%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : HEN010-4 : TPTP v9.3.1. Released v1.0.0.
% 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 01:37:25 PM UTC 2026
% Result : Unsatisfiable 0.85s 1.28s
% Output : CNFRefutation 0.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 14
% Syntax : Number of formulae : 43 ( 28 unt; 3 def)
% Number of atoms : 107 ( 22 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 43 ( 23 ~; 20 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 52 ( 0 sgn 52 !; 0 ?; 31 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( divide(X0,X1) = zero
| ~ less_equal(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN002-0.ax',quotient_less_equal1) ).
fof(f2,axiom,
! [X0,X1] :
( less_equal(X0,X1)
| divide(X0,X1) != zero ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN002-0.ax',quotient_less_equal2) ).
fof(f3,axiom,
! [X0,X1] : less_equal(divide(X0,X1),X0),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/HEN002-0.ax',quotient_property) ).
fof(f5,axiom,
! [X0] : less_equal(zero,X0),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/HEN002-0.ax',less_equal_and_equal) ).
fof(f7,axiom,
! [X0] : less_equal(X0,identity),
file('/export/starexec/sandbox/benchmark/Axioms/HEN002-0.ax',identity_is_largest) ).
fof(f16,axiom,
! [X2,X0,X1] :
( less_equal(X0,X2)
| ~ less_equal(X1,X2)
| ~ less_equal(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_less_equal) ).
fof(f19,axiom,
! [X2,X0,X1] :
( less_equal(divide(X0,X2),divide(X1,X2))
| ~ less_equal(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',property_of_divide3) ).
fof(f20,axiom,
! [X0] : divide(identity,divide(identity,divide(identity,X0))) = divide(identity,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_inversion_equals_three) ).
fof(f21,plain,
! [X0] : divide(identity,X0) = divide(identity,divide(identity,divide(identity,X0))),
inference(reorient_equations,[],[f20]) ).
fof(f22,negated_conjecture,
divide(identity,a) != divide(divide(identity,a),divide(identity,divide(identity,a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_property_of_inversion) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( ( divide(X0,X1) = zero )
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] :
( less_equal(X0,X1)
| ( divide(X0,X1) != zero ) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] : less_equal(divide(X0,X1),X0),
inference(cnf_transformation,[],[f3]) ).
tcf(c_69,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_70,plain,
! [X0: $i] : less_equal(zero,X0),
inference(cnf_transformation,[],[f5]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ less_equal(X1,X0)
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_72,plain,
! [X0: $i] : less_equal(X0,identity),
inference(cnf_transformation,[],[f7]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i,X2: $i] :
( less_equal(X0,X2)
| ~ less_equal(X1,X2)
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i,X2: $i] :
( less_equal(divide(X0,X2),divide(X1,X2))
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_81,plain,
! [X0: $i] : divide(identity,divide(identity,divide(identity,X0))) = divide(identity,X0),
inference(cnf_transformation,[],[f21]) ).
tcf(c_82,negated_conjecture,
divide(divide(identity,a),divide(identity,divide(identity,a))) != divide(identity,a),
inference(cnf_transformation,[],[f22]) ).
tcf(c_219,definition,
iPr_def_10 = divide(identity,a),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_220,definition,
iPr_def_11 = divide(identity,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_221,definition,
iPr_def_12 = divide(iPr_def_10,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_222,negated_conjecture,
iPr_def_12 != iPr_def_10,
inference(demodulation,[status(thm)],[c_82,c_220,c_219,c_221]) ).
tcf(c_500,plain,
less_equal(iPr_def_12,iPr_def_10),
inference(superposition,[status(thm)],[c_221,c_68]) ).
tcf(c_591,plain,
divide(identity,divide(identity,iPr_def_10)) = iPr_def_10,
inference(superposition,[status(thm)],[c_219,c_81]) ).
tcf(c_596,plain,
divide(identity,iPr_def_11) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_591,c_220]) ).
tcf(c_640,plain,
( ( iPr_def_12 = iPr_def_10 )
| ~ less_equal(iPr_def_12,iPr_def_10)
| ~ less_equal(iPr_def_10,iPr_def_12) ),
inference(instantiation,[status(thm)],[c_71]) ).
tcf(c_717,plain,
( less_equal(iPr_def_10,iPr_def_12)
| ( divide(iPr_def_10,iPr_def_12) != zero ) ),
inference(instantiation,[status(thm)],[c_67]) ).
