%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE024+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 : n018.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 4.30s 1.30s
% Output : CNFRefutation 4.30s
% 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/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(f11,axiom,
! [X0] : multiplication(zero,X0) = zero,
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/KLE001+1.ax',test_2) ).
fof(f15,axiom,
! [X0,X1] :
( test(X0)
=> ( c(X0) = X1
<=> complement(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax',test_3) ).
fof(f17,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/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f18,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)],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( ~ test(X0)
| ( c(X0) = X1
<=> complement(X0,X1) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f21,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,[],[f18]) ).
fof(f22,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,[],[f21]) ).
fof(f26,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(f27,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,[],[f26]) ).
fof(f28,plain,
! [X0,X1] :
( ~ test(X0)
| ( ( c(X0) != X1
| complement(X0,X1) )
& ( ~ complement(X0,X1)
| c(X0) = X1 ) ) ),
inference(nnf_transformation,[],[f19]) ).
fof(f29,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)],[f22]) ).
fof(f32,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f34,plain,
! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f37,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f40,plain,
! [X0] : zero = multiplication(zero,X0),
inference(cnf_transformation,[],[f11]) ).
fof(f44,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| zero = multiplication(X1,X0) ),
inference(cnf_transformation,[],[f27]) ).
fof(f47,plain,
! [X0,X1] :
( ~ test(X0)
| c(X0) != X1
| complement(X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f51,plain,
test(sK2),
inference(cnf_transformation,[],[f29]) ).
fof(f52,plain,
multiplication(c(sK2),sK1) = addition(multiplication(sK1,c(sK3)),multiplication(c(sK2),sK1)),
inference(cnf_transformation,[],[f29]) ).
fof(f53,plain,
zero != multiplication(multiplication(sK2,sK1),c(sK3)),
inference(cnf_transformation,[],[f29]) ).
fof(f54,plain,
! [X0] :
( ~ test(X0)
| complement(X0,c(X0)) ),
inference(equality_resolution,[],[f47]) ).
tcf(c_51,plain,
! [X0: $i] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f32]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] : multiplication(multiplication(X0,X1),X2) = multiplication(X0,multiplication(X1,X2)),
inference(cnf_transformation,[],[f34]) ).
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,[],[f37]) ).
tcf(c_59,plain,
! [X0: $i] : multiplication(zero,X0) = zero,
inference(cnf_transformation,[],[f40]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( ( multiplication(X0,X1) = zero )
| ~ complement(X0,X1) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_67,plain,
! [X0: $i] :
( complement(X0,c(X0))
| ~ test(X0) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_69,negated_conjecture,
multiplication(multiplication(sK2,sK1),c(sK3)) != zero,
inference(cnf_transformation,[],[f53]) ).
tcf(c_70,negated_conjecture,
addition(multiplication(sK1,c(sK3)),multiplication(c(sK2),sK1)) = multiplication(c(sK2),sK1),
inference(cnf_transformation,[],[f52]) ).
tcf(c_71,negated_conjecture,
test(sK2),
inference(cnf_transformation,[],[f51]) ).
tcf(c_193,plain,
multiplication(sK2,multiplication(sK1,c(sK3))) != zero,
inference(demodulation,[status(thm)],[c_69,c_53]) ).
tcf(c_473,definition,
iPr_def_10 = c(sK3),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_474,definition,
iPr_def_11 = multiplication(sK1,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_475,definition,
iPr_def_12 = multiplication(sK2,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_476,definition,
iPr_def_13 = c(sK2),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_477,definition,
iPr_def_14 = multiplication(iPr_def_13,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_478,definition,
iPr_def_15 = addition(iPr_def_11,iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_479,plain,
iPr_def_12 != zero,
inference(demodulation,[status(thm)],[c_193,c_473,c_474,c_475]) ).
tcf(c_481,negated_conjecture,
test(sK2),
inference(demodulation,[status(thm)],[c_71]) ).
tcf(c_482,negated_conjecture,
iPr_def_15 = iPr_def_14,
inference(demodulation,[status(thm)],[c_70,c_476,c_477,c_478]) ).
tcf(c_746,plain,
addition(iPr_def_11,iPr_def_14) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_478,c_482]) ).
tcf(c_757,plain,
( complement(sK2,iPr_def_13)
| ~ test(sK2) ),
inference(superposition,[status(thm)],[c_476,c_67]) ).
