%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : HEN010-5 : TPTP v9.3.1. Bugfixed v1.2.1.
% 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 0.92s 1.21s
% Output : CNFRefutation 0.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 12
% Syntax : Number of formulae : 65 ( 45 unt; 3 def)
% Number of atoms : 162 ( 91 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 58 ( 31 ~; 27 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 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 : 5 ( 3 usr; 4 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 81 ( 0 sgn 81 !; 0 ?; 47 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : divide(divide(X0,X1),X0) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/HEN003-0.ax',quotient_smaller_than_numerator) ).
fof(f2,axiom,
! [X2,X0,X1] : divide(divide(divide(X0,X1),divide(X2,X1)),divide(divide(X0,X2),X1)) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/HEN003-0.ax',quotient_property) ).
fof(f3,plain,
! [X2,X0,X1] : zero = divide(divide(divide(X0,X1),divide(X2,X1)),divide(divide(X0,X2),X1)),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X0] : divide(zero,X0) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/HEN003-0.ax',zero_is_smallest) ).
fof(f5,plain,
! [X0] : zero = divide(zero,X0),
inference(reorient_equations,[],[f4]) ).
fof(f6,axiom,
! [X0,X1] :
( X0 = X1
| divide(X1,X0) != zero
| divide(X0,X1) != zero ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN003-0.ax',divide_and_equal) ).
fof(f7,plain,
! [X0,X1] :
( X0 = X1
| zero != divide(X1,X0)
| divide(X0,X1) != zero ),
inference(reorient_equations,[],[f6]) ).
fof(f8,axiom,
! [X0] : divide(X0,identity) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/HEN003-0.ax',identity_is_largest) ).
fof(f9,plain,
! [X0] : zero = divide(X0,identity),
inference(reorient_equations,[],[f8]) ).
fof(f10,axiom,
! [X2,X0,X1] :
( divide(X0,X2) = zero
| divide(X1,X2) != zero
| divide(X0,X1) != zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_divide_to_zero) ).
fof(f11,plain,
! [X2,X0,X1] :
( zero = divide(X0,X2)
| zero != divide(X1,X2)
| divide(X0,X1) != zero ),
inference(reorient_equations,[],[f10]) ).
fof(f12,axiom,
! [X2,X0,X1] :
( divide(divide(X0,X2),X1) = zero
| divide(divide(X0,X1),X2) != zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',property_of_divide1) ).
fof(f13,plain,
! [X2,X0,X1] :
( zero = divide(divide(X0,X2),X1)
| zero != divide(divide(X0,X1),X2) ),
inference(reorient_equations,[],[f12]) ).
fof(f14,axiom,
! [X2,X0,X1] :
( divide(divide(X0,X2),divide(X1,X2)) = zero
| divide(X0,X1) != zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',property_of_divide3) ).
fof(f15,plain,
! [X2,X0,X1] :
( zero = divide(divide(X0,X2),divide(X1,X2))
| divide(X0,X1) != zero ),
inference(reorient_equations,[],[f14]) ).
fof(f16,negated_conjecture,
divide(identity,a) != divide(divide(identity,a),divide(identity,divide(identity,a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] : divide(divide(X0,X1),X0) = zero,
inference(cnf_transformation,[],[f1]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] : divide(divide(divide(X0,X1),divide(X2,X1)),divide(divide(X0,X2),X1)) = zero,
inference(cnf_transformation,[],[f3]) ).
tcf(c_60,plain,
! [X0: $i] : divide(zero,X0) = zero,
inference(cnf_transformation,[],[f5]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( divide(X1,X0) != zero )
| ( divide(X0,X1) != zero ) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_62,plain,
! [X0: $i] : divide(X0,identity) = zero,
inference(cnf_transformation,[],[f9]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( divide(X0,X2) = zero )
| ( divide(X1,X2) != zero )
| ( divide(X0,X1) != zero ) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( divide(divide(X0,X2),X1) = zero )
| ( divide(divide(X0,X1),X2) != zero ) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( divide(divide(X0,X2),divide(X1,X2)) = zero )
| ( divide(X0,X1) != zero ) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_66,negated_conjecture,
divide(divide(identity,a),divide(identity,divide(identity,a))) != divide(identity,a),
inference(cnf_transformation,[],[f16]) ).
tcf(c_124,definition,
iPr_def_10 = divide(identity,a),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_125,definition,
iPr_def_11 = divide(identity,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_126,definition,
iPr_def_12 = divide(iPr_def_10,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_127,negated_conjecture,
iPr_def_12 != iPr_def_10,
inference(demodulation,[status(thm)],[c_66,c_125,c_124,c_126]) ).
tcf(c_188,plain,
divide(iPr_def_12,iPr_def_10) = zero,
inference(superposition,[status(thm)],[c_126,c_58]) ).
