TSTP Solution File: NUM924+3 by SRASS---0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : SRASS---0.1
% Problem : NUM924+3 : TPTP v5.3.0. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : SRASS -q2 -a 0 10 10 10 -i3 -n60 %s
% Computer : art03.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2800MHz
% Memory : 2005MB
% OS : Linux 2.6.32.26-175.fc12.i686.PAE
% CPULimit : 300s
% DateTime : Sun Dec 4 00:28:22 EST 2011
% Result : Theorem 156.60s
% Output : Solution 156.60s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Reading problem from /tmp/SystemOnTPTP6708/NUM924+3.tptp
% Adding relevance values
% Extracting the conjecture
% Sorting axioms by relevance
% Looking for THM ...
% WARNING: TreeLimitedRun lost 0.12s, total lost is 0.12s
% found
% SZS status THM for /tmp/SystemOnTPTP6708/NUM924+3.tptp
% SZS output start Solution for /tmp/SystemOnTPTP6708/NUM924+3.tptp
% TreeLimitedRun: ----------------------------------------------------------
% TreeLimitedRun: /home/graph/tptp/Systems/EP---1.4/eproof_ram --print-statistics -xAuto -tAuto --cpu-limit=60 --memory-limit=Auto --tstp-format /tmp/SRASS.s.p
% TreeLimitedRun: CPU time limit is 60s
% TreeLimitedRun: WC time limit is 120s
% TreeLimitedRun: PID is 6996
% TreeLimitedRun: ----------------------------------------------------------
% PrfWatch: 0.00 CPU 0.02 WC
% # Garbage collection reclaimed 520 unused term cells.
% # Garbage collection reclaimed 8226 unused term cells.
% # Garbage collection reclaimed 7087 unused term cells.
% # Garbage collection reclaimed 6443 unused term cells.
% # Garbage collection reclaimed 5131 unused term cells.
% # Garbage collection reclaimed 4275 unused term cells.
% # Garbage collection reclaimed 3256 unused term cells.
% # Garbage collection reclaimed 2828 unused term cells.
% # Garbage collection reclaimed 1281 unused term cells.
% # Auto-Ordering is analysing problem.
% # Problem is type GHSMNSMLM31LD
% # Auto-mode selected ordering type KBO6
% # Auto-mode selected ordering precedence scheme <invfreqconjmin>
% # Auto-mode selected weight ordering scheme <precrank5>
% #
% # Auto-Heuristic is analysing problem.
% # Problem is type GHSMNSMLM31LD
% # Auto-Mode selected heuristic G_E___107_C48_F1_PI_AE_Q4_CS_SP_PS_S0Y
% # and selection function SelectMaxLComplexAvoidPosPred.
% #
% # Initializing proof state
% # Scanning for AC axioms
% # Garbage collection reclaimed 2451 unused term cells.
% # Garbage collection reclaimed 255 unused term cells.
% # Garbage collection reclaimed 261 unused term cells.
% # Garbage collection reclaimed 258 unused term cells.
% # Garbage collection reclaimed 259 unused term cells.
% # Garbage collection reclaimed 256 unused term cells.
% # Garbage collection reclaimed 257 unused term cells.
% # Garbage collection reclaimed 258 unused term cells.
% # Garbage collection reclaimed 259 unused term cells.
% # Garbage collection reclaimed 255 unused term cells.
% # Garbage collection reclaimed 261 unused term cells.
% # Garbage collection reclaimed 255 unused term cells.
% # Garbage collection reclaimed 264 unused term cells.
% # Garbage collection reclaimed 259 unused term cells.
% # Garbage collection reclaimed 265 unused term cells.
% # Garbage collection reclaimed 259 unused term cells.
% # Garbage collection reclaimed 260 unused term cells.
% # Garbage collection reclaimed 259 unused term cells.
% # Garbage collection reclaimed 257 unused term cells.
% # Garbage collection reclaimed 259 unused term cells.
