0.00/0.04 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.11 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 180 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39 0.24/0.51 % Computer : n026.cluster.edu 0.24/0.51 % Model : x86_64 x86_64 0.24/0.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.24/0.51 % Memory : 8046.5625MB 0.24/0.51 % OS : Linux 6.8.0-71-generic 0.24/0.51 % CPULimit : 1440 0.10/0.51 % WCLimit : 180 0.10/0.52 % DateTime : Mon Jul 27 15:20:34 UTC 2026 0.10/0.52 % CPUTime : 0.10/0.52 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 180 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39 1.52/1.41 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 2.11/1.72 % [INFO] Parsing done (308ms). 2.11/1.74 % [INFO] Running in sequential loop mode. 2.96/2.39 % [INFO] eprover registered as external prover. 3.18/2.40 % [INFO] Scanning for conjecture ... 3.36/2.55 % [INFO] Found a conjecture (or negated_conjecture) and 5 axioms. Running axiom selection ... 3.54/2.60 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms). 3.54/2.62 % [INFO] Problem is higher-order (TPTP THF). 3.54/2.63 % [INFO] Type checking passed. 3.54/2.64 % [CONFIG] Using configuration: timeout(180) with strategy. Searching for refutation ... 117.66/40.42 % [INFO] Killing All external provers ... 117.66/40.43 % Time passed: 39710ms (effective reasoning time: 38675ms) 117.66/40.43 % Solved by strategy 117.66/40.43 % Axioms used in derivation (5): thm/iterate/POLYNOMIAL_FUNCTION_MUL_, thm/iterate/POLYNOMIAL_FUNCTION_CONST_, thm/realax/real_pow_0, thm/realax/real_pow_1, thm/nums/num_INDUCTION_ 117.66/40.44 % No. of inferences in proof: 51 117.66/40.44 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 39710 ms resp. 38675 ms w/o parsing 118.01/40.54 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p 118.01/40.54 thf('type/realax/real_type', type, 'type/realax/real': $tType). 118.01/40.54 thf('type/nums/num_type', type, 'type/nums/num': $tType). 118.01/40.54 thf('const/realax/real_pow_decl', type, 'const/realax/real_pow': ('type/realax/real' > ('type/nums/num' > 'type/realax/real'))). 118.01/40.54 thf('const/realax/real_of_num_decl', type, 'const/realax/real_of_num': ('type/nums/num' > 'type/realax/real')). 118.01/40.54 thf('const/realax/real_mul_decl', type, 'const/realax/real_mul': ('type/realax/real' > ('type/realax/real' > 'type/realax/real'))). 118.01/40.54 thf('const/nums/SUC_decl', type, 'const/nums/SUC': ('type/nums/num' > 'type/nums/num')). 118.01/40.54 thf('const/nums/NUMERAL_decl', type, 'const/nums/NUMERAL': ('type/nums/num' > 'type/nums/num')). 118.01/40.54 thf('const/nums/BIT1_decl', type, 'const/nums/BIT1': ('type/nums/num' > 'type/nums/num')). 118.01/40.54 thf('const/nums/_0_decl', type, 'const/nums/_0': 'type/nums/num'). 118.01/40.54 thf('const/iterate/polynomial_function_decl', type, 'const/iterate/polynomial_function': (('type/realax/real' > 'type/realax/real') > $o)). 118.01/40.54 thf(sk1_decl, type, sk1: ('type/realax/real' > 'type/realax/real')). 118.01/40.54 thf(sk2_decl, type, sk2: 'type/nums/num'). 118.01/40.54 thf(sk3_decl, type, sk3: (('type/nums/num' > $o) > 'type/nums/num')). 118.01/40.54 thf(sk1_def, definition, sk1 = (@+ [A:('type/realax/real' > 'type/realax/real')]: ~ (('const/iterate/polynomial_function' @ (A)) => (! [B:'type/nums/num']: ('const/iterate/polynomial_function' @ (^ [C:'type/realax/real']: ('const/realax/real_pow' @ (A @ C) @ B)))))) ). 