TSTP Solution File: HEN009-1 by iProver---3.9
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%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : HEN009-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 3 02:25:21 EDT 2024
% Result : Unsatisfiable 4.12s 1.17s
% Output : CNFRefutation 4.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 11
% Syntax : Number of clauses : 92 ( 61 unt; 0 nHn; 50 RR)
% Number of literals : 132 ( 59 equ; 43 neg)
% Maximal clause size : 6 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 108 ( 27 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c_49,plain,
quotient(identity,a,idQa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_divide_a) ).
cnf(c_50,plain,
quotient(identity,idQa,idQ_idQa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_divide_idQa) ).
cnf(c_51,plain,
quotient(identity,idQ_idQa,idQ__idQ_idQa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_divide_idQ_idQa) ).
cnf(c_52,negated_conjecture,
idQa != idQ__idQ_idQa,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_one_inversion_equals_three) ).
cnf(c_53,plain,
( ~ less_equal(X0,X1)
| quotient(X0,X1,zero) ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',quotient_less_equal) ).
cnf(c_54,plain,
( ~ quotient(X0,X1,zero)
| less_equal(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',less_equal_quotient) ).
cnf(c_55,plain,
( ~ quotient(X0,X1,X2)
| less_equal(X2,X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',divisor_existence) ).
cnf(c_56,plain,
( ~ quotient(X0,X1,X2)
| ~ quotient(X0,X3,X4)
| ~ quotient(X1,X3,X5)
| ~ quotient(X2,X3,X6)
| ~ quotient(X4,X5,X7)
| less_equal(X7,X6) ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',quotient_property) ).
cnf(c_57,plain,
less_equal(zero,X0),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',zero_is_smallest) ).
cnf(c_58,plain,
( ~ less_equal(X0,X1)
| ~ less_equal(X1,X0)
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',less_equal_and_equal) ).
cnf(c_59,plain,
less_equal(X0,identity),
file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',identity_is_largest) ).
cnf(c_68,plain,
divide(identity,a) = idQa,
inference(well_definedness,[status(thm)],[c_49]) ).
cnf(c_69,plain,
divide(identity,idQa) = idQ_idQa,
inference(well_definedness,[status(thm)],[c_50]) ).
cnf(c_70,plain,
divide(identity,idQ_idQa) = idQ__idQ_idQa,
inference(well_definedness,[status(thm)],[c_51]) ).
cnf(c_71,plain,
( ~ less_equal(X0,X1)
| divide(X0,X1) = zero ),
inference(well_definedness,[status(thm)],[c_53]) ).
cnf(c_72,plain,
( divide(X0,X1) != zero
| less_equal(X0,X1) ),
inference(well_definedness,[status(thm)],[c_54]) ).
cnf(c_73,plain,
( divide(X0,X1) != X2
| less_equal(X2,X0) ),
inference(well_definedness,[status(thm)],[c_55]) ).
cnf(c_75,plain,
( divide(X0,X1) != X2
| divide(X0,X3) != X4
| divide(X1,X3) != X5
| divide(X2,X3) != X6
| divide(X4,X5) != X7
| less_equal(X7,X6) ),
inference(well_definedness,[status(thm)],[c_56]) ).
cnf(c_85,plain,
( less_equal(X2,X0)
| divide(X0,X1) != X2 ),
inference(prop_impl_just,[status(thm)],[c_73]) ).
cnf(c_86,plain,
( divide(X0,X1) != X2
| less_equal(X2,X0) ),
inference(renaming,[status(thm)],[c_85]) ).
cnf(c_165,plain,
less_equal(divide(X0,X1),X0),
inference(unflattening,[status(thm)],[c_86]) ).
cnf(c_179,plain,
less_equal(divide(divide(X0,X1),divide(X2,X1)),divide(divide(X0,X2),X1)),
inference(unflattening,[status(thm)],[c_75]) ).
cnf(c_187,plain,
( less_equal(X0,X1)
| divide(X0,X1) != zero ),
inference(prop_impl_just,[status(thm)],[c_72]) ).
