%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE024+2 : 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 : n005.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 01:52:12 PM UTC 2026
% Result : Theorem 3.84s 1.35s
% Output : CNFRefutation 3.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 13
% Syntax : Number of formulae : 57 ( 40 unt; 6 def)
% Number of atoms : 137 ( 67 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 75 ( 28 ~; 19 |; 20 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 7 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 59 ( 0 sgn 53 !; 6 ?; 14 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] : addition(X0,zero) = X0,
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/KLE001+0.ax',right_distributivity) ).
fof(f11,axiom,
! [X0] : multiplication(zero,X0) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',left_annihilation) ).
fof(f14,axiom,
! [X0,X1] :
( complement(X1,X0)
<=> ( addition(X0,X1) = one
& multiplication(X1,X0) = zero
& multiplication(X0,X1) = zero ) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_2) ).
fof(f15,axiom,
! [X0,X1] :
( test(X0)
=> ( c(X0) = X1
<=> complement(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_3) ).
fof(f19,conjecture,
! [X0,X1,X2] :
( ( test(X2)
& test(X1) )
=> ( addition(multiplication(X0,c(X2)),multiplication(c(X1),X0)) = multiplication(c(X1),X0)
=> multiplication(multiplication(X1,X0),c(X2)) = zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f20,negated_conjecture,
~ ! [X0,X1,X2] :
( ( test(X2)
& test(X1) )
=> ( addition(multiplication(X0,c(X2)),multiplication(c(X1),X0)) = multiplication(c(X1),X0)
=> multiplication(multiplication(X1,X0),c(X2)) = zero ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f21,plain,
! [X0,X1] :
( ~ test(X0)
| ( c(X0) = X1
<=> complement(X0,X1) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f27,plain,
? [X0,X1,X2] :
( test(X2)
& test(X1)
& addition(multiplication(X0,c(X2)),multiplication(c(X1),X0)) = multiplication(c(X1),X0)
& zero != multiplication(multiplication(X1,X0),c(X2)) ),
inference(ennf_transformation,[],[f20]) ).
fof(f28,plain,
? [X0,X1,X2] :
( test(X2)
& test(X1)
& addition(multiplication(X0,c(X2)),multiplication(c(X1),X0)) = multiplication(c(X1),X0)
& zero != multiplication(multiplication(X1,X0),c(X2)) ),
inference(flattening,[],[f27]) ).
fof(f32,plain,
! [X0,X1] :
( ( ~ complement(X1,X0)
| ( addition(X0,X1) = one
& multiplication(X1,X0) = zero
& multiplication(X0,X1) = zero ) )
& ( addition(X0,X1) != one
| zero != multiplication(X1,X0)
| zero != multiplication(X0,X1)
| complement(X1,X0) ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f33,plain,
! [X0,X1] :
( ( ~ complement(X1,X0)
| ( addition(X0,X1) = one
& multiplication(X1,X0) = zero
& multiplication(X0,X1) = zero ) )
& ( addition(X0,X1) != one
| zero != multiplication(X1,X0)
| zero != multiplication(X0,X1)
| complement(X1,X0) ) ),
inference(flattening,[],[f32]) ).
fof(f34,plain,
! [X0,X1] :
( ~ test(X0)
| ( ( c(X0) != X1
| complement(X0,X1) )
& ( ~ complement(X0,X1)
| c(X0) = X1 ) ) ),
inference(nnf_transformation,[],[f21]) ).
fof(f35,plain,
( test(sK3)
& test(sK2)
& multiplication(c(sK2),sK1) = addition(multiplication(sK1,c(sK3)),multiplication(c(sK2),sK1))
& zero != multiplication(multiplication(sK2,sK1),c(sK3)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3)],[f28]) ).
fof(f38,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f40,plain,
! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f43,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f46,plain,
! [X0] : zero = multiplication(zero,X0),
inference(cnf_transformation,[],[f11]) ).
fof(f50,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| zero = multiplication(X1,X0) ),
inference(cnf_transformation,[],[f33]) ).
fof(f53,plain,
! [X0,X1] :
( ~ test(X0)
| c(X0) != X1
| complement(X0,X1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f59,plain,
test(sK2),
inference(cnf_transformation,[],[f35]) ).
fof(f60,plain,
multiplication(c(sK2),sK1) = addition(multiplication(sK1,c(sK3)),multiplication(c(sK2),sK1)),
inference(cnf_transformation,[],[f35]) ).
fof(f61,plain,
zero != multiplication(multiplication(sK2,sK1),c(sK3)),
inference(cnf_transformation,[],[f35]) ).
fof(f62,plain,
! [X0] :
( ~ test(X0)
| complement(X0,c(X0)) ),
inference(equality_resolution,[],[f53]) ).
tcf(c_51,plain,
! [X0: $i] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f38]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] : multiplication(multiplication(X0,X1),X2) = multiplication(X0,multiplication(X1,X2)),
inference(cnf_transformation,[],[f40]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] : addition(multiplication(X0,X1),multiplication(X0,X2)) = multiplication(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f43]) ).
tcf(c_59,plain,
! [X0: $i] : multiplication(zero,X0) = zero,
inference(cnf_transformation,[],[f46]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( ( multiplication(X0,X1) = zero )
| ~ complement(X0,X1) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_67,plain,
! [X0: $i] :
( complement(X0,c(X0))
| ~ test(X0) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_71,negated_conjecture,
multiplication(multiplication(sK2,sK1),c(sK3)) != zero,
inference(cnf_transformation,[],[f61]) ).
tcf(c_72,negated_conjecture,
addition(multiplication(sK1,c(sK3)),multiplication(c(sK2),sK1)) = multiplication(c(sK2),sK1),
inference(cnf_transformation,[],[f60]) ).