% # Presaturation interreduction done
% # Proof found!
% # SZS status Theorem
% # Parsed axioms : 1230
% # Removed by relevancy pruning : 0
% # Initial clauses : 1824
% # Removed in clause preprocessing : 95
% # Initial clauses in saturation : 1729
% # Processed clauses : 1724
% # ...of these trivial : 122
% # ...subsumed : 336
% # ...remaining for further processing: 1265
% # Other redundant clauses eliminated : 29
% # Clauses deleted for lack of memory : 0
% # Backward-subsumed : 3
% # Backward-rewritten : 12
% # Generated clauses : 29
% # ...of the previous two non-trivial : 24
% # Contextual simplify-reflections : 42
% # Paramodulations : 0
% # Factorizations : 0
% # Equation resolutions : 29
% # Current number of processed clauses: 1221
% # Positive orientable unit clauses: 205
% # Positive unorientable unit clauses: 46
% # Negative unit clauses : 31
% # Non-unit-clauses : 939
% # Current number of unprocessed clauses: 29
% # ...number of literals in the above : 48
% # Clause-clause subsumption calls (NU) : 42667
% # Rec. Clause-clause subsumption calls : 31786
% # Unit Clause-clause subsumption calls : 85
% # Rewrite failures with RHS unbound : 0
% # Indexed BW rewrite attempts : 1534
% # Indexed BW rewrite successes : 127
% # Backwards rewriting index : 1096 leaves, 2.63+/-6.275 terms/leaf
% # Paramod-from index : 287 leaves, 2.45+/-6.170 terms/leaf
% # Paramod-into index : 1014 leaves, 2.35+/-5.346 terms/leaf
% # SZS output start CNFRefutation.
% fof(64, axiom,![X8]:bit1(X8)=hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X8)),X8),file('/tmp/SRASS.s.p', fact_236_Bit1__def)).
% fof(96, axiom,![X8]:bit0(X8)=hAPP_int_int(plus_plus_int(X8),X8),file('/tmp/SRASS.s.p', fact_182_Bit0__def)).
% fof(118, axiom,![X97]:hAPP_nat_int(power_power_int(X97),number_number_of_nat(bit0(bit1(pls))))=hAPP_int_int(times_times_int(X97),X97),file('/tmp/SRASS.s.p', fact_203_power2__eq__square)).
% fof(165, axiom,pls=zero_zero_int,file('/tmp/SRASS.s.p', fact_172_Pls__def)).
% fof(171, axiom,![X112]:![X113]:![X114]:hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X112),X113)),X114)=hAPP_int_int(plus_plus_int(X112),hAPP_int_int(plus_plus_int(X113),X114)),file('/tmp/SRASS.s.p', fact_132_zadd__assoc)).
% fof(172, axiom,![X1]:![X2]:![X40]:hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X2),X40))=hAPP_int_int(plus_plus_int(X2),hAPP_int_int(plus_plus_int(X1),X40)),file('/tmp/SRASS.s.p', fact_133_zadd__left__commute)).
% fof(173, axiom,![X40]:![X49]:hAPP_int_int(plus_plus_int(X40),X49)=hAPP_int_int(plus_plus_int(X49),X40),file('/tmp/SRASS.s.p', fact_134_zadd__commute)).
% fof(256, axiom,hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),t)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),zero_zero_int))),file('/tmp/SRASS.s.p', fact_2__096_I4_A_K_Am_A_L_A1_J_A_K_At_A_060_A_I4_A_K_Am_A_L_A1_J_A_K_A0_096)).
% fof(262, axiom,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls))))),one_one_int)=hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),t),file('/tmp/SRASS.s.p', fact_3_t)).
% fof(481, axiom,hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)=number_number_of_nat(bit0(bit1(pls))),file('/tmp/SRASS.s.p', fact_87_nat__1__add__1)).