cnf(c_188,plain,
( divide(X0,X1) != zero
| less_equal(X0,X1) ),
inference(renaming,[status(thm)],[c_187]) ).
cnf(c_189,plain,
( ~ less_equal(X0,X1)
| divide(X0,X1) = zero ),
inference(prop_impl_just,[status(thm)],[c_71]) ).
cnf(c_254,negated_conjecture,
idQa != idQ__idQ_idQa,
inference(demodulation,[status(thm)],[c_52]) ).
cnf(c_447,plain,
divide(zero,X0) = zero,
inference(superposition,[status(thm)],[c_57,c_189]) ).
cnf(c_448,plain,
divide(X0,identity) = zero,
inference(superposition,[status(thm)],[c_59,c_189]) ).
cnf(c_449,plain,
divide(divide(X0,X1),X0) = zero,
inference(superposition,[status(thm)],[c_165,c_189]) ).
cnf(c_459,plain,
( ~ less_equal(X0,zero)
| X0 = zero ),
inference(superposition,[status(thm)],[c_57,c_58]) ).
cnf(c_461,plain,
( ~ less_equal(X0,divide(X0,X1))
| divide(X0,X1) = X0 ),
inference(superposition,[status(thm)],[c_165,c_58]) ).
cnf(c_545,plain,
less_equal(divide(divide(X0,a),idQa),divide(divide(X0,identity),a)),
inference(superposition,[status(thm)],[c_68,c_179]) ).
cnf(c_546,plain,
less_equal(divide(divide(X0,idQa),idQ_idQa),divide(divide(X0,identity),idQa)),
inference(superposition,[status(thm)],[c_69,c_179]) ).
cnf(c_547,plain,
less_equal(divide(divide(X0,idQ_idQa),idQ__idQ_idQa),divide(divide(X0,identity),idQ_idQa)),
inference(superposition,[status(thm)],[c_70,c_179]) ).
cnf(c_548,plain,
less_equal(divide(divide(X0,X1),zero),divide(divide(X0,zero),X1)),
inference(superposition,[status(thm)],[c_447,c_179]) ).
cnf(c_552,plain,
less_equal(divide(divide(X0,X0),divide(X1,X0)),zero),
inference(superposition,[status(thm)],[c_449,c_179]) ).
cnf(c_559,plain,
( ~ less_equal(divide(divide(X0,X1),X2),divide(divide(X0,X2),divide(X1,X2)))
| divide(divide(X0,X2),divide(X1,X2)) = divide(divide(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_179,c_58]) ).
cnf(c_560,plain,
divide(divide(divide(X0,X1),divide(X2,X1)),divide(divide(X0,X2),X1)) = zero,
inference(superposition,[status(thm)],[c_179,c_189]) ).
cnf(c_567,plain,
less_equal(divide(divide(X0,idQ_idQa),idQ__idQ_idQa),divide(zero,idQ_idQa)),
inference(light_normalisation,[status(thm)],[c_547,c_448]) ).
cnf(c_568,plain,
less_equal(divide(divide(X0,idQa),idQ_idQa),divide(zero,idQa)),
inference(light_normalisation,[status(thm)],[c_546,c_448]) ).
cnf(c_569,plain,
less_equal(divide(divide(X0,a),idQa),divide(zero,a)),
inference(light_normalisation,[status(thm)],[c_545,c_448]) ).
cnf(c_615,plain,
less_equal(divide(divide(X0,X0),zero),zero),
inference(superposition,[status(thm)],[c_449,c_552]) ).
cnf(c_639,plain,
divide(divide(idQa,divide(X0,a)),divide(divide(identity,X0),a)) = zero,
inference(superposition,[status(thm)],[c_68,c_560]) ).
cnf(c_1020,plain,
divide(divide(X0,X0),zero) = zero,
inference(superposition,[status(thm)],[c_615,c_459]) ).
cnf(c_1281,plain,
( ~ less_equal(divide(X0,X0),zero)
| divide(divide(X0,X0),zero) = divide(X0,X0) ),
inference(superposition,[status(thm)],[c_1020,c_461]) ).
