%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : HEN007-4 : 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 : n008.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 01:37:23 PM UTC 2026
% Result : Unsatisfiable 0.28s 1.10s
% Output : CNFRefutation 3.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 14
% Syntax : Number of formulae : 54 ( 40 unt; 2 def)
% Number of atoms : 103 ( 22 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 39 ( 21 ~; 18 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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 : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 59 ( 0 sgn 59 !; 0 ?; 37 :)
% 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(f10,axiom,
! [X0] : divide(zero,X0) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',zero_divide_anything_is_zero) ).
fof(f11,plain,
! [X0] : zero = divide(zero,X0),
inference(reorient_equations,[],[f10]) ).
fof(f12,axiom,
! [X0] : divide(X0,X0) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_divide_x_is_zero) ).
fof(f13,plain,
! [X0] : zero = divide(X0,X0),
inference(reorient_equations,[],[f12]) ).
fof(f16,axiom,
! [X2,X0,X1] :
( less_equal(X0,X2)
| ~ less_equal(X1,X2)
| ~ less_equal(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_of_less_equal) ).
fof(f17,axiom,
! [X2,X0,X1] :
( less_equal(divide(X0,X2),X1)
| ~ less_equal(divide(X0,X1),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_of_divide1) ).
fof(f18,axiom,
less_equal(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_LE_b) ).
fof(f19,negated_conjecture,
~ less_equal(divide(c,b),divide(c,a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_c_divide_b_LE_c_divide_a) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( ( divide(X0,X1) = zero )
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( less_equal(X0,X1)
| ( divide(X0,X1) != zero ) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] : less_equal(divide(X0,X1),X0),
inference(cnf_transformation,[],[f3]) ).
tcf(c_67,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_68,plain,
! [X0: $i] : less_equal(zero,X0),
inference(cnf_transformation,[],[f5]) ).
tcf(c_69,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] : divide(zero,X0) = zero,
inference(cnf_transformation,[],[f11]) ).
tcf(c_73,plain,
! [X0: $i] : divide(X0,X0) = zero,
inference(cnf_transformation,[],[f13]) ).
tcf(c_75,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_76,plain,
! [X0: $i,X1: $i,X2: $i] :
( less_equal(divide(X0,X2),X1)
| ~ less_equal(divide(X0,X1),X2) ),
inference(cnf_transformation,[],[f17]) ).
tcf(c_77,plain,
less_equal(a,b),
inference(cnf_transformation,[],[f18]) ).
tcf(c_78,negated_conjecture,
~ less_equal(divide(c,b),divide(c,a)),
inference(cnf_transformation,[],[f19]) ).
tcf(c_187,definition,
iPr_def_10 = divide(c,b),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_188,definition,
iPr_def_11 = divide(c,a),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_189,negated_conjecture,
~ less_equal(iPr_def_10,iPr_def_11),
inference(demodulation,[status(thm)],[c_78,c_188,c_187]) ).
tcf(c_424,plain,
less_equal(iPr_def_11,c),
inference(superposition,[status(thm)],[c_188,c_66]) ).
tcf(c_427,plain,
divide(a,b) = zero,
inference(superposition,[status(thm)],[c_77,c_64]) ).
tcf(c_438,plain,
! [X0: $i] : less_equal(X0,X0),
inference(superposition,[status(thm)],[c_73,c_65]) ).
tcf(c_450,plain,
divide(iPr_def_11,c) = zero,
inference(superposition,[status(thm)],[c_424,c_64]) ).
tcf(c_521,plain,
! [X0: $i,X1: $i] : less_equal(divide(X0,divide(X0,X1)),X1),
inference(superposition,[status(thm)],[c_438,c_76]) ).
tcf(c_566,plain,
! [X0: $i] :
( ( X0 = zero )
| ~ less_equal(X0,zero) ),
inference(superposition,[status(thm)],[c_68,c_69]) ).
tcf(c_605,plain,
! [X0: $i] : less_equal(divide(iPr_def_10,divide(X0,b)),divide(divide(c,X0),b)),
inference(superposition,[status(thm)],[c_187,c_67]) ).
tcf(c_633,plain,
! [X0: $i] : less_equal(divide(divide(iPr_def_11,X0),divide(c,X0)),divide(zero,X0)),
inference(superposition,[status(thm)],[c_450,c_67]) ).
tcf(c_645,plain,
! [X0: $i] : less_equal(divide(divide(iPr_def_11,X0),divide(c,X0)),zero),
inference(light_normalisation,[status(thm)],[c_633,c_72]) ).
tcf(c_968,plain,
! [X0: $i] : divide(X0,divide(X0,zero)) = zero,
inference(superposition,[status(thm)],[c_521,c_566]) ).
tcf(c_1456,plain,
! [X0: $i] : less_equal(X0,divide(X0,zero)),
inference(superposition,[status(thm)],[c_968,c_65]) ).
tcf(c_1520,plain,
! [X0: $i] :
( ( divide(X0,zero) = X0 )
| ~ less_equal(divide(X0,zero),X0) ),
inference(superposition,[status(thm)],[c_1456,c_69]) ).