tcf(c_754,plain,
! [X0: $i] :
( less_equal(divide(X0,iPr_def_10),iPr_def_11)
| ~ less_equal(X0,identity) ),
inference(superposition,[status(thm)],[c_220,c_80]) ).
tcf(c_765,plain,
! [X0: $i] : less_equal(divide(X0,iPr_def_10),iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_754,c_72]) ).
tcf(c_838,plain,
! [X0: $i] :
( ( X0 = zero )
| ~ less_equal(X0,zero) ),
inference(superposition,[status(thm)],[c_70,c_71]) ).
tcf(c_893,plain,
! [X0: $i] : divide(divide(X0,iPr_def_10),iPr_def_11) = zero,
inference(superposition,[status(thm)],[c_765,c_66]) ).
tcf(c_1203,plain,
! [X0: $i] : less_equal(divide(divide(X0,iPr_def_11),iPr_def_12),divide(divide(X0,iPr_def_10),iPr_def_11)),
inference(superposition,[status(thm)],[c_221,c_69]) ).
tcf(c_1241,plain,
! [X0: $i] : less_equal(divide(divide(X0,iPr_def_11),iPr_def_12),zero),
inference(light_normalisation,[status(thm)],[c_1203,c_893]) ).
tcf(c_1487,plain,
! [X0: $i,X1: $i] :
( less_equal(divide(divide(X1,iPr_def_11),iPr_def_12),X0)
| ~ less_equal(zero,X0) ),
inference(superposition,[status(thm)],[c_1241,c_77]) ).
tcf(c_1490,plain,
! [X0: $i,X1: $i] : less_equal(divide(divide(X0,iPr_def_11),iPr_def_12),X1),
inference(forward_subsumption_resolution,[status(thm)],[c_1487,c_70]) ).
tcf(c_1498,plain,
! [X0: $i] : less_equal(divide(iPr_def_10,iPr_def_12),X0),
inference(superposition,[status(thm)],[c_596,c_1490]) ).
tcf(c_1565,plain,
divide(iPr_def_10,iPr_def_12) = zero,
inference(superposition,[status(thm)],[c_1498,c_838]) ).
tcf(c_1570,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1565,c_717,c_640,c_500,c_222]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN010-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n009.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Wed Sep 23 16:16:59 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 0.85/1.28 % SZS status Started for theBenchmark.p
% 0.85/1.28 % SZS status Unsatisfiable for theBenchmark.p
% 0.85/1.28
% 0.85/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.85/1.28
% 0.85/1.28 % ------ iProver source info
% 0.85/1.28
% 0.85/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 0.85/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.85/1.28 % git: non_committed_changes: false
% 0.85/1.28
% 0.85/1.28 % ------ Parsing...% successful
% 0.85/1.28
% 0.85/1.28
% 0.85/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.85/1.28
% 0.85/1.28 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 0.85/1.28
% 0.85/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.85/1.28
% 0.85/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.85/1.28 % ------ Proving...
% 0.85/1.28 % ------ Problem Properties
% 0.85/1.28
% 0.85/1.28 %
% 0.85/1.28 % clauses 20
% 0.85/1.28 % conjectures 1
% 0.85/1.28 % EPR 5
% 0.85/1.28 % Horn 20
% 0.85/1.28 % unary 13
% 0.85/1.28 % binary 5
% 0.85/1.28 % lits 29
% 0.85/1.28 % lits eq 12
% 0.85/1.28 % fd_pure 0
% 0.85/1.28 % fd_pseudo 0
% 0.85/1.28 % fd_cond 0
% 0.85/1.28 % fd_pseudo_cond 1
% 0.85/1.28 % AC symbols 0
% 0.85/1.28
% 0.85/1.28 % ------ Schedule dynamic 5 is on
% 0.85/1.28
% 0.85/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.85/1.28
% 0.85/1.28
% 0.85/1.28 % ------
% 0.85/1.28 % Current options:
% 0.85/1.28 % ------
% 0.85/1.28
% 0.85/1.28
% 0.85/1.28 %
% 0.85/1.28
% 0.85/1.28 % ------ Proving...
% 0.85/1.28 %
% 0.85/1.28
% 0.85/1.28 % SZS status Unsatisfiable for theBenchmark.p
% 0.85/1.28
% 0.85/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.85/1.28
% 0.85/1.28
%------------------------------------------------------------------------------