%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE119+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 : n013.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 01:52:27 PM UTC 2026
% Result : Theorem 1.13s 1.29s
% Output : CNFRefutation 1.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 48 ( 48 unt; 0 def)
% Number of atoms : 48 ( 47 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 11 ( 11 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 49 ( 0 sgn 47 !; 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(f3,axiom,
! [X0] : addition(X0,zero) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
fof(f10,axiom,
! [X0] : multiplication(X0,zero) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',right_annihilation) ).
fof(f16,axiom,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',domain4) ).
fof(f17,axiom,
! [X0] : multiplication(X0,coantidomain(X0)) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',codomain1) ).
fof(f19,axiom,
! [X0] : addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',codomain3) ).
fof(f20,axiom,
! [X0] : codomain(X0) = coantidomain(coantidomain(X0)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',codomain4) ).
fof(f24,axiom,
! [X0,X1] : backward_diamond(X0,X1) = codomain(multiplication(codomain(X1),X0)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+6.ax',backward_diamond) ).
fof(f27,conjecture,
! [X0,X1] : addition(backward_diamond(zero,domain(X0)),domain(X1)) = domain(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f28,negated_conjecture,
~ ! [X0,X1] : addition(backward_diamond(zero,domain(X0)),domain(X1)) = domain(X1),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f29,plain,
? [X0,X1] : domain(X1) != addition(backward_diamond(zero,domain(X0)),domain(X1)),
inference(ennf_transformation,[],[f28]) ).
fof(f30,plain,
domain(sK1) != addition(backward_diamond(zero,domain(sK0)),domain(sK1)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f29]) ).
fof(f31,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f32,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f33,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f37,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f40,plain,
! [X0] : zero = multiplication(X0,zero),
inference(cnf_transformation,[],[f10]) ).
fof(f45,plain,
! [X0] : antidomain(antidomain(X0)) = domain(X0),
inference(cnf_transformation,[],[f16]) ).
fof(f46,plain,
! [X0] : zero = multiplication(X0,coantidomain(X0)),
inference(cnf_transformation,[],[f17]) ).
fof(f48,plain,
! [X0] : one = addition(coantidomain(coantidomain(X0)),coantidomain(X0)),
inference(cnf_transformation,[],[f19]) ).
fof(f49,plain,
! [X0] : coantidomain(coantidomain(X0)) = codomain(X0),
inference(cnf_transformation,[],[f20]) ).
fof(f53,plain,
! [X0,X1] : backward_diamond(X0,X1) = codomain(multiplication(codomain(X1),X0)),
inference(cnf_transformation,[],[f24]) ).
fof(f56,plain,
domain(sK1) != addition(backward_diamond(zero,domain(sK0)),domain(sK1)),
inference(cnf_transformation,[],[f30]) ).
fof(f58,plain,
! [X0,X1] : backward_diamond(X0,X1) = coantidomain(coantidomain(multiplication(coantidomain(coantidomain(X1)),X0))),
inference(definition_unfolding,[],[f53,f49,f49]) ).
fof(f63,plain,
antidomain(antidomain(sK1)) != addition(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(sK0)))),zero))),antidomain(antidomain(sK1))),
inference(definition_unfolding,[],[f56,f45,f58,f45,f45]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f31]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] : addition(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f32]) ).
tcf(c_51,plain,
! [X0: $i] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f33]) ).
tcf(c_55,plain,
! [X0: $i] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f37]) ).
tcf(c_58,plain,
! [X0: $i] : multiplication(X0,zero) = zero,
inference(cnf_transformation,[],[f40]) ).
tcf(c_63,plain,
! [X0: $i] : multiplication(X0,coantidomain(X0)) = zero,
inference(cnf_transformation,[],[f46]) ).
tcf(c_65,plain,
! [X0: $i] : addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one,
inference(cnf_transformation,[],[f48]) ).
tcf(c_66,negated_conjecture,
addition(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(sK0)))),zero))),antidomain(antidomain(sK1))) != antidomain(antidomain(sK1)),
inference(cnf_transformation,[],[f63]) ).
tcf(c_83,plain,
! [X0: $i] : addition(coantidomain(X0),coantidomain(coantidomain(X0))) = one,
inference(theory_normalisation,[status(thm)],[c_65,c_50,c_49]) ).
