%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : HEN010-3 : 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 : n014.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 0.87s 1.29s
% Output : CNFRefutation 0.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 11
% Syntax : Number of formulae : 77 ( 64 unt; 3 def)
% Number of atoms : 190 ( 36 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 36 ( 20 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 2 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 : 63 ( 0 sgn 63 !; 0 ?; 50 :)
% 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(f8,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_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_63,plain,
! [X0: $i] : less_equal(X0,identity),
inference(cnf_transformation,[],[f7]) ).
tcf(c_64,negated_conjecture,
divide(divide(identity,a),divide(identity,divide(identity,a))) != divide(identity,a),
inference(cnf_transformation,[],[f8]) ).
tcf(c_129,definition,
iPr_def_10 = divide(identity,a),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_130,definition,
iPr_def_11 = divide(identity,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_131,definition,
iPr_def_12 = divide(iPr_def_10,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_132,negated_conjecture,
iPr_def_12 != iPr_def_10,
inference(demodulation,[status(thm)],[c_64,c_130,c_129,c_131]) ).
tcf(c_306,plain,
less_equal(iPr_def_12,iPr_def_10),
inference(superposition,[status(thm)],[c_131,c_59]) ).
tcf(c_309,plain,
! [X0: $i,X1: $i] : divide(divide(X0,X1),X0) = zero,
inference(superposition,[status(thm)],[c_59,c_57]) ).
tcf(c_310,plain,
! [X0: $i] : divide(zero,X0) = zero,
inference(superposition,[status(thm)],[c_61,c_57]) ).
tcf(c_311,plain,
! [X0: $i] : divide(X0,identity) = zero,
inference(superposition,[status(thm)],[c_63,c_57]) ).
tcf(c_336,plain,
! [X0: $i] :
( ( X0 = zero )
| ~ less_equal(X0,zero) ),
inference(superposition,[status(thm)],[c_61,c_62]) ).
tcf(c_338,plain,
( ( iPr_def_10 = iPr_def_12 )
| ~ less_equal(iPr_def_10,iPr_def_12) ),
inference(superposition,[status(thm)],[c_306,c_62]) ).
tcf(c_349,plain,
! [X0: $i] : less_equal(divide(iPr_def_10,divide(X0,a)),divide(divide(identity,X0),a)),
inference(superposition,[status(thm)],[c_129,c_60]) ).
tcf(c_351,plain,
! [X0: $i] : less_equal(divide(iPr_def_12,divide(X0,iPr_def_11)),divide(divide(iPr_def_10,X0),iPr_def_11)),
inference(superposition,[status(thm)],[c_131,c_60]) ).
tcf(c_352,plain,
! [X0: $i] : less_equal(divide(divide(X0,a),iPr_def_10),divide(divide(X0,identity),a)),
inference(superposition,[status(thm)],[c_129,c_60]) ).
tcf(c_353,plain,
! [X0: $i] : less_equal(divide(divide(X0,iPr_def_10),iPr_def_11),divide(divide(X0,identity),iPr_def_10)),
inference(superposition,[status(thm)],[c_130,c_60]) ).
tcf(c_360,plain,
! [X0: $i] : less_equal(divide(divide(X0,iPr_def_10),iPr_def_11),divide(zero,iPr_def_10)),
inference(light_normalisation,[status(thm)],[c_353,c_311]) ).
tcf(c_361,plain,
! [X0: $i] : less_equal(divide(divide(X0,a),iPr_def_10),divide(zero,a)),
inference(light_normalisation,[status(thm)],[c_352,c_311]) ).
tcf(c_375,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_62]) ).
tcf(c_390,plain,
! [X0: $i,X1: $i] : less_equal(divide(divide(X0,X1),zero),divide(divide(X0,zero),X1)),
inference(superposition,[status(thm)],[c_310,c_60]) ).
tcf(c_434,plain,
! [X0: $i,X1: $i] : less_equal(divide(divide(X0,X0),divide(X1,X0)),zero),
inference(superposition,[status(thm)],[c_309,c_60]) ).
tcf(c_477,plain,
~ less_equal(iPr_def_10,iPr_def_12),
inference(global_subsumption_just,[status(thm)],[c_338,c_132,c_306,c_375]) ).
tcf(c_479,plain,
! [X0: $i] : less_equal(divide(divide(X0,iPr_def_10),iPr_def_11),zero),
inference(demodulation,[status(thm)],[c_360,c_310]) ).
tcf(c_487,plain,
! [X0: $i] : divide(divide(X0,iPr_def_10),iPr_def_11) = zero,
inference(superposition,[status(thm)],[c_479,c_336]) ).
tcf(c_679,plain,
! [X0: $i] : less_equal(divide(divide(X0,a),iPr_def_10),zero),
inference(demodulation,[status(thm)],[c_361,c_310]) ).
