%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : HEN009-6 : 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 : n017.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 4.08s 1.28s
% Output : CNFRefutation 4.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 17
% Syntax : Number of formulae : 68 ( 39 unt; 0 def)
% Number of atoms : 112 ( 49 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 90 ( 46 ~; 44 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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 : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 77 ( 0 sgn 77 !; 0 ?; 57 :)
% 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(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(f10,axiom,
! [X0] : divide(zero,X0) = zero,
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',x_divide_x_is_zero) ).
fof(f13,plain,
! [X0] : zero = divide(X0,X0),
inference(reorient_equations,[],[f12]) ).
fof(f14,axiom,
! [X2,X0,X1] :
( less_equal(divide(X0,X2),X1)
| ~ less_equal(divide(X0,X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',property_of_divide1) ).
fof(f15,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(f17,axiom,
divide(identity,a) = b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',id_divide_a_is_b) ).
fof(f18,axiom,
divide(identity,b) = c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',id_divide_b_is_c) ).
fof(f19,axiom,
divide(identity,c) = d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',id_divide_c_is_d) ).
fof(f20,negated_conjecture,
b != d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_b_equals_d) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( ( divide(X0,X1) = zero )
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] :
( less_equal(X0,X1)
| ( divide(X0,X1) != zero ) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] : less_equal(divide(X0,X1),X0),
inference(cnf_transformation,[],[f3]) ).
tcf(c_70,plain,
! [X0: $i] : less_equal(zero,X0),
inference(cnf_transformation,[],[f5]) ).
tcf(c_71,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] : less_equal(X0,identity),
inference(cnf_transformation,[],[f7]) ).
tcf(c_74,plain,
! [X0: $i] : divide(zero,X0) = zero,
inference(cnf_transformation,[],[f11]) ).
tcf(c_75,plain,
! [X0: $i] : divide(X0,X0) = zero,
inference(cnf_transformation,[],[f13]) ).
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,[],[f14]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i,X2: $i] :
( less_equal(divide(X0,X2),divide(X1,X2))
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_79,plain,
divide(identity,a) = b,
inference(cnf_transformation,[],[f17]) ).
tcf(c_80,plain,
divide(identity,b) = c,
inference(cnf_transformation,[],[f18]) ).
tcf(c_81,plain,
divide(identity,c) = d,
inference(cnf_transformation,[],[f19]) ).
tcf(c_82,negated_conjecture,
b != d,
inference(cnf_transformation,[],[f20]) ).
tcf(c_302,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_304,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_306,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( less_equal(X0,X2)
| ~ less_equal(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_547,plain,
! [X0: $i] : less_equal(X0,X0),
inference(superposition,[status(thm)],[c_75,c_67]) ).
tcf(c_581,plain,
! [X0: $i,X1: $i] : less_equal(divide(X0,divide(X0,X1)),X1),
inference(superposition,[status(thm)],[c_547,c_76]) ).
tcf(c_588,plain,
less_equal(divide(identity,b),a),
inference(superposition,[status(thm)],[c_79,c_581]) ).
tcf(c_589,plain,
less_equal(divide(identity,c),b),
inference(superposition,[status(thm)],[c_80,c_581]) ).
tcf(c_593,plain,
less_equal(d,b),
inference(light_normalisation,[status(thm)],[c_589,c_81]) ).
tcf(c_594,plain,
less_equal(c,a),
inference(light_normalisation,[status(thm)],[c_588,c_80]) ).
tcf(c_598,plain,
divide(c,a) = zero,
inference(superposition,[status(thm)],[c_594,c_66]) ).
tcf(c_622,plain,
( ( b = d )
| ~ less_equal(d,b)
| ~ less_equal(b,d) ),
inference(instantiation,[status(thm)],[c_71]) ).
tcf(c_670,plain,
! [X0: $i,X1: $i] :
( less_equal(b,d)
| ~ less_equal(X0,X1)
| ( d != X1 )
| ( b != X0 ) ),
inference(instantiation,[status(thm)],[c_306]) ).
tcf(c_697,plain,
! [X0: $i,X1: $i] :
( less_equal(divide(X0,X1),zero)
| ~ less_equal(X0,zero) ),
inference(superposition,[status(thm)],[c_74,c_77]) ).
tcf(c_701,plain,
! [X0: $i] :
( less_equal(divide(X0,c),d)
| ~ less_equal(X0,identity) ),
inference(superposition,[status(thm)],[c_81,c_77]) ).
tcf(c_704,plain,
! [X0: $i] :
( less_equal(divide(X0,a),zero)
| ~ less_equal(X0,c) ),
inference(superposition,[status(thm)],[c_598,c_77]) ).
tcf(c_712,plain,
! [X0: $i] : less_equal(divide(X0,c),d),
inference(forward_subsumption_resolution,[status(thm)],[c_701,c_72]) ).
tcf(c_750,plain,
b = b,
inference(instantiation,[status(thm)],[c_302]) ).
tcf(c_751,plain,
! [X0: $i,X1: $i] :
( ( b = X0 )
| ( b != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_304]) ).
tcf(c_767,plain,
! [X0: $i] :
( ( X0 = zero )
| ~ less_equal(X0,zero) ),
inference(superposition,[status(thm)],[c_70,c_71]) ).
tcf(c_822,plain,
! [X0: $i] :
( ( b = X0 )
| ( b != b )
| ( X0 != b ) ),
inference(instantiation,[status(thm)],[c_751]) ).
tcf(c_976,plain,
( ( b = divide(identity,a) )
| ( b != b )
| ( divide(identity,a) != b ) ),
inference(instantiation,[status(thm)],[c_822]) ).
