%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE011+1 : 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 : n009.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 01:52:08 PM UTC 2026
% Result : Theorem 4.14s 1.31s
% Output : CNFRefutation 4.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 10
% Syntax : Number of formulae : 76 ( 60 unt; 0 def)
% Number of atoms : 117 ( 80 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 70 ( 29 ~; 18 |; 17 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 7 ( 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 87 ( 0 sgn 83 !; 4 ?; 34 :)
% 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(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
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(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(f17,conjecture,
! [X0,X1] :
( ( test(X0)
& test(X1) )
=> one = addition(addition(multiplication(addition(X1,c(X1)),X0),multiplication(addition(X0,c(X0)),X1)),multiplication(c(X0),c(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f18,negated_conjecture,
~ ! [X0,X1] :
( ( test(X0)
& test(X1) )
=> one = addition(addition(multiplication(addition(X1,c(X1)),X0),multiplication(addition(X0,c(X0)),X1)),multiplication(c(X0),c(X1))) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
? [X0,X1] :
( test(X0)
& test(X1)
& one != addition(addition(multiplication(addition(X1,c(X1)),X0),multiplication(addition(X0,c(X0)),X1)),multiplication(c(X0),c(X1))) ),
inference(ennf_transformation,[],[f18]) ).
fof(f20,plain,
? [X0,X1] :
( test(X0)
& test(X1)
& one != addition(addition(multiplication(addition(X1,c(X1)),X0),multiplication(addition(X0,c(X0)),X1)),multiplication(c(X0),c(X1))) ),
inference(flattening,[],[f19]) ).
fof(f22,plain,
! [X0,X1] :
( ~ test(X0)
| ( c(X0) = X1
<=> complement(X0,X1) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f23,plain,
( test(sK0)
& test(sK1)
& one != addition(addition(multiplication(addition(sK1,c(sK1)),sK0),multiplication(addition(sK0,c(sK0)),sK1)),multiplication(c(sK0),c(sK1))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f20]) ).
fof(f24,plain,
! [X0,X1] :
( ~ test(X0)
| ( ( c(X0) != X1
| complement(X0,X1) )
& ( ~ complement(X0,X1)
| c(X0) = X1 ) ) ),
inference(nnf_transformation,[],[f22]) ).
fof(f28,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(f29,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,[],[f28]) ).
fof(f30,plain,
test(sK0),
inference(cnf_transformation,[],[f23]) ).
fof(f31,plain,
test(sK1),
inference(cnf_transformation,[],[f23]) ).
fof(f32,plain,
one != addition(addition(multiplication(addition(sK1,c(sK1)),sK0),multiplication(addition(sK0,c(sK0)),sK1)),multiplication(c(sK0),c(sK1))),
inference(cnf_transformation,[],[f23]) ).
fof(f33,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f34,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f35,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f36,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f37,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f39,plain,
! [X0,X1] :
( ~ test(X0)
| c(X0) != X1
| complement(X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f44,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(cnf_transformation,[],[f29]) ).
fof(f48,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f49,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f53,plain,
! [X0] :
( ~ test(X0)
| complement(X0,c(X0)) ),
inference(equality_resolution,[],[f39]) ).
tcf(c_49,negated_conjecture,
addition(addition(multiplication(addition(sK1,c(sK1)),sK0),multiplication(addition(sK0,c(sK0)),sK1)),multiplication(c(sK0),c(sK1))) != one,
inference(cnf_transformation,[],[f32]) ).
tcf(c_50,negated_conjecture,
test(sK1),
inference(cnf_transformation,[],[f31]) ).
tcf(c_51,negated_conjecture,
test(sK0),
inference(cnf_transformation,[],[f30]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i] : addition(multiplication(X0,X1),multiplication(X2,X1)) = multiplication(addition(X0,X2),X1),
inference(cnf_transformation,[],[f33]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] : addition(multiplication(X0,X1),multiplication(X0,X2)) = multiplication(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f34]) ).
tcf(c_54,plain,
! [X0: $i] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f35]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] : addition(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f36]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f37]) ).
tcf(c_59,plain,
! [X0: $i] :
( complement(X0,c(X0))
| ~ test(X0) ),
inference(cnf_transformation,[],[f53]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( ( addition(X1,X0) = one )
| ~ complement(X0,X1) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_67,plain,
! [X0: $i] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f48]) ).