tcf(c_84,negated_conjecture,
addition(antidomain(antidomain(sK1)),coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(sK0)))),zero)))) != antidomain(antidomain(sK1)),
inference(theory_normalisation,[status(thm)],[c_66,c_50,c_49]) ).
tcf(c_350,plain,
addition(antidomain(antidomain(sK1)),coantidomain(coantidomain(zero))) != antidomain(antidomain(sK1)),
inference(superposition,[status(thm)],[c_58,c_84]) ).
tcf(c_353,plain,
coantidomain(one) = zero,
inference(superposition,[status(thm)],[c_55,c_63]) ).
tcf(c_355,plain,
! [X0: $i] : addition(zero,X0) = X0,
inference(superposition,[status(thm)],[c_51,c_49]) ).
tcf(c_388,plain,
addition(zero,coantidomain(zero)) = one,
inference(superposition,[status(thm)],[c_353,c_83]) ).
tcf(c_400,plain,
coantidomain(zero) = one,
inference(superposition,[status(thm)],[c_355,c_388]) ).
tcf(c_567,plain,
addition(antidomain(antidomain(sK1)),coantidomain(one)) != antidomain(antidomain(sK1)),
inference(superposition,[status(thm)],[c_400,c_350]) ).
tcf(c_573,plain,
coantidomain(one) = zero,
inference(superposition,[status(thm)],[c_63,c_55]) ).
tcf(c_581,plain,
addition(antidomain(antidomain(sK1)),zero) != antidomain(antidomain(sK1)),
inference(superposition,[status(thm)],[c_573,c_567]) ).
tcf(c_582,plain,
addition(zero,antidomain(antidomain(sK1))) != antidomain(antidomain(sK1)),
inference(theory_normalisation,[status(thm)],[c_581,c_50,c_49]) ).
tcf(c_593,plain,
! [X0: $i] : addition(zero,X0) = X0,
inference(superposition,[status(thm)],[c_49,c_51]) ).
tcf(c_606,plain,
$false,
inference(superposition,[status(thm)],[c_593,c_582]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE119+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 : n013.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
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Wed Sep 23 18:59:21 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.43
% 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...
% 1.13/1.29 % SZS status Started for theBenchmark.p
% 1.13/1.29 % SZS status Theorem for theBenchmark.p
% 1.13/1.29
% 1.13/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.13/1.29
% 1.13/1.29 % ------ iProver source info
% 1.13/1.29
% 1.13/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 1.13/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.13/1.29 % git: non_committed_changes: false
% 1.13/1.29
% 1.13/1.29 % ------ Parsing...
% 1.13/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.13/1.29
% 1.13/1.29 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 1.13/1.29
% 1.13/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.13/1.29
% 1.13/1.29 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 1.13/1.29 % ------ Proving...
% 1.13/1.29 % ------ Problem Properties
% 1.13/1.29
% 1.13/1.29 %
% 1.13/1.29 % clauses 18
% 1.13/1.29 % conjectures 1
% 1.13/1.29 % EPR 0
% 1.13/1.29 % Horn 18
% 1.13/1.29 % unary 18
% 1.13/1.29 % binary 0
% 1.13/1.29 % lits 18
% 1.13/1.29 % lits eq 18
% 1.13/1.29 % fd_pure 0
% 1.13/1.29 % fd_pseudo 0
% 1.13/1.29 % fd_cond 0
% 1.13/1.29 % fd_pseudo_cond 0
% 1.13/1.29 % AC symbols 1
% 1.13/1.29
% 1.13/1.29 % ------ Input Options Time Limit: Unbounded
% 1.13/1.29
% 1.13/1.29
% 1.13/1.29 % ------
% 1.13/1.29 % Current options:
% 1.13/1.29 % ------
% 1.13/1.29
% 1.13/1.29
% 1.13/1.29 %
% 1.13/1.29
% 1.13/1.29 % ------ Proving...
% 1.13/1.29 %
% 1.13/1.29
% 1.13/1.29 % SZS status Theorem for theBenchmark.p
% 1.13/1.29
% 1.13/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.13/1.29
% 1.13/1.29
%------------------------------------------------------------------------------