% fof(503, axiom,![X40]:![X49]:hAPP_int_int(times_times_int(X40),X49)=hAPP_int_int(times_times_int(X49),X40),file('/tmp/SRASS.s.p', fact_35_zmult__commute)).
% fof(622, axiom,![X413]:hAPP_int_int(times_times_int(X413),zero_zero_int)=zero_zero_int,file('/tmp/SRASS.s.p', fact_367_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J)).
% fof(696, axiom,twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int))=hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),t),file('/tmp/SRASS.s.p', fact_1068__096sum2sq_A_Is_M_A1_J_A_061_A_I4_A_K_Am_A_L_A1_J_A_K_At_096)).
% fof(1230, conjecture,hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls))))),one_one_int)),zero_zero_int)),file('/tmp/SRASS.s.p', conj_0)).
% fof(1231, negated_conjecture,~(hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls))))),one_one_int)),zero_zero_int))),inference(assume_negation,[status(cth)],[1230])).
% fof(1338, negated_conjecture,~(hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls))))),one_one_int)),zero_zero_int))),inference(fof_simplification,[status(thm)],[1231,theory(equality)])).
% fof(1533, plain,![X9]:bit1(X9)=hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X9)),X9),inference(variable_rename,[status(thm)],[64])).
% cnf(1534,plain,(bit1(X1)=hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X1)),X1)),inference(split_conjunct,[status(thm)],[1533])).
% fof(1655, plain,![X9]:bit0(X9)=hAPP_int_int(plus_plus_int(X9),X9),inference(variable_rename,[status(thm)],[96])).
% cnf(1656,plain,(bit0(X1)=hAPP_int_int(plus_plus_int(X1),X1)),inference(split_conjunct,[status(thm)],[1655])).
% fof(1741, plain,![X98]:hAPP_nat_int(power_power_int(X98),number_number_of_nat(bit0(bit1(pls))))=hAPP_int_int(times_times_int(X98),X98),inference(variable_rename,[status(thm)],[118])).
% cnf(1742,plain,(hAPP_nat_int(power_power_int(X1),number_number_of_nat(bit0(bit1(pls))))=hAPP_int_int(times_times_int(X1),X1)),inference(split_conjunct,[status(thm)],[1741])).
% cnf(1871,plain,(pls=zero_zero_int),inference(split_conjunct,[status(thm)],[165])).
% fof(1889, plain,![X115]:![X116]:![X117]:hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X115),X116)),X117)=hAPP_int_int(plus_plus_int(X115),hAPP_int_int(plus_plus_int(X116),X117)),inference(variable_rename,[status(thm)],[171])).
% cnf(1890,plain,(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X1),X2)),X3)=hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X2),X3))),inference(split_conjunct,[status(thm)],[1889])).
% fof(1891, plain,![X41]:![X42]:![X43]:hAPP_int_int(plus_plus_int(X41),hAPP_int_int(plus_plus_int(X42),X43))=hAPP_int_int(plus_plus_int(X42),hAPP_int_int(plus_plus_int(X41),X43)),inference(variable_rename,[status(thm)],[172])).
% cnf(1892,plain,(hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X2),X3))=hAPP_int_int(plus_plus_int(X2),hAPP_int_int(plus_plus_int(X1),X3))),inference(split_conjunct,[status(thm)],[1891])).
% fof(1893, plain,![X50]:![X51]:hAPP_int_int(plus_plus_int(X50),X51)=hAPP_int_int(plus_plus_int(X51),X50),inference(variable_rename,[status(thm)],[173])).
% cnf(1894,plain,(hAPP_int_int(plus_plus_int(X1),X2)=hAPP_int_int(plus_plus_int(X2),X1)),inference(split_conjunct,[status(thm)],[1893])).
% cnf(2167,plain,(hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),t)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),zero_zero_int)))),inference(split_conjunct,[status(thm)],[256])).
% cnf(2191,plain,(hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls))))),one_one_int)=hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),t)),inference(split_conjunct,[status(thm)],[262])).