cnf(c_1283,plain,
less_equal(divide(X0,X0),zero),
inference(superposition,[status(thm)],[c_1020,c_188]) ).
cnf(c_1294,plain,
divide(divide(X0,X0),zero) = divide(X0,X0),
inference(forward_subsumption_resolution,[status(thm)],[c_1281,c_1283]) ).
cnf(c_1295,plain,
divide(X0,X0) = zero,
inference(light_normalisation,[status(thm)],[c_1294,c_1020]) ).
cnf(c_1531,plain,
less_equal(divide(divide(X0,idQ_idQa),idQ__idQ_idQa),zero),
inference(demodulation,[status(thm)],[c_567,c_447]) ).
cnf(c_1539,plain,
divide(divide(X0,idQ_idQa),idQ__idQ_idQa) = zero,
inference(superposition,[status(thm)],[c_1531,c_459]) ).
cnf(c_1553,plain,
less_equal(divide(X0,idQ_idQa),idQ__idQ_idQa),
inference(superposition,[status(thm)],[c_1539,c_188]) ).
cnf(c_1663,plain,
less_equal(divide(divide(X0,idQa),idQ_idQa),zero),
inference(demodulation,[status(thm)],[c_568,c_447]) ).
cnf(c_1671,plain,
divide(divide(X0,idQa),idQ_idQa) = zero,
inference(superposition,[status(thm)],[c_1663,c_459]) ).
cnf(c_1685,plain,
less_equal(divide(X0,idQa),idQ_idQa),
inference(superposition,[status(thm)],[c_1671,c_188]) ).
cnf(c_1696,plain,
( ~ less_equal(zero,divide(divide(X0,idQ_idQa),divide(idQa,idQ_idQa)))
| divide(divide(X0,idQ_idQa),divide(idQa,idQ_idQa)) = divide(divide(X0,idQa),idQ_idQa) ),
inference(superposition,[status(thm)],[c_1671,c_559]) ).
cnf(c_1701,plain,
( ~ less_equal(zero,divide(divide(X0,idQ_idQa),divide(idQa,idQ_idQa)))
| divide(divide(X0,idQ_idQa),divide(idQa,idQ_idQa)) = zero ),
inference(light_normalisation,[status(thm)],[c_1696,c_1671]) ).
cnf(c_1702,plain,
divide(divide(X0,idQ_idQa),divide(idQa,idQ_idQa)) = zero,
inference(forward_subsumption_resolution,[status(thm)],[c_1701,c_57]) ).
cnf(c_1749,plain,
( ~ less_equal(idQ_idQa,divide(X0,idQa))
| divide(X0,idQa) = idQ_idQa ),
inference(superposition,[status(thm)],[c_1685,c_58]) ).
cnf(c_1753,plain,
less_equal(divide(divide(X0,a),idQa),zero),
inference(demodulation,[status(thm)],[c_569,c_447]) ).
cnf(c_1761,plain,
divide(divide(X0,a),idQa) = zero,
inference(superposition,[status(thm)],[c_1753,c_459]) ).
cnf(c_1935,plain,
less_equal(divide(X0,a),idQa),
inference(superposition,[status(thm)],[c_1761,c_188]) ).
cnf(c_1948,plain,
( ~ less_equal(zero,divide(divide(X0,idQa),divide(a,idQa)))
| divide(divide(X0,idQa),divide(a,idQa)) = divide(divide(X0,a),idQa) ),
inference(superposition,[status(thm)],[c_1761,c_559]) ).
cnf(c_1953,plain,
( ~ less_equal(zero,divide(divide(X0,idQa),divide(a,idQa)))
| divide(divide(X0,idQa),divide(a,idQa)) = zero ),
inference(light_normalisation,[status(thm)],[c_1948,c_1761]) ).
cnf(c_1954,plain,
divide(divide(X0,idQa),divide(a,idQa)) = zero,
inference(forward_subsumption_resolution,[status(thm)],[c_1953,c_57]) ).