tcf(c_686,plain,
! [X0: $i] : divide(divide(X0,a),iPr_def_10) = zero,
inference(superposition,[status(thm)],[c_679,c_336]) ).
tcf(c_726,plain,
! [X0: $i] : less_equal(divide(X0,iPr_def_10),iPr_def_11),
inference(superposition,[status(thm)],[c_487,c_58]) ).
tcf(c_733,plain,
! [X0: $i] : less_equal(divide(divide(X0,iPr_def_11),divide(iPr_def_10,iPr_def_11)),zero),
inference(superposition,[status(thm)],[c_487,c_60]) ).
tcf(c_734,plain,
! [X0: $i] : less_equal(divide(divide(X0,iPr_def_11),iPr_def_12),zero),
inference(light_normalisation,[status(thm)],[c_733,c_131]) ).
tcf(c_792,plain,
! [X0: $i] : divide(divide(X0,iPr_def_11),iPr_def_12) = zero,
inference(superposition,[status(thm)],[c_734,c_336]) ).
tcf(c_843,plain,
! [X0: $i] : less_equal(divide(X0,a),iPr_def_10),
inference(superposition,[status(thm)],[c_686,c_58]) ).
tcf(c_850,plain,
! [X0: $i] : less_equal(divide(divide(X0,iPr_def_10),divide(a,iPr_def_10)),zero),
inference(superposition,[status(thm)],[c_686,c_60]) ).
tcf(c_887,plain,
! [X0: $i] : less_equal(divide(X0,iPr_def_11),iPr_def_12),
inference(superposition,[status(thm)],[c_792,c_58]) ).
tcf(c_950,plain,
! [X0: $i] : less_equal(divide(divide(X0,X0),zero),zero),
inference(superposition,[status(thm)],[c_309,c_434]) ).
tcf(c_982,plain,
! [X0: $i] : divide(divide(X0,X0),zero) = zero,
inference(superposition,[status(thm)],[c_950,c_336]) ).
tcf(c_993,plain,
! [X0: $i] : less_equal(divide(X0,X0),zero),
inference(superposition,[status(thm)],[c_982,c_58]) ).
tcf(c_1029,plain,
! [X0: $i] : divide(X0,X0) = zero,
inference(superposition,[status(thm)],[c_993,c_336]) ).
tcf(c_1141,plain,
less_equal(divide(iPr_def_11,divide(a,iPr_def_10)),zero),
inference(superposition,[status(thm)],[c_130,c_850]) ).
tcf(c_1154,plain,
divide(iPr_def_11,divide(a,iPr_def_10)) = zero,
inference(superposition,[status(thm)],[c_1141,c_336]) ).
tcf(c_1170,plain,
less_equal(iPr_def_11,divide(a,iPr_def_10)),
inference(superposition,[status(thm)],[c_1154,c_58]) ).
tcf(c_1201,plain,
( ( divide(a,iPr_def_10) = iPr_def_11 )
| ~ less_equal(divide(a,iPr_def_10),iPr_def_11) ),
inference(superposition,[status(thm)],[c_1170,c_62]) ).
tcf(c_1203,plain,
divide(a,iPr_def_10) = iPr_def_11,
inference(forward_subsumption_resolution,[status(thm)],[c_1201,c_726]) ).
tcf(c_1207,plain,
divide(iPr_def_11,a) = zero,
inference(superposition,[status(thm)],[c_1203,c_309]) ).
tcf(c_1421,plain,
less_equal(divide(iPr_def_10,zero),divide(divide(identity,iPr_def_11),a)),
inference(superposition,[status(thm)],[c_1207,c_349]) ).
tcf(c_1807,plain,
less_equal(divide(iPr_def_12,divide(identity,iPr_def_11)),divide(zero,iPr_def_11)),
inference(superposition,[status(thm)],[c_311,c_351]) ).
tcf(c_1833,plain,
less_equal(divide(iPr_def_12,divide(identity,iPr_def_11)),zero),
inference(demodulation,[status(thm)],[c_1807,c_310]) ).
tcf(c_1836,plain,
divide(iPr_def_12,divide(identity,iPr_def_11)) = zero,
inference(superposition,[status(thm)],[c_1833,c_336]) ).
tcf(c_1841,plain,
less_equal(iPr_def_12,divide(identity,iPr_def_11)),
inference(superposition,[status(thm)],[c_1836,c_58]) ).
tcf(c_1867,plain,
( ( divide(identity,iPr_def_11) = iPr_def_12 )
| ~ less_equal(divide(identity,iPr_def_11),iPr_def_12) ),
inference(superposition,[status(thm)],[c_1841,c_62]) ).
tcf(c_1869,plain,
divide(identity,iPr_def_11) = iPr_def_12,
inference(forward_subsumption_resolution,[status(thm)],[c_1867,c_887]) ).