118.01/40.54 thf(sk2_def, definition, sk2 = (@+ [A:'type/nums/num']: ~ ('const/iterate/polynomial_function' @ (^ [B:'type/realax/real']: ('const/realax/real_pow' @ (sk1 @ B) @ A)))) ). 118.01/40.54 thf(sk3_def, definition, sk3 = (^ [A:('type/nums/num' > $o)]: (@+ [B:'type/nums/num']: ~ ((A @ B) => (A @ ('const/nums/SUC' @ B))))) ). 118.01/40.54 thf(4,axiom,((! [A:'type/realax/real']: ('const/iterate/polynomial_function' @ (^ [B:'type/realax/real']: (A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/POLYNOMIAL_FUNCTION_CONST_')). 118.01/40.54 thf(22,plain,((! [A:'type/realax/real']: ('const/iterate/polynomial_function' @ (^ [B:'type/realax/real']: (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])). 118.01/40.54 thf(23,plain,(! [A:'type/realax/real'] : (('const/iterate/polynomial_function' @ (^ [B:'type/realax/real']: (A))))),inference(cnf,[status(esa)],[22])). 118.01/40.54 thf(3,axiom,((! [A:('type/nums/num' > $o)]: ((! [B:'type/nums/num']: (A @ B)) <= (! [B:'type/nums/num']: ((A @ ('const/nums/SUC' @ B)) <= (A @ B)) & (A @ ('const/nums/NUMERAL' @ 'const/nums/_0')))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/nums/num_INDUCTION_')). 118.01/40.54 thf(13,plain,((! [A:('type/nums/num' > $o)]: ((! [B:'type/nums/num']: ((A @ B) => (A @ ('const/nums/SUC' @ B))) & (A @ ('const/nums/NUMERAL' @ 'const/nums/_0'))) => (! [B:'type/nums/num']: (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])). 118.01/40.54 thf(14,plain,(! [B:'type/nums/num',A:('type/nums/num' > $o)] : ((((A @ (sk3 @ (A))) | ~ (A @ ('const/nums/NUMERAL' @ 'const/nums/_0')) | (A @ B)) & (~ (A @ ('const/nums/SUC' @ (sk3 @ (A)))) | ~ (A @ ('const/nums/NUMERAL' @ 'const/nums/_0')) | (A @ B))))),inference(cnf,[status(esa)],[13])). 118.01/40.54 thf(15,plain,(! [B:'type/nums/num',A:('type/nums/num' > $o)] : ((A @ (sk3 @ (A))) | (~ (A @ ('const/nums/NUMERAL' @ 'const/nums/_0'))) | (A @ B))),inference(cnfConj,[status(thm)],[14])). 118.01/40.54 thf(1,conjecture,((! [A:('type/realax/real' > 'type/realax/real'),B:'type/nums/num']: (('const/iterate/polynomial_function' @ (^ [C:'type/realax/real']: ('const/realax/real_pow' @ (A @ C) @ B))) <= ('const/iterate/polynomial_function' @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/POLYNOMIAL_FUNCTION_POW_')). 118.01/40.54 thf(2,negated_conjecture,((~ (! [A:('type/realax/real' > 'type/realax/real'),B:'type/nums/num']: (('const/iterate/polynomial_function' @ (^ [C:'type/realax/real']: ('const/realax/real_pow' @ (A @ C) @ B))) <= ('const/iterate/polynomial_function' @ A))))),inference(neg_conjecture,[status(cth)],[1])). 118.01/40.54 thf(8,plain,((~ (! [A:('type/realax/real' > 'type/realax/real'),B:'type/nums/num']: (('const/iterate/polynomial_function' @ (A)) => ('const/iterate/polynomial_function' @ (^ [C:'type/realax/real']: ('const/realax/real_pow' @ (A @ C) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])). 118.01/40.54 thf(9,plain,((~ (! [A:('type/realax/real' > 'type/realax/real')]: (('const/iterate/polynomial_function' @ (A)) => (! [B:'type/nums/num']: ('const/iterate/polynomial_function' @ (^ [C:'type/realax/real']: ('const/realax/real_pow' @ (A @ C) @ B)))))))),inference(miniscope,[status(thm)],[8])). 118.01/40.54 thf(10,plain,((('const/iterate/polynomial_function' @ (sk1)) & ~ ('const/iterate/polynomial_function' @ (^ [A:'type/realax/real']: ('const/realax/real_pow' @ (sk1 @ A) @ sk2))))),inference(cnf,[status(esa)],[9])). 