tcf(c_761,plain,
complement(sK2,iPr_def_13),
inference(forward_subsumption_resolution,[status(thm)],[c_757,c_481]) ).
tcf(c_814,plain,
multiplication(sK2,iPr_def_13) = zero,
inference(superposition,[status(thm)],[c_761,c_64]) ).
tcf(c_961,plain,
! [X0: $i] : multiplication(sK2,multiplication(iPr_def_13,X0)) = multiplication(zero,X0),
inference(superposition,[status(thm)],[c_814,c_53]) ).
tcf(c_964,plain,
! [X0: $i] : multiplication(sK2,multiplication(iPr_def_13,X0)) = zero,
inference(light_normalisation,[status(thm)],[c_961,c_59]) ).
tcf(c_1016,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_11),multiplication(X0,iPr_def_14)) = multiplication(X0,iPr_def_14),
inference(superposition,[status(thm)],[c_746,c_56]) ).
tcf(c_1099,plain,
addition(iPr_def_12,multiplication(sK2,iPr_def_14)) = multiplication(sK2,iPr_def_14),
inference(superposition,[status(thm)],[c_475,c_1016]) ).
tcf(c_1509,plain,
multiplication(sK2,iPr_def_14) = zero,
inference(superposition,[status(thm)],[c_477,c_964]) ).
tcf(c_1512,plain,
addition(iPr_def_12,zero) = zero,
inference(demodulation,[status(thm)],[c_1099,c_1509]) ).
tcf(c_1522,plain,
zero = iPr_def_12,
inference(demodulation,[status(thm)],[c_1512,c_51]) ).
tcf(c_1537,plain,
iPr_def_12 != iPr_def_12,
inference(demodulation,[status(thm)],[c_479,c_1522]) ).
tcf(c_1538,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_1537]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE024+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.38 % Computer : n018.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Wed Sep 23 18:41:50 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 0.10/0.43
% 0.10/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.43
% 0.10/0.43 % Detected problem language: tptp
% 0.10/0.44 % Proving...
% 4.30/1.30 % SZS status Started for theBenchmark.p
% 4.30/1.30 % SZS status Theorem for theBenchmark.p
% 4.30/1.30
% 4.30/1.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.30/1.30
% 4.30/1.30 % ------ iProver source info
% 4.30/1.30
% 4.30/1.30 % git: date: 2026-07-19 20:42:38 +0200
% 4.30/1.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.30/1.30 % git: non_committed_changes: false
% 4.30/1.30
% 4.30/1.30 % ------ Parsing...
% 4.30/1.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.30/1.30
% 4.30/1.30 % ------ Preprocessing... sup_sim: 1 sf_s rm: 1 0s sf_e pe_s pe_e %
% 4.30/1.30
% 4.30/1.30 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.30/1.30
% 4.30/1.30 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.30/1.30 % ------ Proving...
% 4.30/1.30 % ------ Problem Properties
% 4.30/1.30
% 4.30/1.30 %
% 4.30/1.30 % clauses 30
% 4.30/1.30 % conjectures 3
% 4.30/1.30 % EPR 5
% 4.30/1.30 % Horn 29
% 4.30/1.30 % unary 21
% 4.30/1.30 % binary 7
% 4.30/1.30 % lits 42
% 4.30/1.30 % lits eq 27
% 4.30/1.30 % fd_pure 0
% 4.30/1.30 % fd_pseudo 0
% 4.30/1.30 % fd_cond 0
% 4.30/1.30 % fd_pseudo_cond 1
% 4.30/1.30 % AC symbols 1
% 4.30/1.30
% 4.30/1.30 % ------ Schedule dynamic 5 is on
% 4.30/1.30
% 4.30/1.30 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.30/1.30
% 4.30/1.30
% 4.30/1.30 % ------
% 4.30/1.30 % Current options:
% 4.30/1.30 % ------
% 4.30/1.30
% 4.30/1.30
% 4.30/1.30 %
% 4.30/1.30
% 4.30/1.30 % ------ Proving...
% 4.30/1.30 %
% 4.30/1.30
% 4.30/1.30 % SZS status Theorem for theBenchmark.p
% 4.30/1.30
% 4.30/1.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.30/1.31
% 4.30/1.31
%------------------------------------------------------------------------------