tcf(c_192,plain,
! [X0: $i] : divide(divide(iPr_def_10,divide(X0,a)),divide(divide(identity,X0),a)) = zero,
inference(superposition,[status(thm)],[c_124,c_59]) ).
tcf(c_259,plain,
( ( iPr_def_12 = iPr_def_10 )
| ( divide(iPr_def_12,iPr_def_10) != zero )
| ( divide(iPr_def_10,iPr_def_12) != zero ) ),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_273,plain,
! [X0: $i,X1: $i] : divide(divide(X0,X0),X1) = zero,
inference(superposition,[status(thm)],[c_58,c_64]) ).
tcf(c_283,plain,
! [X0: $i] :
( ( divide(divide(iPr_def_12,X0),iPr_def_10) = zero )
| ( divide(zero,X0) != zero ) ),
inference(superposition,[status(thm)],[c_188,c_64]) ).
tcf(c_285,plain,
! [X0: $i] : divide(divide(iPr_def_12,X0),iPr_def_10) = zero,
inference(ground_joinability,[status(thm)],[c_283,c_60]) ).
tcf(c_319,plain,
! [X0: $i,X1: $i] : divide(divide(X0,X1),divide(identity,X1)) = zero,
inference(superposition,[status(thm)],[c_62,c_65]) ).
tcf(c_356,plain,
! [X0: $i] :
( ( X0 = zero )
| ( divide(X0,zero) != zero ) ),
inference(superposition,[status(thm)],[c_60,c_61]) ).
tcf(c_360,plain,
( ( iPr_def_10 = iPr_def_12 )
| ( divide(iPr_def_10,iPr_def_12) != zero ) ),
inference(superposition,[status(thm)],[c_188,c_61]) ).
tcf(c_609,plain,
divide(iPr_def_12,divide(identity,iPr_def_11)) = zero,
inference(superposition,[status(thm)],[c_126,c_319]) ).
tcf(c_615,plain,
! [X0: $i] : divide(divide(X0,a),iPr_def_10) = zero,
inference(superposition,[status(thm)],[c_124,c_319]) ).
tcf(c_617,plain,
! [X0: $i] : divide(divide(X0,iPr_def_10),iPr_def_11) = zero,
inference(superposition,[status(thm)],[c_125,c_319]) ).
tcf(c_737,plain,
! [X0: $i] : divide(divide(iPr_def_12,X0),divide(divide(identity,iPr_def_11),X0)) = zero,
inference(superposition,[status(thm)],[c_609,c_65]) ).
tcf(c_771,plain,
! [X0: $i] : divide(divide(X0,iPr_def_10),a) = zero,
inference(superposition,[status(thm)],[c_615,c_64]) ).
tcf(c_819,plain,
! [X0: $i] : divide(divide(divide(X0,iPr_def_11),divide(iPr_def_10,iPr_def_11)),zero) = zero,
inference(superposition,[status(thm)],[c_617,c_59]) ).
tcf(c_822,plain,
! [X0: $i] : divide(divide(divide(X0,iPr_def_11),iPr_def_12),zero) = zero,
inference(light_normalisation,[status(thm)],[c_819,c_126]) ).
tcf(c_845,plain,
divide(iPr_def_11,a) = zero,
inference(superposition,[status(thm)],[c_125,c_771]) ).
tcf(c_1607,plain,
! [X0: $i,X1: $i] :
( ( divide(divide(divide(X1,iPr_def_11),iPr_def_12),X0) = zero )
| ( divide(zero,X0) != zero ) ),
inference(superposition,[status(thm)],[c_822,c_63]) ).
tcf(c_1620,plain,
! [X0: $i,X1: $i] : divide(divide(divide(X0,iPr_def_11),iPr_def_12),X1) = zero,
inference(ground_joinability,[status(thm)],[c_1607,c_60]) ).
tcf(c_3595,plain,
! [X0: $i] : divide(X0,X0) = zero,
inference(superposition,[status(thm)],[c_273,c_356]) ).
tcf(c_3600,plain,
! [X0: $i] : divide(divide(X0,iPr_def_11),iPr_def_12) = zero,
inference(superposition,[status(thm)],[c_1620,c_356]) ).
tcf(c_3638,plain,
! [X0: $i,X1: $i] : divide(divide(X0,divide(X0,X1)),X1) = zero,
inference(superposition,[status(thm)],[c_3595,c_64]) ).
tcf(c_4009,plain,
! [X0: $i] : divide(X0,divide(X0,zero)) = zero,
inference(superposition,[status(thm)],[c_3638,c_356]) ).
tcf(c_4212,plain,
divide(iPr_def_10,iPr_def_12) != zero,
inference(global_subsumption_just,[status(thm)],[c_360,c_127,c_188,c_259]) ).
