%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE021+3 : 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 : n026.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 01:52:10 PM UTC 2026
% Result : Theorem 1.42s 1.29s
% Output : CNFRefutation 1.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 47 ( 31 unt; 3 def)
% Number of atoms : 99 ( 52 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 64 ( 28 ~; 19 |; 11 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 54 ( 0 sgn 52 !; 2 ?; 13 :)
% 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(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
fof(f9,axiom,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',left_distributivity) ).
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] :
( test(X1)
=> X0 = addition(multiplication(X1,X0),multiplication(c(X1),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f20,negated_conjecture,
~ ! [X0,X1] :
( test(X1)
=> X0 = addition(multiplication(X1,X0),multiplication(c(X1),X0)) ),
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] :
( test(X1)
& addition(multiplication(X1,X0),multiplication(c(X1),X0)) != X0 ),
inference(ennf_transformation,[],[f20]) ).
fof(f31,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(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(flattening,[],[f31]) ).
fof(f33,plain,
! [X0,X1] :
( ~ test(X0)
| ( ( c(X0) != X1
| complement(X0,X1) )
& ( ~ complement(X0,X1)
| c(X0) = X1 ) ) ),
inference(nnf_transformation,[],[f21]) ).
fof(f34,plain,
( test(sK2)
& sK1 != addition(multiplication(sK2,sK1),multiplication(c(sK2),sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X0,sK1),skolemize(X1,sK2)],[f27]) ).
fof(f35,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f36,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f41,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f43,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f48,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(cnf_transformation,[],[f32]) ).
fof(f52,plain,
! [X0,X1] :
( ~ test(X0)
| c(X0) != X1
| complement(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f57,plain,
test(sK2),
inference(cnf_transformation,[],[f34]) ).
fof(f58,plain,
sK1 != addition(multiplication(sK2,sK1),multiplication(c(sK2),sK1)),
inference(cnf_transformation,[],[f34]) ).
fof(f59,plain,
! [X0] :
( ~ test(X0)
| complement(X0,c(X0)) ),
inference(equality_resolution,[],[f52]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f35]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] : addition(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f36]) ).
tcf(c_55,plain,
! [X0: $i] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f41]) ).
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,[],[f43]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( ( addition(X1,X0) = one )
| ~ complement(X0,X1) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_67,plain,
! [X0: $i] :
( complement(X0,c(X0))
| ~ test(X0) ),
inference(cnf_transformation,[],[f59]) ).
tcf(c_71,negated_conjecture,
addition(multiplication(sK2,sK1),multiplication(c(sK2),sK1)) != sK1,
inference(cnf_transformation,[],[f58]) ).
tcf(c_72,negated_conjecture,
test(sK2),
inference(cnf_transformation,[],[f57]) ).
tcf(c_203,plain,
multiplication(addition(c(sK2),sK2),sK1) != sK1,
inference(ac_demodulation,[status(thm)],[c_71,c_57,c_50,c_49]) ).
tcf(c_205,plain,
multiplication(addition(sK2,c(sK2)),sK1) != sK1,
inference(theory_normalisation,[status(thm)],[c_203,c_50,c_49]) ).
tcf(c_378,definition,
iPr_def_10 = c(sK2),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_379,definition,
iPr_def_11 = addition(sK2,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_380,definition,
iPr_def_12 = multiplication(iPr_def_11,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_381,plain,
iPr_def_12 != sK1,
inference(demodulation,[status(thm)],[c_205,c_378,c_379,c_380]) ).
tcf(c_382,negated_conjecture,
test(sK2),
inference(demodulation,[status(thm)],[c_72]) ).
tcf(c_648,plain,
addition(iPr_def_10,sK2) = iPr_def_11,
inference(theory_normalisation,[status(thm)],[c_379,c_50,c_49]) ).
tcf(c_660,plain,
( complement(sK2,iPr_def_10)
| ~ test(sK2) ),
inference(superposition,[status(thm)],[c_378,c_67]) ).
tcf(c_664,plain,
complement(sK2,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_660,c_382]) ).
tcf(c_711,plain,
addition(iPr_def_10,sK2) = one,
inference(superposition,[status(thm)],[c_664,c_65]) ).
tcf(c_712,plain,
one = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_711,c_648]) ).
tcf(c_719,plain,
! [X0: $i] : multiplication(iPr_def_11,X0) = X0,
inference(demodulation,[status(thm)],[c_55,c_712]) ).
tcf(c_721,plain,
sK1 = iPr_def_12,
inference(demodulation,[status(thm)],[c_380,c_719]) ).
tcf(c_722,plain,
iPr_def_12 != iPr_def_12,
inference(demodulation,[status(thm)],[c_381,c_721]) ).
tcf(c_723,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_722]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE021+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.38 % Computer : n026.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Wed Sep 23 18:41:25 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
% 0.09/0.44 % Proving...
% 1.42/1.29 % SZS status Started for theBenchmark.p
% 1.42/1.29 % SZS status Theorem for theBenchmark.p
% 1.42/1.29
% 1.42/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.42/1.29
% 1.42/1.29 % ------ iProver source info
% 1.42/1.29
% 1.42/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 1.42/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.42/1.29 % git: non_committed_changes: false
% 1.42/1.29
% 1.42/1.29 % ------ Parsing...
% 1.42/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.42/1.29
% 1.42/1.29 % ------ Preprocessing... sup_sim: 4 sf_s rm: 1 0s sf_e pe_s pe_e %
% 1.42/1.29
% 1.42/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.42/1.29
% 1.42/1.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.42/1.29 % ------ Proving...
% 1.42/1.29 % ------ Problem Properties
% 1.42/1.29
% 1.42/1.29 %
% 1.42/1.29 % clauses 27
% 1.42/1.29 % conjectures 1
% 1.42/1.29 % EPR 3
% 1.42/1.29 % Horn 26
% 1.42/1.29 % unary 16
% 1.42/1.29 % binary 7
% 1.42/1.29 % lits 43
% 1.42/1.29 % lits eq 25
% 1.42/1.29 % fd_pure 0
% 1.42/1.29 % fd_pseudo 0
% 1.42/1.29 % fd_cond 0
% 1.42/1.29 % fd_pseudo_cond 1
% 1.42/1.29 % AC symbols 1
% 1.42/1.29
% 1.42/1.29 % ------ Schedule dynamic 5 is on
% 1.42/1.29
% 1.42/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.42/1.29
% 1.42/1.29
% 1.42/1.29 % ------
% 1.42/1.29 % Current options:
% 1.42/1.29 % ------
% 1.42/1.29
% 1.42/1.29
% 1.42/1.29 %
% 1.42/1.29
% 1.42/1.29 % ------ Proving...
% 1.42/1.29 %
% 1.42/1.29
% 1.42/1.29 % SZS status Theorem for theBenchmark.p
% 1.42/1.29
% 1.42/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.42/1.29
% 1.42/1.29
%------------------------------------------------------------------------------