%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : HEN010-6 : 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 : n016.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 3.98s 1.30s
% Output : CNFRefutation 3.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 13
% Syntax : Number of formulae : 39 ( 27 unt; 3 def)
% Number of atoms : 98 ( 22 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 33 ( 18 ~; 15 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 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 : 40 ( 0 sgn 40 !; 0 ?; 22 :)
% 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(f18,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(f19,axiom,
! [X0] : divide(identity,divide(identity,divide(identity,X0))) = divide(identity,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_inversion_equals_three) ).
fof(f20,plain,
! [X0] : divide(identity,X0) = divide(identity,divide(identity,divide(identity,X0))),
inference(reorient_equations,[],[f19]) ).
fof(f21,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_65,plain,
! [X0: $i,X1: $i] :
( ( divide(X0,X1) = zero )
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( less_equal(X0,X1)
| ( divide(X0,X1) != zero ) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] : less_equal(divide(X0,X1),X0),
inference(cnf_transformation,[],[f3]) ).
tcf(c_68,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_69,plain,
! [X0: $i] : less_equal(zero,X0),
inference(cnf_transformation,[],[f5]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ less_equal(X1,X0)
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_71,plain,
! [X0: $i] : less_equal(X0,identity),
inference(cnf_transformation,[],[f7]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i,X2: $i] :
( less_equal(divide(X0,X2),divide(X1,X2))
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_79,plain,
! [X0: $i] : divide(identity,divide(identity,divide(identity,X0))) = divide(identity,X0),
inference(cnf_transformation,[],[f20]) ).
tcf(c_80,negated_conjecture,
divide(divide(identity,a),divide(identity,divide(identity,a))) != divide(identity,a),
inference(cnf_transformation,[],[f21]) ).
tcf(c_203,definition,
iPr_def_10 = divide(identity,a),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_204,definition,
iPr_def_11 = divide(identity,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_205,definition,
iPr_def_12 = divide(iPr_def_10,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_206,negated_conjecture,
iPr_def_12 != iPr_def_10,
inference(demodulation,[status(thm)],[c_80,c_204,c_203,c_205]) ).
tcf(c_470,plain,
less_equal(iPr_def_12,iPr_def_10),
inference(superposition,[status(thm)],[c_205,c_67]) ).
tcf(c_588,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_70]) ).
tcf(c_601,plain,
( less_equal(iPr_def_10,iPr_def_12)
| ( divide(iPr_def_10,iPr_def_12) != zero ) ),
inference(instantiation,[status(thm)],[c_66]) ).
tcf(c_710,plain,
! [X0: $i] :
( less_equal(divide(X0,iPr_def_10),iPr_def_11)
| ~ less_equal(X0,identity) ),
inference(superposition,[status(thm)],[c_204,c_78]) ).
tcf(c_721,plain,
! [X0: $i] : less_equal(divide(X0,iPr_def_10),iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_710,c_71]) ).
tcf(c_825,plain,
divide(identity,divide(identity,iPr_def_10)) = iPr_def_10,
inference(superposition,[status(thm)],[c_203,c_79]) ).
tcf(c_837,plain,
divide(identity,iPr_def_11) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_825,c_204]) ).
tcf(c_916,plain,
! [X0: $i] : divide(divide(X0,iPr_def_10),iPr_def_11) = zero,
inference(superposition,[status(thm)],[c_721,c_65]) ).
tcf(c_1172,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_205,c_68]) ).
tcf(c_1214,plain,
! [X0: $i] : less_equal(divide(divide(X0,iPr_def_11),iPr_def_12),zero),
inference(light_normalisation,[status(thm)],[c_1172,c_916]) ).
tcf(c_1382,plain,
less_equal(divide(iPr_def_10,iPr_def_12),zero),
inference(superposition,[status(thm)],[c_837,c_1214]) ).
tcf(c_1398,plain,
( ( divide(iPr_def_10,iPr_def_12) = zero )
| ~ less_equal(zero,divide(iPr_def_10,iPr_def_12)) ),
inference(superposition,[status(thm)],[c_1382,c_70]) ).
tcf(c_1400,plain,
divide(iPr_def_10,iPr_def_12) = zero,
inference(forward_subsumption_resolution,[status(thm)],[c_1398,c_69]) ).
tcf(c_1403,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1400,c_601,c_588,c_470,c_206]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : HEN010-6 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n016.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 16:21:43 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.42 Running first-order theorem proving
% 0.09/0.42 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
% 0.09/0.43
% 0.09/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.43
% 0.09/0.43 % Detected problem language: tptp
% 0.09/0.44 % Proving...
% 3.98/1.30 % SZS status Started for theBenchmark.p
% 3.98/1.30 % SZS status Unsatisfiable for theBenchmark.p
% 3.98/1.30
% 3.98/1.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.98/1.30
% 3.98/1.30 % ------ iProver source info
% 3.98/1.30
% 3.98/1.30 % git: date: 2026-07-19 20:42:38 +0200
% 3.98/1.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.98/1.30 % git: non_committed_changes: false
% 3.98/1.30
% 3.98/1.30 % ------ Parsing...% successful
% 3.98/1.30
% 3.98/1.30
% 3.98/1.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.98/1.30
% 3.98/1.30 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 3.98/1.30
% 3.98/1.30 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.98/1.30
% 3.98/1.30 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.98/1.30 % ------ Proving...
% 3.98/1.30 % ------ Problem Properties
% 3.98/1.30
% 3.98/1.30 %
% 3.98/1.30 % clauses 19
% 3.98/1.30 % conjectures 1
% 3.98/1.30 % EPR 4
% 3.98/1.30 % Horn 19
% 3.98/1.30 % unary 13
% 3.98/1.30 % binary 5
% 3.98/1.30 % lits 26
% 3.98/1.30 % lits eq 12
% 3.98/1.30 % fd_pure 0
% 3.98/1.30 % fd_pseudo 0
% 3.98/1.30 % fd_cond 0
% 3.98/1.30 % fd_pseudo_cond 1
% 3.98/1.30 % AC symbols 0
% 3.98/1.30
% 3.98/1.30 % ------ Schedule dynamic 5 is on
% 3.98/1.30
% 3.98/1.30 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.98/1.30
% 3.98/1.30
% 3.98/1.30 % ------
% 3.98/1.30 % Current options:
% 3.98/1.30 % ------
% 3.98/1.30
% 3.98/1.30
% 3.98/1.30 %
% 3.98/1.30
% 3.98/1.30 % ------ Proving...
% 3.98/1.30 %
% 3.98/1.30
% 3.98/1.30 % SZS status Unsatisfiable for theBenchmark.p
% 3.98/1.30
% 3.98/1.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.98/1.30
% 3.98/1.30
%------------------------------------------------------------------------------