% cnf(2866,plain,(hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)=number_number_of_nat(bit0(bit1(pls)))),inference(split_conjunct,[status(thm)],[481])).
% fof(2921, plain,![X50]:![X51]:hAPP_int_int(times_times_int(X50),X51)=hAPP_int_int(times_times_int(X51),X50),inference(variable_rename,[status(thm)],[503])).
% cnf(2922,plain,(hAPP_int_int(times_times_int(X1),X2)=hAPP_int_int(times_times_int(X2),X1)),inference(split_conjunct,[status(thm)],[2921])).
% fof(3238, plain,![X414]:hAPP_int_int(times_times_int(X414),zero_zero_int)=zero_zero_int,inference(variable_rename,[status(thm)],[622])).
% cnf(3239,plain,(hAPP_int_int(times_times_int(X1),zero_zero_int)=zero_zero_int),inference(split_conjunct,[status(thm)],[3238])).
% cnf(3432,plain,(twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int))=hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(bit0(bit0(bit1(pls))))),m)),one_one_int)),t)),inference(split_conjunct,[status(thm)],[696])).
% cnf(5176,negated_conjecture,(~hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(bit0(bit1(pls))))),one_one_int)),zero_zero_int))),inference(split_conjunct,[status(thm)],[1338])).
% cnf(5287,plain,(hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)=number_number_of_nat(hAPP_int_int(plus_plus_int(bit1(pls)),bit1(pls)))),inference(rw,[status(thm)],[2866,1656,theory(equality)]),['unfolding']).
% cnf(5308,plain,(hAPP_nat_int(power_power_int(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(bit1(pls)),bit1(pls))))=hAPP_int_int(times_times_int(X1),X1)),inference(rw,[status(thm)],[1742,1656,theory(equality)]),['unfolding']).
% cnf(5363,plain,(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(bit1(pls)),bit1(pls))),hAPP_int_int(plus_plus_int(bit1(pls)),bit1(pls))))),m)),one_one_int)),t)=twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int))),inference(rw,[status(thm)],[inference(rw,[status(thm)],[3432,1656,theory(equality)]),1656,theory(equality)]),['unfolding']).
% cnf(5371,plain,(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(bit1(pls)),bit1(pls))),hAPP_int_int(plus_plus_int(bit1(pls)),bit1(pls))))),m)),one_one_int)),t)=hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(hAPP_int_int(plus_plus_int(bit1(pls)),bit1(pls))))),one_one_int)),inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[2191,1656,theory(equality)]),1656,theory(equality)]),1656,theory(equality)]),['unfolding']).
% cnf(5380,plain,(hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(bit1(pls)),bit1(pls))),hAPP_int_int(plus_plus_int(bit1(pls)),bit1(pls))))),m)),one_one_int)),t)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(bit1(pls)),bit1(pls))),hAPP_int_int(plus_plus_int(bit1(pls)),bit1(pls))))),m)),one_one_int)),zero_zero_int)))),inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[2167,1656,theory(equality)]),1656,theory(equality)]),1656,theory(equality)]),1656,theory(equality)]),['unfolding']).
% cnf(5515,negated_conjecture,(~hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(hAPP_int_int(plus_plus_int(bit1(pls)),bit1(pls))))),one_one_int)),zero_zero_int))),inference(rw,[status(thm)],[5176,1656,theory(equality)]),['unfolding']).
% cnf(5549,plain,(hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)=number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),inference(rw,[status(thm)],[inference(rw,[status(thm)],[5287,1534,theory(equality)]),1534,theory(equality)]),['unfolding']).
% cnf(5567,plain,(hAPP_nat_int(power_power_int(X1),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))=hAPP_int_int(times_times_int(X1),X1)),inference(rw,[status(thm)],[inference(rw,[status(thm)],[5308,1534,theory(equality)]),1534,theory(equality)]),['unfolding']).