tcf(c_68,plain,
! [X0: $i] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f49]) ).
tcf(c_88,negated_conjecture,
addition(multiplication(c(sK0),c(sK1)),addition(multiplication(addition(sK1,c(sK1)),sK0),multiplication(addition(sK0,c(sK0)),sK1))) != one,
inference(theory_normalisation,[status(thm)],[c_49,c_55,c_56]) ).
tcf(c_700,plain,
! [X0: $i,X1: $i,X2: $i] : addition(X0,addition(X1,X2)) = addition(X1,addition(X0,X2)),
inference(superposition,[status(thm)],[c_55,c_56]) ).
tcf(c_703,plain,
addition(multiplication(addition(sK1,c(sK1)),sK0),addition(multiplication(c(sK0),c(sK1)),multiplication(addition(sK0,c(sK0)),sK1))) != one,
inference(theory_normalisation,[status(thm)],[c_88,c_55,c_56]) ).
tcf(c_704,plain,
addition(multiplication(sK1,sK0),addition(multiplication(c(sK1),sK0),addition(multiplication(sK0,sK1),addition(multiplication(c(sK0),sK1),multiplication(c(sK0),c(sK1)))))) != one,
inference(demodulation,[status(thm)],[c_703,c_52,c_55,c_56,c_700]) ).
tcf(c_710,plain,
! [X0: $i,X1: $i] : addition(X0,addition(X1,X0)) = addition(X1,X0),
inference(superposition,[status(thm)],[c_54,c_700]) ).
tcf(c_728,plain,
complement(sK1,c(sK1)),
inference(superposition,[status(thm)],[c_50,c_59]) ).
tcf(c_729,plain,
complement(sK0,c(sK0)),
inference(superposition,[status(thm)],[c_51,c_59]) ).
tcf(c_834,plain,
addition(c(sK1),sK1) = one,
inference(superposition,[status(thm)],[c_728,c_66]) ).
tcf(c_835,plain,
addition(c(sK0),sK0) = one,
inference(superposition,[status(thm)],[c_729,c_66]) ).
tcf(c_840,plain,
addition(sK0,c(sK0)) = one,
inference(theory_normalisation,[status(thm)],[c_835,c_55,c_56]) ).
tcf(c_841,plain,
addition(sK1,c(sK1)) = one,
inference(theory_normalisation,[status(thm)],[c_834,c_55,c_56]) ).
tcf(c_957,plain,
! [X0: $i] : addition(sK0,addition(c(sK0),X0)) = addition(one,X0),
inference(superposition,[status(thm)],[c_840,c_55]) ).
tcf(c_964,plain,
! [X0: $i] : addition(sK1,addition(c(sK1),X0)) = addition(one,X0),
inference(superposition,[status(thm)],[c_841,c_55]) ).
tcf(c_1027,plain,
! [X0: $i] : addition(sK0,addition(X0,c(sK0))) = addition(one,X0),
inference(superposition,[status(thm)],[c_56,c_957]) ).
tcf(c_1036,plain,
addition(c(sK0),sK0) = addition(one,sK0),
inference(superposition,[status(thm)],[c_957,c_710]) ).
tcf(c_1037,plain,
addition(sK0,c(sK0)) = addition(one,sK0),
inference(theory_normalisation,[status(thm)],[c_1036,c_55,c_56]) ).
tcf(c_1038,plain,
addition(one,sK0) = one,
inference(light_normalisation,[status(thm)],[c_1037,c_840]) ).
tcf(c_1123,plain,
addition(c(sK1),sK1) = addition(one,sK1),
inference(superposition,[status(thm)],[c_964,c_710]) ).
tcf(c_1124,plain,
addition(sK1,c(sK1)) = addition(one,sK1),
inference(theory_normalisation,[status(thm)],[c_1123,c_55,c_56]) ).
tcf(c_1125,plain,
addition(one,sK1) = one,
inference(light_normalisation,[status(thm)],[c_1124,c_841]) ).
tcf(c_1144,plain,
! [X0: $i] : addition(multiplication(sK1,X0),multiplication(c(sK1),X0)) = multiplication(one,X0),
inference(superposition,[status(thm)],[c_841,c_52]) ).
tcf(c_1160,plain,
! [X0: $i] : addition(multiplication(one,X0),multiplication(sK0,X0)) = multiplication(one,X0),
inference(superposition,[status(thm)],[c_1038,c_52]) ).
