%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : HEN009-2 : 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 : n002.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 3.20s 6.31s
% Output : CNFRefutation 3.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 42 ( 20 unt; 0 def)
% Number of atoms : 113 ( 14 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 88 ( 45 ~; 43 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 76 ( 0 sgn 76 !; 0 ?; 58 :)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0,X1] :
( X0 = X1
| ~ less_equal(X1,X0)
| ~ less_equal(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',less_equal_and_equal) ).
fof(f7,axiom,
! [X0] : less_equal(X0,identity),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN001-0.ax',identity_is_largest) ).
fof(f15,axiom,
! [X2,X3,X0,X1,X4] :
( less_equal(X4,X1)
| ~ quotient(X0,X3,X4)
| ~ less_equal(X2,X3)
| ~ quotient(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xQyLEz_implies_xQzLEy) ).
fof(f16,axiom,
! [X2,X3,X0,X1,X4] :
( less_equal(X3,X4)
| ~ quotient(X2,X0,X4)
| ~ quotient(X2,X1,X3)
| ~ less_equal(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xLEy_implies_zQyLEzQx) ).
fof(f17,axiom,
! [X2,X3,X0,X1,X4] :
( less_equal(X3,X4)
| ~ quotient(X1,X2,X4)
| ~ quotient(X0,X2,X3)
| ~ less_equal(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xLEy_implies_xQzLEyQz) ).
fof(f18,axiom,
quotient(identity,a,idQa),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_divide_a) ).
fof(f19,axiom,
quotient(identity,idQa,idQ_idQa),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_divide_idQa) ).
fof(f20,axiom,
quotient(identity,idQ_idQa,idQ__idQ_idQa),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_divide_idQ_idQa) ).
fof(f21,negated_conjecture,
idQa != idQ__idQ_idQa,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_one_inversion_equals_three) ).
tcf(c_75,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ less_equal(X1,X0)
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_76,plain,
! [X0: $i] : less_equal(X0,identity),
inference(cnf_transformation,[],[f7]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( less_equal(X4,X1)
| ~ less_equal(X2,X3)
| ~ quotient(X0,X3,X4)
| ~ quotient(X0,X1,X2) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( less_equal(X4,X2)
| ~ less_equal(X1,X3)
| ~ quotient(X0,X3,X4)
| ~ quotient(X0,X1,X2) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( less_equal(X2,X4)
| ~ less_equal(X0,X3)
| ~ quotient(X3,X1,X4)
| ~ quotient(X0,X1,X2) ),
inference(cnf_transformation,[],[f17]) ).
tcf(c_87,plain,
quotient(identity,a,idQa),
inference(cnf_transformation,[],[f18]) ).
tcf(c_88,plain,
quotient(identity,idQa,idQ_idQa),
inference(cnf_transformation,[],[f19]) ).
tcf(c_89,plain,
quotient(identity,idQ_idQa,idQ__idQ_idQa),
inference(cnf_transformation,[],[f20]) ).
tcf(c_90,negated_conjecture,
idQa != idQ__idQ_idQa,
inference(cnf_transformation,[],[f21]) ).
tcf(c_102,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( less_equal(X4,X1)
| ~ less_equal(X2,X3)
| ( divide(X0,X3) != X4 )
| ( divide(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_84]) ).
tcf(c_104,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( less_equal(X4,X2)
| ~ less_equal(X1,X3)
| ( divide(X0,X3) != X4 )
| ( divide(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_85]) ).
tcf(c_106,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( less_equal(X2,X4)
| ~ less_equal(X0,X3)
| ( divide(X3,X1) != X4 )
| ( divide(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_86]) ).
tcf(c_108,plain,
divide(identity,a) = idQa,
inference(well_definedness,[status(thm)],[c_87]) ).
tcf(c_109,plain,
divide(identity,idQa) = idQ_idQa,
inference(well_definedness,[status(thm)],[c_88]) ).
tcf(c_110,plain,
divide(identity,idQ_idQa) = idQ__idQ_idQa,
inference(well_definedness,[status(thm)],[c_89]) ).
tcf(c_278,plain,
! [X0: $i,X1: $i,X2: $i] :
( less_equal(divide(X0,X2),divide(X1,X2))
| ~ less_equal(X0,X1) ),
inference(unflattening,[status(thm)],[c_106]) ).
tcf(c_283,plain,
! [X0: $i,X1: $i,X2: $i] :
( less_equal(divide(X2,X1),divide(X2,X0))
| ~ less_equal(X0,X1) ),
inference(unflattening,[status(thm)],[c_104]) ).
tcf(c_288,plain,
! [X0: $i,X1: $i,X2: $i] :
( less_equal(divide(X0,X2),X1)
| ~ less_equal(divide(X0,X1),X2) ),
inference(unflattening,[status(thm)],[c_102]) ).
tcf(c_306,plain,
! [X0: $i,X1: $i,X2: $i] :
( less_equal(divide(X2,X1),divide(X2,X0))
| ~ less_equal(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_283]) ).
tcf(c_308,plain,
! [X0: $i,X1: $i,X2: $i] :
( less_equal(divide(X0,X2),divide(X1,X2))
| ~ less_equal(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_278]) ).
tcf(c_310,plain,
! [X0: $i,X1: $i,X2: $i] :
( less_equal(divide(X0,X2),X1)
| ~ less_equal(divide(X0,X1),X2) ),
inference(prop_impl_just,[status(thm)],[c_288]) ).