tcf(c_4336,plain,
! [X0: $i,X1: $i] : divide(divide(divide(X0,iPr_def_11),X1),divide(iPr_def_12,X1)) = zero,
inference(superposition,[status(thm)],[c_3600,c_65]) ).
tcf(c_5033,plain,
! [X0: $i] :
( ( divide(X0,zero) = X0 )
| ( divide(divide(X0,zero),X0) != zero ) ),
inference(superposition,[status(thm)],[c_4009,c_61]) ).
tcf(c_5075,plain,
! [X0: $i] : divide(X0,zero) = X0,
inference(ground_joinability,[status(thm)],[c_5033,c_58]) ).
tcf(c_6973,plain,
! [X0: $i] :
( ( divide(divide(identity,iPr_def_11),X0) = divide(iPr_def_12,X0) )
| ( divide(divide(divide(identity,iPr_def_11),X0),divide(iPr_def_12,X0)) != zero ) ),
inference(superposition,[status(thm)],[c_737,c_61]) ).
tcf(c_7001,plain,
! [X0: $i] : divide(divide(identity,iPr_def_11),X0) = divide(iPr_def_12,X0),
inference(ground_joinability,[status(thm)],[c_6973,c_4336]) ).
tcf(c_7072,plain,
divide(divide(iPr_def_10,divide(iPr_def_11,a)),divide(iPr_def_12,a)) = zero,
inference(superposition,[status(thm)],[c_7001,c_192]) ).
tcf(c_7102,plain,
divide(divide(iPr_def_10,zero),divide(iPr_def_12,a)) = zero,
inference(light_normalisation,[status(thm)],[c_7072,c_845]) ).
tcf(c_7326,plain,
divide(iPr_def_10,divide(iPr_def_12,a)) = zero,
inference(demodulation,[status(thm)],[c_7102,c_5075]) ).
tcf(c_7334,plain,
( ( divide(iPr_def_12,a) = iPr_def_10 )
| ( divide(divide(iPr_def_12,a),iPr_def_10) != zero ) ),
inference(superposition,[status(thm)],[c_7326,c_61]) ).
tcf(c_7351,plain,
divide(iPr_def_12,a) = iPr_def_10,
inference(ground_joinability,[status(thm)],[c_7334,c_285]) ).
tcf(c_7417,plain,
divide(iPr_def_10,iPr_def_12) = zero,
inference(superposition,[status(thm)],[c_7351,c_58]) ).
tcf(c_7429,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_7417,c_4212]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN010-5 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n009.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Wed Sep 23 16:17:13 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 0.11/0.43
% 0.11/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.43
% 0.11/0.43 % Detected problem language: tptp
% 0.11/0.44 % Proving...
% 0.92/1.21 % SZS status Started for theBenchmark.p
% 0.92/1.21 % SZS status Unsatisfiable for theBenchmark.p
% 0.92/1.21
% 0.92/1.21 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.92/1.21
% 0.92/1.21 % ------ iProver source info
% 0.92/1.21
% 0.92/1.21 % git: date: 2026-07-19 20:42:38 +0200
% 0.92/1.21 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.92/1.21 % git: non_committed_changes: false
% 0.92/1.21
% 0.92/1.21 % ------ Parsing...% successful
% 0.92/1.21
% 0.92/1.21
% 0.92/1.21 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.92/1.21
% 0.92/1.21 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 0.92/1.21
% 0.92/1.21 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.92/1.21
% 0.92/1.21 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 0.92/1.21 % ------ Proving...
% 0.92/1.21 % ------ Problem Properties
% 0.92/1.21
% 0.92/1.21 %
% 0.92/1.21 % clauses 12
% 0.92/1.21 % conjectures 1
% 0.92/1.21 % EPR 1
% 0.92/1.21 % Horn 12
% 0.92/1.21 % unary 8
% 0.92/1.21 % binary 2
% 0.92/1.21 % lits 18
% 0.92/1.21 % lits eq 18
% 0.92/1.21 % fd_pure 0
% 0.92/1.21 % fd_pseudo 0
% 0.92/1.21 % fd_cond 0
% 0.92/1.21 % fd_pseudo_cond 1
% 0.92/1.21 % AC symbols 0
% 0.92/1.21
% 0.92/1.21 % ------ Schedule dynamic 5 is on
% 0.92/1.21
% 0.92/1.21 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.92/1.21
% 0.92/1.21
% 0.92/1.21 % ------
% 0.92/1.21 % Current options:
% 0.92/1.21 % ------
% 0.92/1.21
% 0.92/1.21
% 0.92/1.21 %
% 0.92/1.21
% 0.92/1.21 % ------ Proving...
% 0.92/1.21 %
% 0.92/1.21
% 0.92/1.21 % SZS status Unsatisfiable for theBenchmark.p
% 0.92/1.21
% 0.92/1.21 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.92/1.21
% 0.92/1.21
%------------------------------------------------------------------------------