%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE035+2 : 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 : n012.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 01:52:14 PM UTC 2026
% Result : Theorem 2.31s 0.96s
% Output : CNFRefutation 2.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 48 ( 36 unt; 0 def)
% Number of atoms : 78 ( 37 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 50 ( 20 ~; 8 |; 19 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 74 ( 0 sgn 66 !; 8 ?; 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(f3,axiom,
! [X0] : addition(X0,zero) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
fof(f5,axiom,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_associativity) ).
fof(f8,axiom,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',right_distributivity) ).
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(f19,conjecture,
! [X0,X1,X2,X3] :
( ( leq(multiplication(multiplication(X2,X1),c(X3)),zero)
& leq(multiplication(multiplication(X2,X0),c(X3)),zero)
& test(X2)
& test(X3) )
=> leq(multiplication(multiplication(X2,addition(X0,X1)),c(X3)),zero) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f20,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( leq(multiplication(multiplication(X2,X1),c(X3)),zero)
& leq(multiplication(multiplication(X2,X0),c(X3)),zero)
& test(X2)
& test(X3) )
=> leq(multiplication(multiplication(X2,addition(X0,X1)),c(X3)),zero) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f21,plain,
? [X0,X1,X2,X3] :
( leq(multiplication(multiplication(X2,X1),c(X3)),zero)
& leq(multiplication(multiplication(X2,X0),c(X3)),zero)
& test(X2)
& test(X3)
& ~ leq(multiplication(multiplication(X2,addition(X0,X1)),c(X3)),zero) ),
inference(ennf_transformation,[],[f20]) ).
fof(f22,plain,
? [X0,X1,X2,X3] :
( leq(multiplication(multiplication(X2,X1),c(X3)),zero)
& leq(multiplication(multiplication(X2,X0),c(X3)),zero)
& test(X2)
& test(X3)
& ~ leq(multiplication(multiplication(X2,addition(X0,X1)),c(X3)),zero) ),
inference(flattening,[],[f21]) ).
fof(f28,plain,
( leq(multiplication(multiplication(sK2,sK1),c(sK3)),zero)
& leq(multiplication(multiplication(sK2,sK0),c(sK3)),zero)
& test(sK2)
& test(sK3)
& ~ leq(multiplication(multiplication(sK2,addition(sK0,sK1)),c(sK3)),zero) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f22]) ).
fof(f29,plain,
! [X0,X1] :
( ( ~ leq(X0,X1)
| addition(X0,X1) = X1 )
& ( addition(X0,X1) != X1
| leq(X0,X1) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f30,plain,
leq(multiplication(multiplication(sK2,sK1),c(sK3)),zero),
inference(cnf_transformation,[],[f28]) ).
fof(f31,plain,
leq(multiplication(multiplication(sK2,sK0),c(sK3)),zero),
inference(cnf_transformation,[],[f28]) ).
fof(f34,plain,
~ leq(multiplication(multiplication(sK2,addition(sK0,sK1)),c(sK3)),zero),
inference(cnf_transformation,[],[f28]) ).
fof(f35,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f36,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f38,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f39,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f40,plain,
! [X0,X1] :
( ~ leq(X0,X1)
| addition(X0,X1) = X1 ),
inference(cnf_transformation,[],[f29]) ).
fof(f45,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f48,plain,
! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
tcf(c_49,negated_conjecture,
~ leq(multiplication(multiplication(sK2,addition(sK0,sK1)),c(sK3)),zero),
inference(cnf_transformation,[],[f34]) ).
tcf(c_52,negated_conjecture,
leq(multiplication(multiplication(sK2,sK0),c(sK3)),zero),
inference(cnf_transformation,[],[f31]) ).
tcf(c_53,negated_conjecture,
leq(multiplication(multiplication(sK2,sK1),c(sK3)),zero),
inference(cnf_transformation,[],[f30]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] : addition(multiplication(X0,X1),multiplication(X2,X1)) = multiplication(addition(X0,X2),X1),
inference(cnf_transformation,[],[f35]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] : addition(multiplication(X0,X1),multiplication(X0,X2)) = multiplication(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f36]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] : addition(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f38]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f39]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( ( addition(X0,X1) = X1 )
| ~ leq(X0,X1) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_64,plain,
! [X0: $i] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f45]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i] : multiplication(multiplication(X0,X1),X2) = multiplication(X0,multiplication(X1,X2)),
inference(cnf_transformation,[],[f48]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i] :
( ( addition(X0,X1) = X1 )
| ~ leq(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_60]) ).
tcf(c_175,plain,
leq(multiplication(sK2,multiplication(sK0,c(sK3))),zero),
inference(demodulation,[status(thm)],[c_52,c_67]) ).
tcf(c_176,plain,
leq(multiplication(sK2,multiplication(sK1,c(sK3))),zero),
inference(demodulation,[status(thm)],[c_53,c_67]) ).
tcf(c_177,plain,
~ leq(multiplication(sK2,multiplication(addition(sK0,sK1),c(sK3))),zero),
inference(demodulation,[status(thm)],[c_49,c_67]) ).