tcf(c_1167,plain,
! [X0: $i] : addition(X0,multiplication(sK0,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1160,c_67]) ).
tcf(c_1172,plain,
! [X0: $i] : addition(multiplication(sK1,X0),multiplication(c(sK1),X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1144,c_67]) ).
tcf(c_1219,plain,
! [X0: $i] : addition(multiplication(X0,sK1),multiplication(X0,c(sK1))) = multiplication(X0,one),
inference(superposition,[status(thm)],[c_841,c_53]) ).
tcf(c_1254,plain,
! [X0: $i] : addition(multiplication(X0,sK1),multiplication(X0,c(sK1))) = X0,
inference(light_normalisation,[status(thm)],[c_1219,c_68]) ).
tcf(c_1257,plain,
addition(multiplication(sK1,sK0),addition(multiplication(c(sK1),sK0),addition(multiplication(sK0,sK1),c(sK0)))) != one,
inference(demodulation,[status(thm)],[c_704,c_1254]) ).
tcf(c_1436,plain,
! [X0: $i] : addition(one,addition(sK1,X0)) = addition(one,X0),
inference(superposition,[status(thm)],[c_1125,c_55]) ).
tcf(c_1708,plain,
addition(one,multiplication(sK0,sK1)) = addition(one,sK1),
inference(superposition,[status(thm)],[c_1167,c_1436]) ).
tcf(c_1711,plain,
addition(one,multiplication(sK0,sK1)) = one,
inference(light_normalisation,[status(thm)],[c_1708,c_1125]) ).
tcf(c_2348,plain,
! [X0: $i,X1: $i] : addition(multiplication(sK1,X0),addition(multiplication(c(sK1),X0),X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[c_1172,c_55]) ).
tcf(c_2363,plain,
addition(sK0,addition(multiplication(sK0,sK1),c(sK0))) != one,
inference(demodulation,[status(thm)],[c_1257,c_2348]) ).
tcf(c_2364,plain,
$false,
inference(ground_joinability,[status(thm)],[c_2363,c_1027,c_1711]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE011+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n009.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Wed Sep 23 18:34:43 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 0.10/0.43
% 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...
% 4.14/1.31 % SZS status Started for theBenchmark.p
% 4.14/1.31 % SZS status Theorem for theBenchmark.p
% 4.14/1.31
% 4.14/1.31 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.14/1.31
% 4.14/1.31 % ------ iProver source info
% 4.14/1.31
% 4.14/1.31 % git: date: 2026-07-19 20:42:38 +0200
% 4.14/1.31 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.14/1.31 % git: non_committed_changes: false
% 4.14/1.31
% 4.14/1.31 % ------ Parsing...
% 4.14/1.31 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.14/1.31
% 4.14/1.31 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 4.14/1.31
% 4.14/1.31 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.14/1.31
% 4.14/1.31 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.14/1.31 % ------ Proving...
% 4.14/1.31 % ------ Problem Properties
% 4.14/1.31
% 4.14/1.31 %
% 4.14/1.31 % clauses 23
% 4.14/1.31 % conjectures 3
% 4.14/1.31 % EPR 3
% 4.14/1.31 % Horn 22
% 4.14/1.31 % unary 14
% 4.14/1.31 % binary 7
% 4.14/1.31 % lits 35
% 4.14/1.31 % lits eq 20
% 4.14/1.31 % fd_pure 0
% 4.14/1.31 % fd_pseudo 0
% 4.14/1.31 % fd_cond 0
% 4.14/1.31 % fd_pseudo_cond 1
% 4.14/1.31 % AC symbols 1
% 4.14/1.31
% 4.14/1.31 % ------ Schedule dynamic 5 is on
% 4.14/1.31
% 4.14/1.31 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.14/1.31
% 4.14/1.31
% 4.14/1.31 % ------
% 4.14/1.31 % Current options:
% 4.14/1.31 % ------
% 4.14/1.31
% 4.14/1.31
% 4.14/1.31 %
% 4.14/1.31
% 4.14/1.31 % ------ Proving...
% 4.14/1.31 %
% 4.14/1.31
% 4.14/1.31 % SZS status Theorem for theBenchmark.p
% 4.14/1.31
% 4.14/1.31 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.14/1.31
% 4.14/1.31
%------------------------------------------------------------------------------