%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : HEN008-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/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 01:37:23 PM UTC 2026
% Result : Unsatisfiable 3.49s 1.30s
% Output : CNFRefutation 3.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 27 ( 19 unt; 2 def)
% Number of atoms : 50 ( 13 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 23 ( 13 ~; 10 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 24 ( 0 sgn 24 !; 0 ?; 14 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( divide(X0,X1) = zero
| ~ less_equal(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN002-0.ax',quotient_less_equal1) ).
fof(f2,axiom,
! [X0,X1] :
( less_equal(X0,X1)
| divide(X0,X1) != zero ),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN002-0.ax',quotient_less_equal2) ).
fof(f4,axiom,
! [X2,X0,X1] : less_equal(divide(divide(X0,X1),divide(X2,X1)),divide(divide(X0,X2),X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN002-0.ax',quotient_property) ).
fof(f5,axiom,
! [X0] : less_equal(zero,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN002-0.ax',zero_is_smallest) ).
fof(f6,axiom,
! [X0,X1] :
( X0 = X1
| ~ less_equal(X1,X0)
| ~ less_equal(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN002-0.ax',less_equal_and_equal) ).
fof(f8,axiom,
less_equal(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_LE_b) ).
fof(f9,negated_conjecture,
~ less_equal(divide(a,c),divide(b,c)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_divide_c_LE_b_divide_c) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( ( divide(X0,X1) = zero )
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( less_equal(X0,X1)
| ( divide(X0,X1) != zero ) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i] : less_equal(divide(divide(X0,X1),divide(X2,X1)),divide(divide(X0,X2),X1)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_62,plain,
! [X0: $i] : less_equal(zero,X0),
inference(cnf_transformation,[],[f5]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ less_equal(X1,X0)
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_65,plain,
less_equal(a,b),
inference(cnf_transformation,[],[f8]) ).
tcf(c_66,negated_conjecture,
~ less_equal(divide(a,c),divide(b,c)),
inference(cnf_transformation,[],[f9]) ).
tcf(c_134,definition,
iPr_def_10 = divide(a,c),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_135,definition,
iPr_def_11 = divide(b,c),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_136,negated_conjecture,
~ less_equal(iPr_def_10,iPr_def_11),
inference(demodulation,[status(thm)],[c_66,c_135,c_134]) ).
tcf(c_312,plain,
divide(a,b) = zero,
inference(superposition,[status(thm)],[c_65,c_58]) ).
tcf(c_314,plain,
! [X0: $i] : divide(zero,X0) = zero,
inference(superposition,[status(thm)],[c_62,c_58]) ).
tcf(c_339,plain,
! [X0: $i] :
( ( X0 = zero )
| ~ less_equal(X0,zero) ),
inference(superposition,[status(thm)],[c_62,c_63]) ).
tcf(c_356,plain,
( less_equal(iPr_def_10,iPr_def_11)
| ( divide(iPr_def_10,iPr_def_11) != zero ) ),
inference(instantiation,[status(thm)],[c_59]) ).
tcf(c_391,plain,
! [X0: $i] : less_equal(divide(divide(a,X0),divide(b,X0)),divide(zero,X0)),
inference(superposition,[status(thm)],[c_312,c_61]) ).
tcf(c_393,plain,
! [X0: $i] : less_equal(divide(divide(a,X0),divide(b,X0)),zero),
inference(light_normalisation,[status(thm)],[c_391,c_314]) ).
tcf(c_543,plain,
less_equal(divide(divide(a,c),iPr_def_11),zero),
inference(superposition,[status(thm)],[c_135,c_393]) ).
tcf(c_548,plain,
less_equal(divide(iPr_def_10,iPr_def_11),zero),
inference(light_normalisation,[status(thm)],[c_543,c_134]) ).
tcf(c_555,plain,
divide(iPr_def_10,iPr_def_11) = zero,
inference(superposition,[status(thm)],[c_548,c_339]) ).
tcf(c_557,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_555,c_356,c_136]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN008-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.38 % Computer : n013.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 16:13:41 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.43 Running first-order theorem proving
% 0.10/0.43 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
% 0.10/0.44
% 0.10/0.44 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.44
% 0.10/0.44 % Detected problem language: tptp
% 0.10/0.45 % Proving...
% 3.49/1.30 % SZS status Started for theBenchmark.p
% 3.49/1.30 % SZS status Unsatisfiable for theBenchmark.p
% 3.49/1.30
% 3.49/1.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.49/1.30
% 3.49/1.30 % ------ iProver source info
% 3.49/1.30
% 3.49/1.30 % git: date: 2026-07-19 20:42:38 +0200
% 3.49/1.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.49/1.30 % git: non_committed_changes: false
% 3.49/1.30
% 3.49/1.30 % ------ Parsing...% successful
% 3.49/1.30
% 3.49/1.30
% 3.49/1.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.49/1.30
% 3.49/1.30 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 3.49/1.30
% 3.49/1.30 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.49/1.30
% 3.49/1.30 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.49/1.30 % ------ Proving...
% 3.49/1.30 % ------ Problem Properties
% 3.49/1.30
% 3.49/1.30 %
% 3.49/1.30 % clauses 11
% 3.49/1.30 % conjectures 1
% 3.49/1.30 % EPR 5
% 3.49/1.30 % Horn 11
% 3.49/1.30 % unary 8
% 3.49/1.30 % binary 2
% 3.49/1.30 % lits 15
% 3.49/1.30 % lits eq 5
% 3.49/1.30 % fd_pure 0
% 3.49/1.30 % fd_pseudo 0
% 3.49/1.30 % fd_cond 0
% 3.49/1.30 % fd_pseudo_cond 1
% 3.49/1.30 % AC symbols 0
% 3.49/1.30
% 3.49/1.30 % ------ Schedule dynamic 5 is on
% 3.49/1.30
% 3.49/1.30 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.49/1.30
% 3.49/1.30
% 3.49/1.30 % ------
% 3.49/1.30 % Current options:
% 3.49/1.30 % ------
% 3.49/1.30
% 3.49/1.30
% 3.49/1.30 %
% 3.49/1.30
% 3.49/1.30 % ------ Proving...
% 3.49/1.30 %
% 3.49/1.30
% 3.49/1.30 % SZS status Unsatisfiable for theBenchmark.p
% 3.49/1.30
% 3.49/1.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.49/1.31
% 3.49/1.31
%------------------------------------------------------------------------------