tcf(c_205,plain,
! [X0: $i,X1: $i] :
( ( addition(X0,X1) = X1 )
| ( X1 != zero )
| ( multiplication(sK2,multiplication(sK1,c(sK3))) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_81,c_176]) ).
tcf(c_206,plain,
addition(multiplication(sK2,multiplication(sK1,c(sK3))),zero) = zero,
inference(unflattening,[status(thm)],[c_205]) ).
tcf(c_215,plain,
( ( zero != zero )
| ( multiplication(sK2,multiplication(addition(sK0,sK1),c(sK3))) != multiplication(sK2,multiplication(sK0,c(sK3))) ) ),
inference(resolution_lifted,[status(thm)],[c_175,c_177]) ).
tcf(c_407,plain,
multiplication(sK2,multiplication(addition(sK0,sK1),c(sK3))) != multiplication(sK2,multiplication(sK0,c(sK3))),
inference(equality_resolution_simp,[status(thm)],[c_215]) ).
tcf(c_415,plain,
addition(zero,multiplication(sK2,multiplication(sK1,c(sK3)))) = zero,
inference(theory_normalisation,[status(thm)],[c_206,c_57,c_58]) ).
tcf(c_418,plain,
addition(multiplication(sK2,multiplication(sK0,c(sK3))),multiplication(sK2,multiplication(sK1,c(sK3)))) != multiplication(sK2,multiplication(sK0,c(sK3))),
inference(demodulation,[status(thm)],[c_407,c_54,c_55]) ).
tcf(c_440,plain,
! [X0: $i] : addition(zero,X0) = X0,
inference(superposition,[status(thm)],[c_58,c_64]) ).
tcf(c_442,plain,
multiplication(sK2,multiplication(sK1,c(sK3))) = zero,
inference(demodulation,[status(thm)],[c_415,c_440]) ).
tcf(c_445,plain,
addition(multiplication(sK2,multiplication(sK0,c(sK3))),zero) != multiplication(sK2,multiplication(sK0,c(sK3))),
inference(demodulation,[status(thm)],[c_418,c_442]) ).
tcf(c_446,plain,
addition(zero,multiplication(sK2,multiplication(sK0,c(sK3)))) != multiplication(sK2,multiplication(sK0,c(sK3))),
inference(theory_normalisation,[status(thm)],[c_445,c_57,c_58]) ).
tcf(c_447,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_446,c_440]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : KLE035+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Wed Sep 23 18:42:51 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.03/0.32 Running first-order theorem proving
% 0.03/0.32 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
% 0.03/0.33
% 0.03/0.33 % ======== iProver multi-core TPTP/SMT =========
% 0.03/0.33
% 0.07/0.33 % Detected problem language: tptp
% 0.07/0.33 % Proving...
% 2.31/0.96 % SZS status Started for theBenchmark.p
% 2.31/0.96 % SZS status Theorem for theBenchmark.p
% 2.31/0.96
% 2.31/0.96 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.31/0.96
% 2.31/0.96 % ------ iProver source info
% 2.31/0.96
% 2.31/0.96 % git: date: 2026-07-19 20:42:38 +0200
% 2.31/0.96 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.31/0.96 % git: non_committed_changes: false
% 2.31/0.96
% 2.31/0.96 % ------ Parsing...
% 2.31/0.96 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.31/0.96
% 2.31/0.96 % ------ Preprocessing... sup_sim: 3 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e %
% 2.31/0.96
% 2.31/0.96 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.31/0.96
% 2.31/0.96 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.31/0.96 % ------ Proving...
% 2.31/0.96 % ------ Problem Properties
% 2.31/0.96
% 2.31/0.96 %
% 2.31/0.96 % clauses 19
% 2.31/0.96 % conjectures 2
% 2.31/0.96 % EPR 2
% 2.31/0.96 % Horn 18
% 2.31/0.96 % unary 14
% 2.31/0.96 % binary 3
% 2.31/0.96 % lits 26
% 2.31/0.96 % lits eq 19
% 2.31/0.96 % fd_pure 0
% 2.31/0.96 % fd_pseudo 0
% 2.31/0.96 % fd_cond 0
% 2.31/0.96 % fd_pseudo_cond 0
% 2.31/0.96 % AC symbols 1
% 2.31/0.96
% 2.31/0.96 % ------ Schedule dynamic 5 is on
% 2.31/0.96
% 2.31/0.96 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.31/0.96
% 2.31/0.96
% 2.31/0.96 % ------
% 2.31/0.96 % Current options:
% 2.31/0.96 % ------
% 2.31/0.96
% 2.31/0.96
% 2.31/0.96 %
% 2.31/0.96
% 2.31/0.96 % ------ Proving...
% 2.31/0.96 %
% 2.31/0.96
% 2.31/0.96 % SZS status Theorem for theBenchmark.p
% 2.31/0.96
% 2.31/0.96 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.31/0.96
% 2.31/0.96
%------------------------------------------------------------------------------