118.01/40.54 thf(12,plain,((~ ('const/iterate/polynomial_function' @ (^ [A:'type/realax/real']: ('const/realax/real_pow' @ (sk1 @ A) @ sk2))))),inference(cnfConj,[status(thm)],[10])). 118.01/40.54 thf(49,plain,(! [B:'type/nums/num',A:('type/nums/num' > $o)] : ((A @ (sk3 @ (A))) | (~ (A @ ('const/nums/NUMERAL' @ 'const/nums/_0'))) | ~ (($true)) | ((A @ B) != ('const/iterate/polynomial_function' @ (^ [C:'type/realax/real']: ('const/realax/real_pow' @ (sk1 @ C) @ sk2)))))),inference(paramod_ordered,[status(thm)],[15,12])). 118.01/40.54 thf(50,plain,(! [B:'type/nums/num',A:('type/nums/num' > $o)] : ((A @ (sk3 @ (A))) | (~ (A @ ('const/nums/NUMERAL' @ 'const/nums/_0'))) | ((A @ B) != ('const/iterate/polynomial_function' @ (^ [C:'type/realax/real']: ('const/realax/real_pow' @ (sk1 @ C) @ sk2)))))),inference(simp,[status(thm)],[49])). 118.01/40.54 thf(101,plain,(('const/iterate/polynomial_function' @ (^ [A:'type/realax/real']: ('const/realax/real_pow' @ (sk1 @ A) @ (sk3 @ (^ [B:'type/nums/num']: ('const/iterate/polynomial_function' @ (^ [C:'type/realax/real']: ('const/realax/real_pow' @ (sk1 @ C) @ B)))))))) | (~ ('const/iterate/polynomial_function' @ (^ [A:'type/realax/real']: ('const/realax/real_pow' @ (sk1 @ A) @ ('const/nums/NUMERAL' @ 'const/nums/_0')))))),inference(pre_uni,[status(thm)],[50:[bind(A, $thf(^ [C:'type/nums/num']: ('const/iterate/polynomial_function' @ (^ [D:'type/realax/real']: ('const/realax/real_pow' @ (sk1 @ D) @ C))))),bind(B, $thf(sk2))]])). 118.01/40.54 thf(6,axiom,((! [A:'type/realax/real']: (('const/realax/real_pow' @ A @ ('const/nums/NUMERAL' @ 'const/nums/_0')) = ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/realax/real_pow_0')). 118.01/40.54 thf(27,plain,((! [A:'type/realax/real']: (('const/realax/real_pow' @ A @ ('const/nums/NUMERAL' @ 'const/nums/_0')) = ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])). 118.01/40.54 thf(28,plain,(! [A:'type/realax/real'] : ((('const/realax/real_pow' @ A @ ('const/nums/NUMERAL' @ 'const/nums/_0')) = ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')))))),inference(cnf,[status(esa)],[27])). 118.01/40.54 thf(29,plain,(! [A:'type/realax/real'] : ((('const/realax/real_pow' @ A @ ('const/nums/NUMERAL' @ 'const/nums/_0')) = ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')))))),inference(lifteq,[status(thm)],[28])). 118.01/40.54 thf(3782,plain,(('const/iterate/polynomial_function' @ (^ [A:'type/realax/real']: ('const/realax/real_pow' @ (sk1 @ A) @ (sk3 @ (^ [B:'type/nums/num']: ('const/iterate/polynomial_function' @ (^ [C:'type/realax/real']: ('const/realax/real_pow' @ (sk1 @ C) @ B)))))))) | (~ ('const/iterate/polynomial_function' @ (^ [A:'type/realax/real']: ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))))))),inference(rewrite,[status(thm)],[101,29])). 118.01/40.54 thf(3895,plain,(! [A:'type/realax/real'] : (('const/iterate/polynomial_function' @ (^ [B:'type/realax/real']: ('const/realax/real_pow' @ (sk1 @ B) @ (sk3 @ (^ [C:'type/nums/num']: ('const/iterate/polynomial_function' @ (^ [D:'type/realax/real']: ('const/realax/real_pow' @ (sk1 @ D) @ C)))))))) | ~ (($true)) | (('const/iterate/polynomial_function' @ (^ [B:'type/realax/real']: (A))) != ('const/iterate/polynomial_function' @ (^ [B:'type/realax/real']: ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')))))))),inference(paramod_ordered,[status(thm)],[23,3782])). 