2)) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f15,plain,
? [X0,X1,X2] :
( leq(X0,X1)
& ~ leq(multiplication(X0,X2),multiplication(X1,X2)) ),
inference(ennf_transformation,[],[f14]) ).
fof(f16,plain,
! [X0,X1] :
( ( ~ leq(X0,X1)
| addition(X0,X1) = X1 )
& ( addition(X0,X1) != X1
| leq(X0,X1) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f17,plain,
( leq(sK0,sK1)
& ~ leq(multiplication(sK0,sK2),multiplication(sK1,sK2)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f15]) ).
fof(f18,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f19,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f26,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f29,plain,
! [X0,X1] :
( ~ leq(X0,X1)
| addition(X0,X1) = X1 ),
inference(cnf_transformation,[],[f16]) ).
fof(f30,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f31,plain,
leq(sK0,sK1),
inference(cnf_transformation,[],[f17]) ).
fof(f32,plain,
~ leq(multiplication(sK0,sK2),multiplication(sK1,sK2)),
inference(cnf_transformation,[],[f17]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f18]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] : addition(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f19]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] : addition(multiplication(X0,X1),multiplication(X2,X1)) = multiplication(addition(X0,X2),X1),
inference(cnf_transformation,[],[f26]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( leq(X0,X1)
| ( addition(X0,X1) != X1 ) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( ( addition(X0,X1) = X1 )
| ~ leq(X0,X1) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_62,negated_conjecture,
~ leq(multiplication(sK0,sK2),multiplication(sK1,sK2)),
inference(cnf_transformation,[],[f32]) ).
tcf(c_63,negated_conjecture,
leq(sK0,sK1),
inference(cnf_transformation,[],[f31]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i] :
( ( addition(X0,X1) != X1 )
| leq(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_60]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i] :
( leq(X0,X1)
| ( addition(X0,X1) != X1 ) ),
inference(renaming,[status(thm)],[c_74]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i] :
( ( addition(X0,X1) = X1 )
| ~ leq(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_61]) ).
tcf(c_145,plain,
! [X0: $i,X1: $i] :
( ( multiplication(sK1,sK2) != X1 )
| ( multiplication(sK0,sK2) != X0 )
| ( addition(X0,X1) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_75,c_62]) ).
tcf(c_146,plain,
addition(multiplication(sK0,sK2),multiplication(sK1,sK2)) != multiplication(sK1,sK2),
inference(unflattening,[status(thm)],[c_145]) ).
tcf(c_150,plain,
! [X0: $i,X1: $i] :
( ( addition(X0,X1) = X1 )
| ( X1 != sK1 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_76,c_63]) ).
tcf(c_151,plain,
addition(sK0,sK1) = sK1,
inference(unflattening,[status(thm)],[c_150]) ).
tcf(c_198,plain,
multiplication(addition(sK0,sK1),sK2) != multiplication(sK1,sK2),
inference(ac_demodulation,[status(thm)],[c_146,c_57,c_50,c_49]) ).
tcf(c_200,plain,
multiplication(sK1,sK2) != multiplication(sK1,sK2),
inference(light_normalisation,[status(thm)],[c_198,c_151]) ).
tcf(c_201,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_200]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE002+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.38 % Computer : n016.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 18:38:27 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 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
% 0.13/0.45 % Proving...
% 2.20/1.31 % SZS status Started for theBenchmark.p
% 2.20/1.31 % SZS status Theorem for theBenchmark.p
% 2.20/1.31
% 2.20/1.31 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.20/1.31
% 2.20/1.31 % ------ iProver source info
% 2.20/1.31
% 2.20/1.31 % git: date: 2026-07-19 20:42:38 +0200
% 2.20/1.31 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.20/1.31 % git: non_committed_changes: false
% 2.20/1.31
% 2.20/1.31 % ------ Parsing...
% 2.20/1.31 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.20/1.31
% 2.20/1.31 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e %
% 2.20/1.31
% 2.20/1.31 % SZS status Theorem for theBenchmark.p
% 2.20/1.31
% 2.20/1.31 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.20/1.31
% 2.20/1.31
%------------------------------------------------------------------------------