% cnf(5628,plain,(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int)),t)=twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int))),inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[5363,1534,theory(equality)]),1534,theory(equality)]),1534,theory(equality)]),1534,theory(equality)]),['unfolding']).
% cnf(5636,plain,(hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int)),t)=hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),one_one_int)),inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[5371,1534,theory(equality)]),1534,theory(equality)]),1534,theory(equality)]),1534,theory(equality)]),1534,theory(equality)]),1534,theory(equality)]),['unfolding']).
% cnf(5645,plain,(hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int)),t)),hAPP_int_int(times_times_int(hAPP_int_int(plus_plus_int(hAPP_int_int(times_times_int(number_number_of_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),m)),one_one_int)),zero_zero_int)))),inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[5380,1534,theory(equality)]),1534,theory(equality)]),1534,theory(equality)]),1534,theory(equality)]),1534,theory(equality)]),1534,theory(equality)]),1534,theory(equality)]),1534,theory(equality)]),['unfolding']).
% cnf(5798,negated_conjecture,(~hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),one_one_int)),zero_zero_int))),inference(rw,[status(thm)],[inference(rw,[status(thm)],[5515,1534,theory(equality)]),1534,theory(equality)]),['unfolding']).
% cnf(5837,plain,(hAPP_int_int(times_times_int(X1),pls)=zero_zero_int),inference(rw,[status(thm)],[3239,1871,theory(equality)])).
% cnf(5838,plain,(hAPP_int_int(times_times_int(X1),pls)=pls),inference(rw,[status(thm)],[5837,1871,theory(equality)])).
% cnf(6341,plain,(number_number_of_nat(hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(one_one_int),one_one_int))))))=hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)),inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[5549,1894,theory(equality)]),1894,theory(equality)]),1894,theory(equality)]),1894,theory(equality)]),1890,theory(equality)]),1890,theory(equality)]),1892,theory(equality)]),1892,theory(equality)])).
% cnf(6448,plain,(hAPP_nat_int(power_power_int(X1),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat))=hAPP_int_int(times_times_int(X1),X1)),inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[5567,1894,theory(equality)]),1894,theory(equality)]),1894,theory(equality)]),1894,theory(equality)]),1890,theory(equality)]),1890,theory(equality)]),1892,theory(equality)]),1892,theory(equality)]),6341,theory(equality)])).
% cnf(6543,negated_conjecture,(~hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(s),s))),pls))),inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[5798,1894,theory(equality)]),1894,theory(equality)]),1894,theory(equality)]),1894,theory(equality)]),1890,theory(equality)]),1890,theory(equality)]),1892,theory(equality)]),1892,theory(equality)]),6341,theory(equality)]),6448,theory(equality)]),1894,theory(equality)]),1871,theory(equality)])).
% cnf(6965,plain,(hAPP_int_int(times_times_int(t),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(m),number_number_of_int(hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(plus_plus_int(one_one_int),one_one_int)))))))))))))))=twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int))),inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[5628,1894,theory(equality)]),1894,theory(equality)]),1894,theory(equality)]),1894,theory(equality)]),1890,theory(equality)]),1890,theory(equality)]),1892,theory(equality)]),1892,theory(equality)]),1894,theory(equality)]),1894,theory(equality)]),1894,theory(equality)]),1894,theory(equality)]),1890,theory(equality)]),1890,theory(equality)]),1892,theory(equality)]),1892,theory(equality)]),1890,theory(equality)]),1890,theory(equality)]),1890,theory(equality)]),1890,theory(equality)]),1890,theory(equality)]),1892,theory(equality)]),1892,theory(equality)]),1892,theory(equality)]),1892,theory(equality)]),1892,theory(equality)]),1892,theory(equality)]),1892,theory(equality)]),1892,theory(equality)]),2922,theory(equality)]),1894,theory(equality)]),2922,theory(equality)])).
