%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : HEN004-3 : 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 : n002.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 01:37:20 PM UTC 2026
% Result : Unsatisfiable 3.91s 16.31s
% Output : CNFRefutation 3.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 35 ( 26 unt; 1 def)
% Number of atoms : 61 ( 20 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 28 ( 16 ~; 12 |; 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 : 4 ( 2 usr; 2 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 36 ( 0 sgn 36 !; 0 ?; 24 :)
% 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(f3,axiom,
! [X0,X1] : less_equal(divide(X0,X1),X0),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN002-0.ax',quotient_smaller_than_numerator) ).
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,negated_conjecture,
divide(a,zero) != a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_x_divide_zero_is_x) ).
fof(f9,plain,
a != divide(a,zero),
inference(reorient_equations,[],[f8]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( ( divide(X0,X1) = zero )
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( less_equal(X0,X1)
| ( divide(X0,X1) != zero ) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] : less_equal(divide(X0,X1),X0),
inference(cnf_transformation,[],[f3]) ).
tcf(c_60,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_61,plain,
! [X0: $i] : less_equal(zero,X0),
inference(cnf_transformation,[],[f5]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ less_equal(X1,X0)
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_64,negated_conjecture,
divide(a,zero) != a,
inference(cnf_transformation,[],[f9]) ).
tcf(c_129,definition,
iPr_def_10 = divide(a,zero),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_130,negated_conjecture,
iPr_def_10 != a,
inference(demodulation,[status(thm)],[c_64,c_129]) ).
tcf(c_290,plain,
less_equal(iPr_def_10,a),
inference(superposition,[status(thm)],[c_129,c_59]) ).
tcf(c_293,plain,
! [X0: $i,X1: $i] : divide(divide(X0,X1),X0) = zero,
inference(superposition,[status(thm)],[c_59,c_57]) ).
tcf(c_294,plain,
! [X0: $i] : divide(zero,X0) = zero,
inference(superposition,[status(thm)],[c_61,c_57]) ).
tcf(c_322,plain,
! [X0: $i] :
( ( X0 = zero )
| ~ less_equal(X0,zero) ),
inference(superposition,[status(thm)],[c_61,c_62]) ).
tcf(c_341,plain,
! [X0: $i,X1: $i] : less_equal(divide(divide(X0,X0),divide(X1,X0)),zero),
inference(superposition,[status(thm)],[c_293,c_60]) ).
tcf(c_342,plain,
! [X0: $i] : less_equal(divide(divide(a,X0),divide(zero,X0)),divide(iPr_def_10,X0)),
inference(superposition,[status(thm)],[c_129,c_60]) ).
tcf(c_350,plain,
! [X0: $i] : less_equal(divide(divide(a,X0),zero),divide(iPr_def_10,X0)),
inference(light_normalisation,[status(thm)],[c_342,c_294]) ).
tcf(c_365,plain,
( ( iPr_def_10 = a )
| ~ less_equal(iPr_def_10,a)
| ~ less_equal(a,iPr_def_10) ),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_368,plain,
( less_equal(a,iPr_def_10)
| ( divide(a,iPr_def_10) != zero ) ),
inference(instantiation,[status(thm)],[c_58]) ).
tcf(c_427,plain,
! [X0: $i] : less_equal(divide(divide(X0,X0),zero),zero),
inference(superposition,[status(thm)],[c_293,c_341]) ).
tcf(c_445,plain,
! [X0: $i] : divide(divide(X0,X0),zero) = zero,
inference(superposition,[status(thm)],[c_427,c_322]) ).
tcf(c_450,plain,
! [X0: $i] : less_equal(divide(X0,X0),zero),
inference(superposition,[status(thm)],[c_445,c_58]) ).
tcf(c_472,plain,
! [X0: $i] : divide(X0,X0) = zero,
inference(superposition,[status(thm)],[c_450,c_322]) ).
tcf(c_645,plain,
less_equal(divide(divide(a,iPr_def_10),zero),zero),
inference(superposition,[status(thm)],[c_472,c_350]) ).
tcf(c_700,plain,
divide(divide(a,iPr_def_10),zero) = zero,
inference(superposition,[status(thm)],[c_645,c_322]) ).
tcf(c_706,plain,
less_equal(divide(a,iPr_def_10),zero),
inference(superposition,[status(thm)],[c_700,c_58]) ).
tcf(c_731,plain,
divide(a,iPr_def_10) = zero,
inference(superposition,[status(thm)],[c_706,c_322]) ).
tcf(c_734,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_731,c_368,c_365,c_290,c_130]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN004-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/15.39 % Computer : n002.cluster.edu
% 0.11/15.39 % Model : x86_64 x86_64
% 0.11/15.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/15.39 % Memory : 8046.5625MB
% 0.11/15.39 % OS : Linux 6.8.0-71-generic
% 0.11/15.39 % CPULimit : 300
% 0.11/15.39 % WCLimit : 300
% 0.11/15.40 % DateTime : Wed Sep 23 16:13:35 UTC 2026
% 0.15/15.40 % CPUTime :
% 0.15/15.40 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/15.44 Running first-order theorem proving
% 0.15/15.44 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
% 0.15/15.45
% 0.15/15.45 % ======== iProver multi-core TPTP/SMT =========
% 0.15/15.45
% 0.15/15.45 % Detected problem language: tptp
% 0.15/15.46 % Proving...
% 3.91/16.31 % SZS status Started for theBenchmark.p
% 3.91/16.31 % SZS status Unsatisfiable for theBenchmark.p
% 3.91/16.31
% 3.91/16.31 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.91/16.31
% 3.91/16.31 % ------ iProver source info
% 3.91/16.31
% 3.91/16.31 % git: date: 2026-07-19 20:42:38 +0200
% 3.91/16.31 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.91/16.31 % git: non_committed_changes: false
% 3.91/16.31
% 3.91/16.31 % ------ Parsing...% successful
% 3.91/16.31
% 3.91/16.31
% 3.91/16.31 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.91/16.31
% 3.91/16.31 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 3.91/16.31
% 3.91/16.31 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.91/16.31
% 3.91/16.31 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.91/16.31 % ------ Proving...
% 3.91/16.31 % ------ Problem Properties
% 3.91/16.31
% 3.91/16.31 %
% 3.91/16.31 % clauses 9
% 3.91/16.31 % conjectures 1
% 3.91/16.31 % EPR 4
% 3.91/16.31 % Horn 9
% 3.91/16.31 % unary 6
% 3.91/16.31 % binary 2
% 3.91/16.31 % lits 13
% 3.91/16.31 % lits eq 5
% 3.91/16.31 % fd_pure 0
% 3.91/16.31 % fd_pseudo 0
% 3.91/16.31 % fd_cond 0
% 3.91/16.31 % fd_pseudo_cond 1
% 3.91/16.31 % AC symbols 0
% 3.91/16.31
% 3.91/16.31 % ------ Schedule dynamic 5 is on
% 3.91/16.31
% 3.91/16.31 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.91/16.31
% 3.91/16.31
% 3.91/16.31 % ------
% 3.91/16.31 % Current options:
% 3.91/16.31 % ------
% 3.91/16.31
% 3.91/16.31
% 3.91/16.31 %
% 3.91/16.31
% 3.91/16.31 % ------ Proving...
% 3.91/16.31 %
% 3.91/16.31
% 3.91/16.31 % SZS status Unsatisfiable for theBenchmark.p
% 3.91/16.31
% 3.91/16.31 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.91/16.31
% 3.91/16.31
%------------------------------------------------------------------------------