tcf(c_1872,plain,
less_equal(divide(iPr_def_10,zero),divide(iPr_def_12,a)),
inference(demodulation,[status(thm)],[c_1421,c_1869]) ).
tcf(c_2306,plain,
! [X0: $i] : less_equal(divide(divide(X0,divide(X0,zero)),zero),zero),
inference(superposition,[status(thm)],[c_1029,c_390]) ).
tcf(c_2819,plain,
! [X0: $i] : divide(divide(X0,divide(X0,zero)),zero) = zero,
inference(superposition,[status(thm)],[c_2306,c_336]) ).
tcf(c_3882,plain,
! [X0: $i] : less_equal(divide(X0,divide(X0,zero)),zero),
inference(superposition,[status(thm)],[c_2819,c_58]) ).
tcf(c_3955,plain,
! [X0: $i] : divide(X0,divide(X0,zero)) = zero,
inference(superposition,[status(thm)],[c_3882,c_336]) ).
tcf(c_3970,plain,
! [X0: $i] : less_equal(X0,divide(X0,zero)),
inference(superposition,[status(thm)],[c_3955,c_58]) ).
tcf(c_4180,plain,
! [X0: $i] :
( ( divide(X0,zero) = X0 )
| ~ less_equal(divide(X0,zero),X0) ),
inference(superposition,[status(thm)],[c_3970,c_62]) ).
tcf(c_4184,plain,
! [X0: $i] : divide(X0,zero) = X0,
inference(forward_subsumption_resolution,[status(thm)],[c_4180,c_59]) ).
tcf(c_4198,plain,
less_equal(iPr_def_10,divide(iPr_def_12,a)),
inference(demodulation,[status(thm)],[c_1872,c_4184]) ).
tcf(c_4219,plain,
( ( divide(iPr_def_12,a) = iPr_def_10 )
| ~ less_equal(divide(iPr_def_12,a),iPr_def_10) ),
inference(superposition,[status(thm)],[c_4198,c_62]) ).
tcf(c_4221,plain,
divide(iPr_def_12,a) = iPr_def_10,
inference(forward_subsumption_resolution,[status(thm)],[c_4219,c_843]) ).
tcf(c_4296,plain,
less_equal(iPr_def_10,iPr_def_12),
inference(superposition,[status(thm)],[c_4221,c_59]) ).
tcf(c_4308,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_4296,c_477]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN010-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n014.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Wed Sep 23 16:16:33 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.39 Running first-order theorem proving
% 0.10/0.39 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
% 0.10/0.41
% 0.10/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.41
% 0.10/0.41 % Detected problem language: tptp
% 0.10/0.42 % Proving...
% 0.87/1.29 % SZS status Started for theBenchmark.p
% 0.87/1.29 % SZS status Unsatisfiable for theBenchmark.p
% 0.87/1.29
% 0.87/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.87/1.29
% 0.87/1.29 % ------ iProver source info
% 0.87/1.29
% 0.87/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 0.87/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.87/1.29 % git: non_committed_changes: false
% 0.87/1.29
% 0.87/1.29 % ------ Parsing...% successful
% 0.87/1.29
% 0.87/1.29
% 0.87/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.87/1.29
% 0.87/1.29 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 0.87/1.29
% 0.87/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.87/1.29
% 0.87/1.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.87/1.29 % ------ Proving...
% 0.87/1.29 % ------ Problem Properties
% 0.87/1.29
% 0.87/1.29 %
% 0.87/1.29 % clauses 11
% 0.87/1.29 % conjectures 1
% 0.87/1.29 % EPR 4
% 0.87/1.29 % Horn 11
% 0.87/1.29 % unary 8
% 0.87/1.29 % binary 2
% 0.87/1.29 % lits 15
% 0.87/1.29 % lits eq 7
% 0.87/1.29 % fd_pure 0
% 0.87/1.29 % fd_pseudo 0
% 0.87/1.29 % fd_cond 0
% 0.87/1.29 % fd_pseudo_cond 1
% 0.87/1.29 % AC symbols 0
% 0.87/1.29
% 0.87/1.29 % ------ Schedule dynamic 5 is on
% 0.87/1.29
% 0.87/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.87/1.29
% 0.87/1.29
% 0.87/1.29 % ------
% 0.87/1.29 % Current options:
% 0.87/1.29 % ------
% 0.87/1.29
% 0.87/1.29
% 0.87/1.29 %
% 0.87/1.29
% 0.87/1.29 % ------ Proving...
% 0.87/1.29 %
% 0.87/1.29
% 0.87/1.29 % SZS status Unsatisfiable for theBenchmark.p
% 0.87/1.29
% 0.87/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.87/1.29
% 0.87/1.29
%------------------------------------------------------------------------------