%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : HEN009-3 : 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 : n026.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 01:37:24 PM UTC 2026
% Result : Unsatisfiable 0.85s 1.29s
% Output : CNFRefutation 0.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 11
% Syntax : Number of formulae : 79 ( 67 unt; 0 def)
% Number of atoms : 93 ( 38 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 32 ( 18 ~; 14 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 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 : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 64 ( 0 sgn 64 !; 0 ?; 51 :)
% 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(f9,axiom,
divide(identity,a) = b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',id_divide_a_is_b) ).
fof(f10,axiom,
divide(identity,b) = c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',id_divide_b_is_c) ).
fof(f11,axiom,
divide(identity,c) = d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',id_divide_c_is_d) ).
fof(f12,negated_conjecture,
b != d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_b_equals_d) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( ( divide(X0,X1) = zero )
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] :
( less_equal(X0,X1)
| ( divide(X0,X1) != zero ) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] : less_equal(divide(X0,X1),X0),
inference(cnf_transformation,[],[f3]) ).
tcf(c_64,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_65,plain,
! [X0: $i] : less_equal(zero,X0),
inference(cnf_transformation,[],[f5]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ less_equal(X1,X0)
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_67,plain,
! [X0: $i] : less_equal(X0,identity),
inference(cnf_transformation,[],[f7]) ).
tcf(c_69,plain,
divide(identity,a) = b,
inference(cnf_transformation,[],[f9]) ).
tcf(c_70,plain,
divide(identity,b) = c,
inference(cnf_transformation,[],[f10]) ).
tcf(c_71,plain,
divide(identity,c) = d,
inference(cnf_transformation,[],[f11]) ).
tcf(c_72,negated_conjecture,
b != d,
inference(cnf_transformation,[],[f12]) ).
tcf(c_217,negated_conjecture,
b != d,
inference(demodulation,[status(thm)],[c_72]) ).
tcf(c_394,plain,
! [X0: $i,X1: $i] : divide(divide(X0,X1),X0) = zero,
inference(superposition,[status(thm)],[c_63,c_61]) ).
tcf(c_395,plain,
! [X0: $i] : divide(zero,X0) = zero,
inference(superposition,[status(thm)],[c_65,c_61]) ).
tcf(c_396,plain,
! [X0: $i] : divide(X0,identity) = zero,
inference(superposition,[status(thm)],[c_67,c_61]) ).
tcf(c_428,plain,
! [X0: $i] :
( ( X0 = zero )
| ~ less_equal(X0,zero) ),
inference(superposition,[status(thm)],[c_65,c_66]) ).
tcf(c_439,plain,
! [X0: $i] : less_equal(divide(b,divide(X0,a)),divide(divide(identity,X0),a)),
inference(superposition,[status(thm)],[c_69,c_64]) ).
tcf(c_443,plain,
! [X0: $i] : less_equal(divide(divide(X0,a),b),divide(divide(X0,identity),a)),
inference(superposition,[status(thm)],[c_69,c_64]) ).
tcf(c_444,plain,
! [X0: $i] : less_equal(divide(divide(X0,b),c),divide(divide(X0,identity),b)),
inference(superposition,[status(thm)],[c_70,c_64]) ).
tcf(c_445,plain,
! [X0: $i] : less_equal(divide(divide(X0,c),d),divide(divide(X0,identity),c)),
inference(superposition,[status(thm)],[c_71,c_64]) ).
tcf(c_447,plain,
! [X0: $i,X1: $i] : less_equal(divide(divide(X0,X0),divide(X1,X0)),zero),
inference(superposition,[status(thm)],[c_394,c_64]) ).
tcf(c_456,plain,
! [X0: $i] : less_equal(divide(divide(X0,c),d),divide(zero,c)),
inference(light_normalisation,[status(thm)],[c_445,c_396]) ).
tcf(c_457,plain,
! [X0: $i] : less_equal(divide(divide(X0,b),c),divide(zero,b)),
inference(light_normalisation,[status(thm)],[c_444,c_396]) ).
tcf(c_458,plain,
! [X0: $i] : less_equal(divide(divide(X0,a),b),divide(zero,a)),
inference(light_normalisation,[status(thm)],[c_443,c_396]) ).
tcf(c_496,plain,
! [X0: $i,X1: $i] : less_equal(divide(divide(X0,X1),zero),divide(divide(X0,zero),X1)),
inference(superposition,[status(thm)],[c_395,c_64]) ).
tcf(c_546,plain,
! [X0: $i] : less_equal(divide(divide(X0,X0),zero),zero),
inference(superposition,[status(thm)],[c_394,c_447]) ).