tcf(c_73,negated_conjecture,
test(sK2),
inference(cnf_transformation,[],[f59]) ).
tcf(c_209,plain,
multiplication(sK2,multiplication(sK1,c(sK3))) != zero,
inference(demodulation,[status(thm)],[c_71,c_53]) ).
tcf(c_382,definition,
iPr_def_10 = c(sK3),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_383,definition,
iPr_def_11 = multiplication(sK1,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_384,definition,
iPr_def_12 = multiplication(sK2,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_385,definition,
iPr_def_13 = c(sK2),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_386,definition,
iPr_def_14 = multiplication(iPr_def_13,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_387,definition,
iPr_def_15 = addition(iPr_def_11,iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_388,plain,
iPr_def_12 != zero,
inference(demodulation,[status(thm)],[c_209,c_382,c_383,c_384]) ).
tcf(c_390,negated_conjecture,
test(sK2),
inference(demodulation,[status(thm)],[c_73]) ).
tcf(c_391,negated_conjecture,
iPr_def_15 = iPr_def_14,
inference(demodulation,[status(thm)],[c_72,c_385,c_386,c_387]) ).
tcf(c_679,plain,
addition(iPr_def_11,iPr_def_14) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_387,c_391]) ).
tcf(c_690,plain,
( complement(sK2,iPr_def_13)
| ~ test(sK2) ),
inference(superposition,[status(thm)],[c_385,c_67]) ).
tcf(c_694,plain,
complement(sK2,iPr_def_13),
inference(forward_subsumption_resolution,[status(thm)],[c_690,c_390]) ).
tcf(c_747,plain,
multiplication(sK2,iPr_def_13) = zero,
inference(superposition,[status(thm)],[c_694,c_64]) ).
tcf(c_895,plain,
! [X0: $i] : multiplication(sK2,multiplication(iPr_def_13,X0)) = multiplication(zero,X0),
inference(superposition,[status(thm)],[c_747,c_53]) ).
tcf(c_898,plain,
! [X0: $i] : multiplication(sK2,multiplication(iPr_def_13,X0)) = zero,
inference(light_normalisation,[status(thm)],[c_895,c_59]) ).
tcf(c_949,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_11),multiplication(X0,iPr_def_14)) = multiplication(X0,iPr_def_14),
inference(superposition,[status(thm)],[c_679,c_56]) ).
tcf(c_1040,plain,
addition(iPr_def_12,multiplication(sK2,iPr_def_14)) = multiplication(sK2,iPr_def_14),
inference(superposition,[status(thm)],[c_384,c_949]) ).
tcf(c_1522,plain,
multiplication(sK2,iPr_def_14) = zero,
inference(superposition,[status(thm)],[c_386,c_898]) ).
tcf(c_1525,plain,
addition(iPr_def_12,zero) = zero,
inference(demodulation,[status(thm)],[c_1040,c_1522]) ).
tcf(c_1535,plain,
zero = iPr_def_12,
inference(demodulation,[status(thm)],[c_1525,c_51]) ).
tcf(c_1550,plain,
iPr_def_12 != iPr_def_12,
inference(demodulation,[status(thm)],[c_388,c_1535]) ).
tcf(c_1551,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_1550]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE024+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.36 % Computer : n005.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Wed Sep 23 18:39:33 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.42 Running first-order theorem proving
% 0.13/0.42 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
% 0.13/0.43
% 0.13/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.43
% 0.13/0.44 % Detected problem language: tptp
% 0.13/0.45 % Proving...
% 3.84/1.35 % SZS status Started for theBenchmark.p
% 3.84/1.35 % SZS status Theorem for theBenchmark.p
% 3.84/1.35
% 3.84/1.35 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.84/1.35
% 3.84/1.35 % ------ iProver source info
% 3.84/1.35
% 3.84/1.35 % git: date: 2026-07-19 20:42:38 +0200
% 3.84/1.35 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.84/1.35 % git: non_committed_changes: false
% 3.84/1.35
% 3.84/1.35 % ------ Parsing...
% 3.84/1.35 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.84/1.35
% 3.84/1.35 % ------ Preprocessing... sup_sim: 1 sf_s rm: 1 0s sf_e pe_s pe_e %
% 3.84/1.35
% 3.84/1.35 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.84/1.35
% 3.84/1.35 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.84/1.35 % ------ Proving...
% 3.84/1.35 % ------ Problem Properties
% 3.84/1.35
% 3.84/1.35 %
% 3.84/1.35 % clauses 32
% 3.84/1.35 % conjectures 3
% 3.84/1.35 % EPR 5
% 3.84/1.35 % Horn 31
% 3.84/1.35 % unary 21
% 3.84/1.35 % binary 7
% 3.84/1.35 % lits 48
% 3.84/1.35 % lits eq 29
% 3.84/1.35 % fd_pure 0
% 3.84/1.35 % fd_pseudo 0
% 3.84/1.35 % fd_cond 0
% 3.84/1.35 % fd_pseudo_cond 1
% 3.84/1.35 % AC symbols 1
% 3.84/1.35
% 3.84/1.35 % ------ Schedule dynamic 5 is on
% 3.84/1.35
% 3.84/1.35 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.84/1.35
% 3.84/1.35
% 3.84/1.35 % ------
% 3.84/1.35 % Current options:
% 3.84/1.35 % ------
% 3.84/1.35
% 3.84/1.35
% 3.84/1.35 %
% 3.84/1.35
% 3.84/1.35 % ------ Proving...
% 3.84/1.35 %
% 3.84/1.35
% 3.84/1.35 % SZS status Theorem for theBenchmark.p
% 3.84/1.35
% 3.84/1.35 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.84/1.35
% 3.84/1.35
%------------------------------------------------------------------------------