118.01/40.54 thf(3896,plain,(! [A:'type/realax/real'] : (('const/iterate/polynomial_function' @ (^ [B:'type/realax/real']: ('const/realax/real_pow' @ (sk1 @ B) @ (sk3 @ (^ [C:'type/nums/num']: ('const/iterate/polynomial_function' @ (^ [D:'type/realax/real']: ('const/realax/real_pow' @ (sk1 @ D) @ C)))))))) | (('const/iterate/polynomial_function' @ (^ [B:'type/realax/real']: (A))) != ('const/iterate/polynomial_function' @ (^ [B:'type/realax/real']: ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')))))))),inference(simp,[status(thm)],[3895])). 118.01/40.54 thf(3897,plain,(('const/iterate/polynomial_function' @ (^ [A:'type/realax/real']: ('const/realax/real_pow' @ (sk1 @ A) @ (sk3 @ (^ [B:'type/nums/num']: ('const/iterate/polynomial_function' @ (^ [C:'type/realax/real']: ('const/realax/real_pow' @ (sk1 @ C) @ B))))))))),inference(pattern_uni,[status(thm)],[3896:[bind(A, $thf('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))))]])). 118.01/40.54 thf(11,plain,(('const/iterate/polynomial_function' @ (sk1))),inference(cnfConj,[status(thm)],[10])). 118.01/40.54 thf(7,axiom,((! [A:('type/realax/real' > 'type/realax/real'),B:('type/realax/real' > 'type/realax/real')]: (('const/iterate/polynomial_function' @ (^ [C:'type/realax/real']: ('const/realax/real_mul' @ (A @ C) @ (B @ C)))) <= (('const/iterate/polynomial_function' @ B) & ('const/iterate/polynomial_function' @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/POLYNOMIAL_FUNCTION_MUL_')). 118.01/40.54 thf(30,plain,((! [A:('type/realax/real' > 'type/realax/real'),B:('type/realax/real' > 'type/realax/real')]: ((('const/iterate/polynomial_function' @ (B)) & ('const/iterate/polynomial_function' @ (A))) => ('const/iterate/polynomial_function' @ (^ [C:'type/realax/real']: ('const/realax/real_mul' @ (A @ C) @ (B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])). 118.01/40.54 thf(31,plain,(! [B:('type/realax/real' > 'type/realax/real'),A:('type/realax/real' > 'type/realax/real')] : ((~ ('const/iterate/polynomial_function' @ (B))) | (~ ('const/iterate/polynomial_function' @ (A))) | ('const/iterate/polynomial_function' @ (^ [C:'type/realax/real']: ('const/realax/real_mul' @ (A @ C) @ (B @ C)))))),inference(cnf,[status(esa)],[30])). 118.01/40.54 thf(156,plain,(! [B:('type/realax/real' > 'type/realax/real'),A:('type/realax/real' > 'type/realax/real')] : ((~ ('const/iterate/polynomial_function' @ (B))) | ~ (($true)) | ('const/iterate/polynomial_function' @ (^ [C:'type/realax/real']: ('const/realax/real_mul' @ (A @ C) @ (B @ C)))) | (('const/iterate/polynomial_function' @ (sk1)) != ('const/iterate/polynomial_function' @ (A))))),inference(paramod_ordered,[status(thm)],[11,31])). 118.01/40.54 thf(157,plain,(! [B:('type/realax/real' > 'type/realax/real'),A:('type/realax/real' > 'type/realax/real')] : ((~ ('const/iterate/polynomial_function' @ (B))) | ('const/iterate/polynomial_function' @ (^ [C:'type/realax/real']: ('const/realax/real_mul' @ (A @ C) @ (B @ C)))) | (('const/iterate/polynomial_function' @ (sk1)) != ('const/iterate/polynomial_function' @ (A))))),inference(simp,[status(thm)],[156])). 118.01/40.54 thf(158,plain,(! [A:('type/realax/real' > 'type/realax/real')] : ((~ ('const/iterate/polynomial_function' @ (A))) | ('const/iterate/polynomial_function' @ (^ [B:'type/realax/real']: ('const/realax/real_mul' @ (sk1 @ B) @ (A @ B)))))),inference(pattern_uni,[status(thm)],[157:[bind(A, $thf(sk1)),bind(B, $thf(B))]])). 