tcf(c_570,plain,
! [X0: $i] : less_equal(divide(divide(X0,c),d),zero),
inference(demodulation,[status(thm)],[c_456,c_395]) ).
tcf(c_577,plain,
! [X0: $i] : divide(divide(X0,c),d) = zero,
inference(superposition,[status(thm)],[c_570,c_428]) ).
tcf(c_622,plain,
! [X0: $i] : divide(divide(X0,X0),zero) = zero,
inference(superposition,[status(thm)],[c_546,c_428]) ).
tcf(c_691,plain,
! [X0: $i] : less_equal(divide(X0,c),d),
inference(superposition,[status(thm)],[c_577,c_62]) ).
tcf(c_728,plain,
! [X0: $i] : less_equal(divide(X0,X0),zero),
inference(superposition,[status(thm)],[c_622,c_62]) ).
tcf(c_758,plain,
! [X0: $i] : divide(X0,X0) = zero,
inference(superposition,[status(thm)],[c_728,c_428]) ).
tcf(c_770,plain,
! [X0: $i] : less_equal(divide(divide(X0,b),c),zero),
inference(demodulation,[status(thm)],[c_457,c_395]) ).
tcf(c_777,plain,
! [X0: $i] : divide(divide(X0,b),c) = zero,
inference(superposition,[status(thm)],[c_770,c_428]) ).
tcf(c_782,plain,
! [X0: $i] : less_equal(divide(divide(X0,a),b),zero),
inference(demodulation,[status(thm)],[c_458,c_395]) ).
tcf(c_789,plain,
! [X0: $i] : divide(divide(X0,a),b) = zero,
inference(superposition,[status(thm)],[c_782,c_428]) ).
tcf(c_818,plain,
! [X0: $i] : less_equal(divide(X0,b),c),
inference(superposition,[status(thm)],[c_777,c_62]) ).
tcf(c_823,plain,
! [X0: $i] : less_equal(divide(divide(X0,c),divide(b,c)),zero),
inference(superposition,[status(thm)],[c_777,c_64]) ).
tcf(c_844,plain,
! [X0: $i] : less_equal(divide(X0,a),b),
inference(superposition,[status(thm)],[c_789,c_62]) ).
tcf(c_849,plain,
! [X0: $i] : less_equal(divide(divide(X0,b),divide(a,b)),zero),
inference(superposition,[status(thm)],[c_789,c_64]) ).
tcf(c_892,plain,
less_equal(divide(d,divide(b,c)),zero),
inference(superposition,[status(thm)],[c_71,c_823]) ).
tcf(c_905,plain,
divide(d,divide(b,c)) = zero,
inference(superposition,[status(thm)],[c_892,c_428]) ).
tcf(c_909,plain,
less_equal(divide(c,divide(a,b)),zero),
inference(superposition,[status(thm)],[c_70,c_849]) ).
tcf(c_942,plain,
divide(c,divide(a,b)) = zero,
inference(superposition,[status(thm)],[c_909,c_428]) ).
tcf(c_945,plain,
less_equal(d,divide(b,c)),
inference(superposition,[status(thm)],[c_905,c_62]) ).
tcf(c_968,plain,
( ( divide(b,c) = d )
| ~ less_equal(divide(b,c),d) ),
inference(superposition,[status(thm)],[c_945,c_66]) ).
tcf(c_970,plain,
divide(b,c) = d,
inference(forward_subsumption_resolution,[status(thm)],[c_968,c_691]) ).
tcf(c_976,plain,
less_equal(d,b),
inference(superposition,[status(thm)],[c_970,c_63]) ).
tcf(c_986,plain,
( ( b = d )
| ~ less_equal(b,d) ),
inference(superposition,[status(thm)],[c_976,c_66]) ).
tcf(c_988,plain,
~ less_equal(b,d),
inference(forward_subsumption_resolution,[status(thm)],[c_986,c_217]) ).
tcf(c_1030,plain,
less_equal(c,divide(a,b)),
inference(superposition,[status(thm)],[c_942,c_62]) ).
tcf(c_1039,plain,
( ( divide(a,b) = c )
| ~ less_equal(divide(a,b),c) ),
inference(superposition,[status(thm)],[c_1030,c_66]) ).
tcf(c_1041,plain,
divide(a,b) = c,
inference(forward_subsumption_resolution,[status(thm)],[c_1039,c_818]) ).
tcf(c_1048,plain,
divide(c,a) = zero,
inference(superposition,[status(thm)],[c_1041,c_394]) ).