tcf(c_1531,plain,
! [X0: $i] : divide(X0,zero) = X0,
inference(forward_subsumption_resolution,[status(thm)],[c_1520,c_66]) ).
tcf(c_1807,plain,
! [X0: $i,X1: $i] :
( less_equal(divide(divide(iPr_def_11,X1),divide(c,X1)),X0)
| ~ less_equal(zero,X0) ),
inference(superposition,[status(thm)],[c_645,c_75]) ).
tcf(c_1814,plain,
! [X0: $i,X1: $i] : less_equal(divide(divide(iPr_def_11,X0),divide(c,X0)),X1),
inference(forward_subsumption_resolution,[status(thm)],[c_1807,c_68]) ).
tcf(c_2224,plain,
! [X0: $i] : less_equal(divide(divide(iPr_def_11,b),iPr_def_10),X0),
inference(superposition,[status(thm)],[c_187,c_1814]) ).
tcf(c_2259,plain,
! [X0: $i] : less_equal(divide(divide(iPr_def_11,b),X0),iPr_def_10),
inference(superposition,[status(thm)],[c_2224,c_76]) ).
tcf(c_2280,plain,
less_equal(divide(iPr_def_10,divide(a,b)),divide(iPr_def_11,b)),
inference(superposition,[status(thm)],[c_188,c_605]) ).
tcf(c_2287,plain,
less_equal(divide(iPr_def_10,zero),divide(iPr_def_11,b)),
inference(light_normalisation,[status(thm)],[c_2280,c_427]) ).
tcf(c_2313,plain,
less_equal(divide(iPr_def_11,b),iPr_def_10),
inference(superposition,[status(thm)],[c_1531,c_2259]) ).
tcf(c_2325,plain,
less_equal(iPr_def_10,divide(iPr_def_11,b)),
inference(demodulation,[status(thm)],[c_2287,c_1531]) ).
tcf(c_2361,plain,
( ( divide(iPr_def_11,b) = iPr_def_10 )
| ~ less_equal(iPr_def_10,divide(iPr_def_11,b)) ),
inference(superposition,[status(thm)],[c_2313,c_69]) ).
tcf(c_2367,plain,
divide(iPr_def_11,b) = iPr_def_10,
inference(forward_subsumption_resolution,[status(thm)],[c_2361,c_2325]) ).
tcf(c_2418,plain,
less_equal(iPr_def_10,iPr_def_11),
inference(superposition,[status(thm)],[c_2367,c_66]) ).
tcf(c_2427,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_2418,c_189]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN007-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n008.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Wed Sep 23 16:14:42 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 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
% 0.14/0.41
% 0.14/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.41
% 0.14/0.41 % Detected problem language: tptp
% 0.14/0.42 % Proving...
% 0.28/1.10 % SZS status Started for theBenchmark.p
% 0.28/1.10 % SZS status Unsatisfiable for theBenchmark.p
% 0.28/1.10
% 0.28/1.10 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.28/1.10
% 0.28/1.10 % ------ iProver source info
% 0.28/1.10
% 0.28/1.10 % git: date: 2026-07-19 20:42:38 +0200
% 0.28/1.10 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.28/1.10 % git: non_committed_changes: false
% 0.28/1.10
% 0.28/1.10 % ------ Parsing...% successful
% 0.28/1.10
% 0.28/1.10
% 0.28/1.10 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.28/1.10
% 0.28/1.10 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 0.28/1.10
% 0.28/1.10 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.28/1.10
% 0.28/1.10 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.28/1.10 % ------ Proving...
% 0.28/1.10 % ------ Problem Properties
% 0.28/1.10
% 0.28/1.10 %
% 0.28/1.10 % clauses 17
% 0.28/1.10 % conjectures 1
% 0.28/1.10 % EPR 6
% 0.28/1.10 % Horn 17
% 0.28/1.10 % unary 12
% 0.28/1.10 % binary 3
% 0.28/1.10 % lits 24
% 0.28/1.10 % lits eq 9
% 0.28/1.10 % fd_pure 0
% 0.28/1.10 % fd_pseudo 0
% 0.28/1.10 % fd_cond 0
% 0.28/1.10 % fd_pseudo_cond 1
% 0.28/1.10 % AC symbols 0
% 0.28/1.10
% 0.28/1.10 % ------ Schedule dynamic 5 is on
% 0.28/1.10
% 0.28/1.10 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.28/1.10
% 0.28/1.10
% 0.28/1.10 % ------
% 0.28/1.10 % Current options:
% 0.28/1.10 % ------
% 0.28/1.10
% 0.28/1.10
% 0.28/1.10 %
% 0.28/1.10
% 0.28/1.10 % ------ Proving...
% 0.28/1.10 %
% 0.28/1.10
% 0.28/1.10 % SZS status Unsatisfiable for theBenchmark.p
% 0.28/1.10
% 0.28/1.10 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.10/1.10
% 3.10/1.10
%------------------------------------------------------------------------------