tcf(c_1014,plain,
! [X0: $i] : less_equal(divide(X0,d),c),
inference(superposition,[status(thm)],[c_712,c_76]) ).
tcf(c_1269,plain,
! [X0: $i] : divide(X0,divide(X0,zero)) = zero,
inference(superposition,[status(thm)],[c_581,c_767]) ).
tcf(c_1333,plain,
! [X0: $i] :
( less_equal(b,d)
| ~ less_equal(divide(identity,a),X0)
| ( d != X0 )
| ( b != divide(identity,a) ) ),
inference(instantiation,[status(thm)],[c_670]) ).
tcf(c_1903,plain,
( less_equal(b,d)
| ~ less_equal(divide(identity,a),d)
| ( d != d )
| ( b != divide(identity,a) ) ),
inference(instantiation,[status(thm)],[c_1333]) ).
tcf(c_1904,plain,
d = d,
inference(instantiation,[status(thm)],[c_302]) ).
tcf(c_1957,plain,
! [X0: $i] : less_equal(X0,divide(X0,zero)),
inference(superposition,[status(thm)],[c_1269,c_67]) ).
tcf(c_2014,plain,
! [X0: $i] :
( ( divide(X0,zero) = X0 )
| ~ less_equal(divide(X0,zero),X0) ),
inference(superposition,[status(thm)],[c_1957,c_71]) ).
tcf(c_2017,plain,
! [X0: $i] : divide(X0,zero) = X0,
inference(forward_subsumption_resolution,[status(thm)],[c_2014,c_68]) ).
tcf(c_2435,plain,
! [X0: $i,X1: $i] :
( less_equal(divide(X0,zero),X1)
| ~ less_equal(X0,zero) ),
inference(superposition,[status(thm)],[c_697,c_76]) ).
tcf(c_2439,plain,
! [X0: $i,X1: $i] :
( less_equal(X0,X1)
| ~ less_equal(X0,zero) ),
inference(light_normalisation,[status(thm)],[c_2435,c_2017]) ).
tcf(c_2538,plain,
! [X0: $i,X1: $i] :
( less_equal(divide(X0,a),X1)
| ~ less_equal(X0,c) ),
inference(superposition,[status(thm)],[c_704,c_2439]) ).
tcf(c_3596,plain,
! [X0: $i,X1: $i] :
( less_equal(divide(X0,X1),a)
| ~ less_equal(X0,c) ),
inference(superposition,[status(thm)],[c_2538,c_76]) ).
tcf(c_3843,plain,
! [X0: $i] :
( less_equal(X0,a)
| ~ less_equal(X0,c) ),
inference(superposition,[status(thm)],[c_2017,c_3596]) ).
tcf(c_3948,plain,
! [X0: $i] : less_equal(divide(X0,d),a),
inference(superposition,[status(thm)],[c_1014,c_3843]) ).
tcf(c_4018,plain,
! [X0: $i] : less_equal(divide(X0,a),d),
inference(superposition,[status(thm)],[c_3948,c_76]) ).
tcf(c_4023,plain,
less_equal(divide(identity,a),d),
inference(instantiation,[status(thm)],[c_4018]) ).
tcf(c_4024,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_4023,c_1904,c_1903,c_976,c_750,c_622,c_593,c_79,c_82]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN009-6 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.35 % Computer : n017.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Wed Sep 23 16:11:14 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 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
% 0.13/0.41
% 0.13/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.41
% 0.13/0.42 % Detected problem language: tptp
% 0.13/0.43 % Proving...
% 4.08/1.28 % SZS status Started for theBenchmark.p
% 4.08/1.28 % SZS status Unsatisfiable for theBenchmark.p
% 4.08/1.28
% 4.08/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.08/1.28
% 4.08/1.28 % ------ iProver source info
% 4.08/1.28
% 4.08/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 4.08/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.08/1.28 % git: non_committed_changes: false
% 4.08/1.28
% 4.08/1.28 % ------ Parsing...% successful
% 4.08/1.28
% 4.08/1.28
% 4.08/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.08/1.28
% 4.08/1.28 % ------ 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 %
% 4.08/1.28
% 4.08/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.08/1.28
% 4.08/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.08/1.28 % ------ Proving...
% 4.08/1.28 % ------ Problem Properties
% 4.08/1.28
% 4.08/1.28 %
% 4.08/1.28 % clauses 16
% 4.08/1.28 % conjectures 1
% 4.08/1.28 % EPR 4
% 4.08/1.28 % Horn 16
% 4.08/1.28 % unary 11
% 4.08/1.28 % binary 4
% 4.08/1.28 % lits 22
% 4.08/1.28 % lits eq 10
% 4.08/1.28 % fd_pure 0
% 4.08/1.28 % fd_pseudo 0
% 4.08/1.28 % fd_cond 0
% 4.08/1.28 % fd_pseudo_cond 1
% 4.08/1.28 % AC symbols 0
% 4.08/1.28
% 4.08/1.28 % ------ Schedule dynamic 5 is on
% 4.08/1.28
% 4.08/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.08/1.28
% 4.08/1.28
% 4.08/1.28 % ------
% 4.08/1.28 % Current options:
% 4.08/1.28 % ------
% 4.08/1.28
% 4.08/1.28
% 4.08/1.28 %
% 4.08/1.28
% 4.08/1.28 % ------ Proving...
% 4.08/1.28 %
% 4.08/1.28
% 4.08/1.28 % SZS status Unsatisfiable for theBenchmark.p
% 4.08/1.28
% 4.08/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.08/1.28
% 4.08/1.28
%------------------------------------------------------------------------------