tcf(c_1180,plain,
less_equal(divide(b,divide(c,a)),divide(d,a)),
inference(superposition,[status(thm)],[c_71,c_439]) ).
tcf(c_1186,plain,
less_equal(divide(b,zero),divide(d,a)),
inference(light_normalisation,[status(thm)],[c_1180,c_1048]) ).
tcf(c_1804,plain,
! [X0: $i] : less_equal(divide(divide(X0,divide(X0,zero)),zero),zero),
inference(superposition,[status(thm)],[c_758,c_496]) ).
tcf(c_2043,plain,
! [X0: $i] : divide(divide(X0,divide(X0,zero)),zero) = zero,
inference(superposition,[status(thm)],[c_1804,c_428]) ).
tcf(c_2339,plain,
! [X0: $i] : less_equal(divide(X0,divide(X0,zero)),zero),
inference(superposition,[status(thm)],[c_2043,c_62]) ).
tcf(c_2374,plain,
! [X0: $i] : divide(X0,divide(X0,zero)) = zero,
inference(superposition,[status(thm)],[c_2339,c_428]) ).
tcf(c_2382,plain,
! [X0: $i] : less_equal(X0,divide(X0,zero)),
inference(superposition,[status(thm)],[c_2374,c_62]) ).
tcf(c_2463,plain,
! [X0: $i] :
( ( divide(X0,zero) = X0 )
| ~ less_equal(divide(X0,zero),X0) ),
inference(superposition,[status(thm)],[c_2382,c_66]) ).
tcf(c_2467,plain,
! [X0: $i] : divide(X0,zero) = X0,
inference(forward_subsumption_resolution,[status(thm)],[c_2463,c_63]) ).
tcf(c_2476,plain,
less_equal(b,divide(d,a)),
inference(demodulation,[status(thm)],[c_1186,c_2467]) ).
tcf(c_2492,plain,
( ( divide(d,a) = b )
| ~ less_equal(divide(d,a),b) ),
inference(superposition,[status(thm)],[c_2476,c_66]) ).
tcf(c_2494,plain,
divide(d,a) = b,
inference(forward_subsumption_resolution,[status(thm)],[c_2492,c_844]) ).
tcf(c_2701,plain,
less_equal(b,d),
inference(superposition,[status(thm)],[c_2494,c_63]) ).
tcf(c_2711,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_2701,c_988]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : HEN009-3 : 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 : n026.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 16:18:26 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.41 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
% 0.09/0.43
% 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...
% 0.85/1.29 % SZS status Started for theBenchmark.p
% 0.85/1.29 % SZS status Unsatisfiable for theBenchmark.p
% 0.85/1.29
% 0.85/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.85/1.29
% 0.85/1.29 % ------ iProver source info
% 0.85/1.29
% 0.85/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 0.85/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.85/1.29 % git: non_committed_changes: false
% 0.85/1.29
% 0.85/1.29 % ------ Parsing...% successful
% 0.85/1.29
% 0.85/1.29
% 0.85/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.85/1.29
% 0.85/1.29 % ------ Preprocessing... sup_sim: 1 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 0.85/1.29
% 0.85/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.85/1.29
% 0.85/1.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.85/1.29 % ------ Proving...
% 0.85/1.29 % ------ Problem Properties
% 0.85/1.29
% 0.85/1.29 %
% 0.85/1.29 % clauses 11
% 0.85/1.29 % conjectures 1
% 0.85/1.29 % EPR 4
% 0.85/1.29 % Horn 11
% 0.85/1.29 % unary 8
% 0.85/1.29 % binary 2
% 0.85/1.29 % lits 15
% 0.85/1.29 % lits eq 7
% 0.85/1.29 % fd_pure 0
% 0.85/1.29 % fd_pseudo 0
% 0.85/1.29 % fd_cond 0
% 0.85/1.29 % fd_pseudo_cond 1
% 0.85/1.29 % AC symbols 0
% 0.85/1.29
% 0.85/1.29 % ------ Schedule dynamic 5 is on
% 0.85/1.29
% 0.85/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.85/1.29
% 0.85/1.29
% 0.85/1.29 % ------
% 0.85/1.29 % Current options:
% 0.85/1.29 % ------
% 0.85/1.29
% 0.85/1.29
% 0.85/1.29 %
% 0.85/1.29
% 0.85/1.29 % ------ Proving...
% 0.85/1.29 %
% 0.85/1.29
% 0.85/1.29 % SZS status Unsatisfiable for theBenchmark.p
% 0.85/1.29
% 0.85/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.85/1.30
% 0.85/1.30
%------------------------------------------------------------------------------