tcf(c_732,plain,
! [X0: $i] :
( less_equal(idQa,divide(identity,X0))
| ~ less_equal(X0,a) ),
inference(superposition,[status(thm)],[c_108,c_306]) ).
tcf(c_773,plain,
! [X0: $i] :
( less_equal(divide(X0,a),idQa)
| ~ less_equal(X0,identity) ),
inference(superposition,[status(thm)],[c_108,c_308]) ).
tcf(c_776,plain,
! [X0: $i] : less_equal(divide(X0,a),idQa),
inference(forward_subsumption_resolution,[status(thm)],[c_773,c_76]) ).
tcf(c_807,plain,
! [X0: $i] :
( less_equal(divide(X0,idQa),idQ_idQa)
| ~ less_equal(X0,identity) ),
inference(superposition,[status(thm)],[c_109,c_308]) ).
tcf(c_808,plain,
! [X0: $i] : less_equal(divide(X0,idQa),idQ_idQa),
inference(forward_subsumption_resolution,[status(thm)],[c_807,c_76]) ).
tcf(c_819,plain,
( ( idQa = idQ__idQ_idQa )
| ~ less_equal(idQ__idQ_idQa,idQa)
| ~ less_equal(idQa,idQ__idQ_idQa) ),
inference(instantiation,[status(thm)],[c_75]) ).
tcf(c_1007,plain,
( less_equal(idQa,idQ__idQ_idQa)
| ~ less_equal(idQ_idQa,a) ),
inference(superposition,[status(thm)],[c_110,c_732]) ).
tcf(c_1033,plain,
! [X0: $i] : less_equal(divide(X0,idQa),a),
inference(superposition,[status(thm)],[c_776,c_310]) ).
tcf(c_1034,plain,
! [X0: $i] : less_equal(divide(X0,idQ_idQa),idQa),
inference(superposition,[status(thm)],[c_808,c_310]) ).
tcf(c_1187,plain,
less_equal(idQ_idQa,a),
inference(superposition,[status(thm)],[c_109,c_1033]) ).
tcf(c_1235,plain,
less_equal(idQ__idQ_idQa,idQa),
inference(superposition,[status(thm)],[c_110,c_1034]) ).
tcf(c_1246,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1235,c_1187,c_1007,c_819,c_90]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN009-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/5.39 % Computer : n002.cluster.edu
% 0.10/5.39 % Model : x86_64 x86_64
% 0.10/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.39 % Memory : 8046.5625MB
% 0.10/5.39 % OS : Linux 6.8.0-71-generic
% 0.10/5.39 % CPULimit : 300
% 0.10/5.39 % WCLimit : 300
% 0.10/5.39 % DateTime : Wed Sep 23 16:17:58 UTC 2026
% 0.10/5.39 % CPUTime :
% 0.10/5.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/5.43 Running first-order theorem proving
% 0.15/5.43 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
% 0.15/5.44
% 0.15/5.44 % ======== iProver multi-core TPTP/SMT =========
% 0.15/5.44
% 0.15/5.45 % Detected problem language: tptp
% 0.15/5.46 % Proving...
% 3.20/6.31 % SZS status Started for theBenchmark.p
% 3.20/6.31 % SZS status Unsatisfiable for theBenchmark.p
% 3.20/6.31
% 3.20/6.31 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.20/6.31
% 3.20/6.31 % ------ iProver source info
% 3.20/6.31
% 3.20/6.31 % git: date: 2026-07-19 20:42:38 +0200
% 3.20/6.31 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.20/6.31 % git: non_committed_changes: false
% 3.20/6.31
% 3.20/6.31 % ------ Parsing...% successful
% 3.20/6.31
% 3.20/6.31
% 3.20/6.31 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.20/6.31
% 3.20/6.31 % ------ Preprocessing... sup_sim: 7 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 %
% 3.20/6.31
% 3.20/6.31 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.20/6.31
% 3.20/6.31 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.20/6.31 % ------ Proving...
% 3.20/6.31 % ------ Problem Properties
% 3.20/6.31
% 3.20/6.31 %
% 3.20/6.31 % clauses 19
% 3.20/6.31 % conjectures 1
% 3.20/6.31 % EPR 5
% 3.20/6.31 % Horn 19
% 3.20/6.31 % unary 12
% 3.20/6.31 % binary 5
% 3.20/6.31 % lits 28
% 3.20/6.31 % lits eq 11
% 3.20/6.31 % fd_pure 0
% 3.20/6.31 % fd_pseudo 0
% 3.20/6.31 % fd_cond 0
% 3.20/6.31 % fd_pseudo_cond 1
% 3.20/6.31 % AC symbols 0
% 3.20/6.31
% 3.20/6.31 % ------ Schedule dynamic 5 is on
% 3.20/6.31
% 3.20/6.31 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.20/6.31
% 3.20/6.31
% 3.20/6.31 % ------
% 3.20/6.31 % Current options:
% 3.20/6.31 % ------
% 3.20/6.31
% 3.20/6.31
% 3.20/6.31 %
% 3.20/6.31
% 3.20/6.31 % ------ Proving...
% 3.20/6.31 %
% 3.20/6.31
% 3.20/6.31 % SZS status Unsatisfiable for theBenchmark.p
% 3.20/6.31
% 3.20/6.31 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.20/6.31
% 3.20/6.31
%------------------------------------------------------------------------------