cnf(c_2420,plain,
less_equal(divide(X0,idQ_idQa),divide(idQa,idQ_idQa)),
inference(superposition,[status(thm)],[c_1702,c_188]) ).
cnf(c_2610,plain,
( ~ less_equal(divide(idQa,idQ_idQa),divide(X0,idQ_idQa))
| divide(X0,idQ_idQa) = divide(idQa,idQ_idQa) ),
inference(superposition,[status(thm)],[c_2420,c_58]) ).
cnf(c_2621,plain,
( ~ less_equal(divide(idQa,idQ_idQa),idQ__idQ_idQa)
| divide(identity,idQ_idQa) = divide(idQa,idQ_idQa) ),
inference(superposition,[status(thm)],[c_70,c_2610]) ).
cnf(c_2630,plain,
( ~ less_equal(divide(idQa,idQ_idQa),idQ__idQ_idQa)
| divide(idQa,idQ_idQa) = idQ__idQ_idQa ),
inference(light_normalisation,[status(thm)],[c_2621,c_70]) ).
cnf(c_2631,plain,
divide(idQa,idQ_idQa) = idQ__idQ_idQa,
inference(forward_subsumption_resolution,[status(thm)],[c_2630,c_1553]) ).
cnf(c_2658,plain,
( ~ less_equal(idQa,idQ__idQ_idQa)
| divide(idQa,idQ_idQa) = idQa ),
inference(superposition,[status(thm)],[c_2631,c_461]) ).
cnf(c_2675,plain,
( ~ less_equal(idQa,idQ__idQ_idQa)
| idQa = idQ__idQ_idQa ),
inference(light_normalisation,[status(thm)],[c_2658,c_2631]) ).
cnf(c_2676,plain,
~ less_equal(idQa,idQ__idQ_idQa),
inference(forward_subsumption_resolution,[status(thm)],[c_2675,c_254]) ).
cnf(c_3118,plain,
less_equal(divide(X0,idQa),divide(a,idQa)),
inference(superposition,[status(thm)],[c_1954,c_188]) ).
cnf(c_3229,plain,
less_equal(idQ_idQa,divide(a,idQa)),
inference(superposition,[status(thm)],[c_69,c_3118]) ).
cnf(c_3242,plain,
divide(a,idQa) = idQ_idQa,
inference(superposition,[status(thm)],[c_3229,c_1749]) ).
cnf(c_3250,plain,
divide(idQ_idQa,a) = zero,
inference(superposition,[status(thm)],[c_3242,c_449]) ).
cnf(c_3303,plain,
divide(divide(idQa,zero),divide(divide(identity,idQ_idQa),a)) = zero,
inference(superposition,[status(thm)],[c_3250,c_639]) ).
cnf(c_3312,plain,
divide(divide(idQa,zero),divide(idQ__idQ_idQa,a)) = zero,
inference(light_normalisation,[status(thm)],[c_3303,c_70]) ).
cnf(c_4003,plain,
less_equal(divide(idQa,zero),divide(idQ__idQ_idQa,a)),
inference(superposition,[status(thm)],[c_3312,c_188]) ).
cnf(c_4134,plain,
( ~ less_equal(divide(idQ__idQ_idQa,a),divide(idQa,zero))
| divide(idQa,zero) = divide(idQ__idQ_idQa,a) ),
inference(superposition,[status(thm)],[c_4003,c_58]) ).
cnf(c_5307,plain,
less_equal(divide(divide(X0,divide(X0,zero)),zero),zero),
inference(superposition,[status(thm)],[c_1295,c_548]) ).
cnf(c_5489,plain,
divide(divide(X0,divide(X0,zero)),zero) = zero,
inference(superposition,[status(thm)],[c_5307,c_459]) ).
cnf(c_5938,plain,
( ~ less_equal(divide(X0,divide(X0,zero)),zero)
| divide(divide(X0,divide(X0,zero)),zero) = divide(X0,divide(X0,zero)) ),
inference(superposition,[status(thm)],[c_5489,c_461]) ).