% cnf(6987,plain,(twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int))=hAPP_int_int(plus_plus_int(hAPP_nat_int(power_power_int(s),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))))),one_one_int)),inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[5636,1894,theory(equality)]),1894,theory(equality)]),1894,theory(equality)]),1894,theory(equality)]),1890,theory(equality)]),1890,theory(equality)]),1892,theory(equality)]),1892,theory(equality)]),1894,theory(equality)]),1894,theory(equality)]),1894,theory(equality)]),1894,theory(equality)]),1890,theory(equality)]),1890,theory(equality)]),1892,theory(equality)]),1892,theory(equality)]),1890,theory(equality)]),1890,theory(equality)]),1890,theory(equality)]),1890,theory(equality)]),1890,theory(equality)]),1892,theory(equality)]),1892,theory(equality)]),1892,theory(equality)]),1892,theory(equality)]),1892,theory(equality)]),1892,theory(equality)]),1892,theory(equality)]),1892,theory(equality)]),2922,theory(equality)]),1894,theory(equality)]),2922,theory(equality)]),6965,theory(equality)])).
% cnf(6988,plain,(twoSqu1241645765sum2sq(product_Pair_int_int(s,one_one_int))=hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(s),s))),inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[6987,1894,theory(equality)]),1894,theory(equality)]),1894,theory(equality)]),1894,theory(equality)]),1890,theory(equality)]),1890,theory(equality)]),1892,theory(equality)]),1892,theory(equality)]),6341,theory(equality)]),6448,theory(equality)]),1894,theory(equality)])).
% cnf(7088,plain,(hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(plus_plus_int(one_one_int),hAPP_int_int(times_times_int(s),s))),pls))),inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[5645,1894,theory(equality)]),1894,theory(equality)]),1894,theory(equality)]),1894,theory(equality)]),1890,theory(equality)]),1890,theory(equality)]),1892,theory(equality)]),1892,theory(equality)]),1894,theory(equality)]),1894,theory(equality)]),1894,theory(equality)]),1894,theory(equality)]),1890,theory(equality)]),1890,theory(equality)]),1892,theory(equality)]),1892,theory(equality)]),1890,theory(equality)]),1890,theory(equality)]),1890,theory(equality)]),1890,theory(equality)]),1890,theory(equality)]),1892,theory(equality)]),1892,theory(equality)]),1892,theory(equality)]),1892,theory(equality)]),1892,theory(equality)]),1892,theory(equality)]),1892,theory(equality)]),1892,theory(equality)]),2922,theory(equality)]),1894,theory(equality)]),2922,theory(equality)]),6965,theory(equality)]),6988,theory(equality)]),1894,theory(equality)]),1894,theory(equality)]),1894,theory(equality)]),1894,theory(equality)]),1890,theory(equality)]),1890,theory(equality)]),1892,theory(equality)]),1892,theory(equality)]),1894,theory(equality)]),1894,theory(equality)]),1894,theory(equality)]),1894,theory(equality)]),1890,theory(equality)]),1890,theory(equality)]),1892,theory(equality)]),1892,theory(equality)]),1890,theory(equality)]),1890,theory(equality)]),1890,theory(equality)]),1890,theory(equality)]),1890,theory(equality)]),1892,theory(equality)]),1892,theory(equality)]),1892,theory(equality)]),1892,theory(equality)]),1892,theory(equality)]),1892,theory(equality)]),1892,theory(equality)]),1892,theory(equality)]),2922,theory(equality)]),1894,theory(equality)]),1871,theory(equality)]),5838,theory(equality)])).
% cnf(7089,plain,($false),inference(sr,[status(thm)],[7088,6543,theory(equality)])).
% cnf(7090,plain,($false),7089,['proof']).
% # SZS output end CNFRefutation
% PrfWatch: 1.09 CPU 1.21 WC
% FINAL PrfWatch: 1.09 CPU 1.21 WC
% SZS output end Solution for /tmp/SystemOnTPTP6708/NUM924+3.tptp
%
%------------------------------------------------------------------------------