%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : HEN006-4 : 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 : n004.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 01:37:22 PM UTC 2026
% Result : Unsatisfiable 3.80s 1.27s
% Output : CNFRefutation 3.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 31 ( 20 unt; 1 def)
% Number of atoms : 55 ( 10 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 33 ( 18 ~; 15 |; 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 : 4 ( 2 usr; 2 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 34 ( 0 sgn 34 !; 0 ?; 19 :)
% 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(f16,axiom,
! [X2,X0,X1] :
( less_equal(X0,X2)
| ~ less_equal(X1,X2)
| ~ less_equal(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_less_equal) ).
fof(f17,axiom,
less_equal(divide(a,b),d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_divide_b_LE_d) ).
fof(f18,negated_conjecture,
~ less_equal(divide(a,d),b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_divide_d_LE_b) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( ( divide(X0,X1) = zero )
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( less_equal(X0,X1)
| ( divide(X0,X1) != zero ) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] : less_equal(divide(X0,X1),X0),
inference(cnf_transformation,[],[f3]) ).
tcf(c_66,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_67,plain,
! [X0: $i] : less_equal(zero,X0),
inference(cnf_transformation,[],[f5]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ less_equal(X1,X0)
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_74,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_75,plain,
less_equal(divide(a,b),d),
inference(cnf_transformation,[],[f17]) ).
tcf(c_76,negated_conjecture,
~ less_equal(divide(a,d),b),
inference(cnf_transformation,[],[f18]) ).
tcf(c_171,definition,
iPr_def_10 = divide(a,d),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_172,negated_conjecture,
~ less_equal(iPr_def_10,b),
inference(demodulation,[status(thm)],[c_76,c_171]) ).
tcf(c_383,plain,
divide(divide(a,b),d) = zero,
inference(superposition,[status(thm)],[c_75,c_63]) ).
tcf(c_524,plain,
! [X0: $i] :
( ( X0 = zero )
| ~ less_equal(X0,zero) ),
inference(superposition,[status(thm)],[c_67,c_68]) ).
tcf(c_575,plain,
less_equal(divide(divide(a,d),divide(b,d)),zero),
inference(superposition,[status(thm)],[c_383,c_66]) ).
tcf(c_592,plain,
less_equal(divide(iPr_def_10,divide(b,d)),zero),
inference(light_normalisation,[status(thm)],[c_575,c_171]) ).
tcf(c_672,plain,
! [X0: $i] :
( less_equal(divide(iPr_def_10,divide(b,d)),X0)
| ~ less_equal(zero,X0) ),
inference(superposition,[status(thm)],[c_592,c_74]) ).
tcf(c_674,plain,
! [X0: $i] : less_equal(divide(iPr_def_10,divide(b,d)),X0),
inference(forward_subsumption_resolution,[status(thm)],[c_672,c_67]) ).
tcf(c_701,plain,
divide(iPr_def_10,divide(b,d)) = zero,
inference(superposition,[status(thm)],[c_674,c_524]) ).
tcf(c_719,plain,
less_equal(iPr_def_10,divide(b,d)),
inference(superposition,[status(thm)],[c_701,c_64]) ).
tcf(c_740,plain,
! [X0: $i] :
( less_equal(iPr_def_10,X0)
| ~ less_equal(divide(b,d),X0) ),
inference(superposition,[status(thm)],[c_719,c_74]) ).
tcf(c_800,plain,
less_equal(iPr_def_10,b),
inference(superposition,[status(thm)],[c_65,c_740]) ).
tcf(c_804,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_800,c_172]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : HEN006-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n004.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 16:12:20 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
% 0.13/0.41 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 3.80/1.27 % SZS status Started for theBenchmark.p
% 3.80/1.27 % SZS status Unsatisfiable for theBenchmark.p
% 3.80/1.27
% 3.80/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.80/1.27
% 3.80/1.27 % ------ iProver source info
% 3.80/1.27
% 3.80/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 3.80/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.80/1.27 % git: non_committed_changes: false
% 3.80/1.27
% 3.80/1.27 % ------ Parsing...% successful
% 3.80/1.27
% 3.80/1.27
% 3.80/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.80/1.27
% 3.80/1.27 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 3.80/1.27
% 3.80/1.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.80/1.27
% 3.80/1.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.80/1.27 % ------ Proving...
% 3.80/1.27 % ------ Problem Properties
% 3.80/1.27
% 3.80/1.27 %
% 3.80/1.27 % clauses 15
% 3.80/1.27 % conjectures 1
% 3.80/1.27 % EPR 5
% 3.80/1.27 % Horn 15
% 3.80/1.27 % unary 11
% 3.80/1.27 % binary 2
% 3.80/1.27 % lits 21
% 3.80/1.27 % lits eq 8
% 3.80/1.27 % fd_pure 0
% 3.80/1.27 % fd_pseudo 0
% 3.80/1.27 % fd_cond 0
% 3.80/1.27 % fd_pseudo_cond 1
% 3.80/1.27 % AC symbols 0
% 3.80/1.27
% 3.80/1.27 % ------ Schedule dynamic 5 is on
% 3.80/1.27
% 3.80/1.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.80/1.27
% 3.80/1.27
% 3.80/1.27 % ------
% 3.80/1.27 % Current options:
% 3.80/1.27 % ------
% 3.80/1.27
% 3.80/1.27
% 3.80/1.27 %
% 3.80/1.27
% 3.80/1.27 % ------ Proving...
% 3.80/1.27 %
% 3.80/1.27
% 3.80/1.27 % SZS status Unsatisfiable for theBenchmark.p
% 3.80/1.27
% 3.80/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.80/1.27
% 3.80/1.27
%------------------------------------------------------------------------------