cnf(c_5940,plain,
less_equal(divide(X0,divide(X0,zero)),zero),
inference(superposition,[status(thm)],[c_5489,c_188]) ).
cnf(c_5955,plain,
divide(divide(X0,divide(X0,zero)),zero) = divide(X0,divide(X0,zero)),
inference(forward_subsumption_resolution,[status(thm)],[c_5938,c_5940]) ).
cnf(c_5956,plain,
divide(X0,divide(X0,zero)) = zero,
inference(light_normalisation,[status(thm)],[c_5955,c_5489]) ).
cnf(c_6033,plain,
less_equal(X0,divide(X0,zero)),
inference(superposition,[status(thm)],[c_5956,c_188]) ).
cnf(c_6287,plain,
divide(X0,zero) = X0,
inference(superposition,[status(thm)],[c_6033,c_461]) ).
cnf(c_6303,plain,
( ~ less_equal(divide(idQ__idQ_idQa,a),idQa)
| divide(idQ__idQ_idQa,a) = idQa ),
inference(demodulation,[status(thm)],[c_4134,c_6287]) ).
cnf(c_6314,plain,
divide(idQ__idQ_idQa,a) = idQa,
inference(forward_subsumption_resolution,[status(thm)],[c_6303,c_1935]) ).
cnf(c_6517,plain,
less_equal(idQa,idQ__idQ_idQa),
inference(superposition,[status(thm)],[c_6314,c_165]) ).
cnf(c_6533,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_6517,c_2676]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : HEN009-1 : TPTP v8.1.2. Released v1.0.0.
% 0.14/0.14 % Command : run_iprover %s %d THM
% 0.14/0.36 % Computer : n007.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu May 2 18:32:05 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.21/0.50 Running first-order theorem proving
% 0.21/0.50 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.12/1.17 % SZS status Started for theBenchmark.p
% 4.12/1.17 % SZS status Unsatisfiable for theBenchmark.p
% 4.12/1.17
% 4.12/1.17 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 4.12/1.17
% 4.12/1.17 ------ iProver source info
% 4.12/1.17
% 4.12/1.17 git: date: 2024-05-02 19:28:25 +0000
% 4.12/1.17 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 4.12/1.17 git: non_committed_changes: false
% 4.12/1.17
% 4.12/1.17 ------ Parsing...successful
% 4.12/1.17
% 4.12/1.17
% 4.12/1.17
% 4.12/1.17 ------ Preprocessing... sup_sim: 4 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
% 4.12/1.17
% 4.12/1.17 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 4.12/1.17
% 4.12/1.17 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.12/1.17 ------ Proving...
% 4.12/1.17 ------ Problem Properties
% 4.12/1.17
% 4.12/1.17
% 4.12/1.17 clauses 11
% 4.12/1.17 conjectures 1
% 4.12/1.17 EPR 4
% 4.12/1.17 Horn 11
% 4.12/1.17 unary 8
% 4.12/1.17 binary 2
% 4.12/1.17 lits 15
% 4.12/1.17 lits eq 7
% 4.12/1.17 fd_pure 0
% 4.12/1.17 fd_pseudo 0
% 4.12/1.17 fd_cond 0
% 4.12/1.17 fd_pseudo_cond 1
% 4.12/1.17 AC symbols 0
% 4.12/1.17
% 4.12/1.17 ------ Schedule dynamic 5 is on
% 4.12/1.17
% 4.12/1.17 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.12/1.17
% 4.12/1.17
% 4.12/1.17 ------
% 4.12/1.17 Current options:
% 4.12/1.17 ------
% 4.12/1.17
% 4.12/1.17
% 4.12/1.17
% 4.12/1.17
% 4.12/1.17 ------ Proving...
% 4.12/1.17
% 4.12/1.17
% 4.12/1.17 % SZS status Unsatisfiable for theBenchmark.p
% 4.12/1.17
% 4.12/1.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.12/1.18
% 4.12/1.18
%------------------------------------------------------------------------------