118.01/40.54 thf(201,plain,(! [A:('type/realax/real' > 'type/realax/real')] : ((~ ('const/iterate/polynomial_function' @ (A))) | ('const/iterate/polynomial_function' @ (^ [B:'type/realax/real']: ('const/realax/real_mul' @ (sk1 @ B) @ (A @ B)))))),inference(simp,[status(thm)],[158])). 118.01/40.54 thf(4038,plain,(! [A:('type/realax/real' > 'type/realax/real')] : (~ (($true)) | ('const/iterate/polynomial_function' @ (^ [B:'type/realax/real']: ('const/realax/real_mul' @ (sk1 @ B) @ (A @ B)))) | (('const/iterate/polynomial_function' @ (^ [B:'type/realax/real']: ('const/realax/real_pow' @ (sk1 @ B) @ (sk3 @ (^ [C:'type/nums/num']: ('const/iterate/polynomial_function' @ (^ [D:'type/realax/real']: ('const/realax/real_pow' @ (sk1 @ D) @ C)))))))) != ('const/iterate/polynomial_function' @ (A))))),inference(paramod_ordered,[status(thm)],[3897,201])). 118.01/40.54 thf(4039,plain,(! [A:('type/realax/real' > 'type/realax/real')] : (('const/iterate/polynomial_function' @ (^ [B:'type/realax/real']: ('const/realax/real_mul' @ (sk1 @ B) @ (A @ B)))) | (('const/iterate/polynomial_function' @ (^ [B:'type/realax/real']: ('const/realax/real_pow' @ (sk1 @ B) @ (sk3 @ (^ [C:'type/nums/num']: ('const/iterate/polynomial_function' @ (^ [D:'type/realax/real']: ('const/realax/real_pow' @ (sk1 @ D) @ C)))))))) != ('const/iterate/polynomial_function' @ (A))))),inference(simp,[status(thm)],[4038])). 118.01/40.54 thf(4040,plain,(('const/iterate/polynomial_function' @ (^ [A:'type/realax/real']: ('const/realax/real_mul' @ (sk1 @ A) @ ('const/realax/real_pow' @ (sk1 @ A) @ (sk3 @ (^ [B:'type/nums/num']: ('const/iterate/polynomial_function' @ (^ [C:'type/realax/real']: ('const/realax/real_pow' @ (sk1 @ C) @ B)))))))))),inference(pattern_uni,[status(thm)],[4039:[bind(A, $thf(^ [B:'type/realax/real']: ('const/realax/real_pow' @ (sk1 @ B) @ (sk3 @ (^ [C:'type/nums/num']: ('const/iterate/polynomial_function' @ (^ [D:'type/realax/real']: ('const/realax/real_pow' @ (sk1 @ D) @ C))))))))]])). 118.01/40.54 thf(5,axiom,((! [A:'type/realax/real',B:'type/nums/num']: (('const/realax/real_pow' @ A @ ('const/nums/SUC' @ B)) = ('const/realax/real_mul' @ A @ ('const/realax/real_pow' @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/realax/real_pow_1')). 118.01/40.54 thf(24,plain,((! [A:'type/realax/real',B:'type/nums/num']: (('const/realax/real_pow' @ A @ ('const/nums/SUC' @ B)) = ('const/realax/real_mul' @ A @ ('const/realax/real_pow' @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])). 118.01/40.54 thf(25,plain,(! [B:'type/nums/num',A:'type/realax/real'] : ((('const/realax/real_pow' @ A @ ('const/nums/SUC' @ B)) = ('const/realax/real_mul' @ A @ ('const/realax/real_pow' @ A @ B))))),inference(cnf,[status(esa)],[24])). 118.01/40.54 thf(26,plain,(! [B:'type/nums/num',A:'type/realax/real'] : ((('const/realax/real_mul' @ A @ ('const/realax/real_pow' @ A @ B)) = ('const/realax/real_pow' @ A @ ('const/nums/SUC' @ B))))),inference(lifteq,[status(thm)],[25])). 118.01/40.54 thf(4086,plain,(('const/iterate/polynomial_function' @ (^ [A:'type/realax/real']: ('const/realax/real_pow' @ (sk1 @ A) @ ('const/nums/SUC' @ (sk3 @ (^ [B:'type/nums/num']: ('const/iterate/polynomial_function' @ (^ [C:'type/realax/real']: ('const/realax/real_pow' @ (sk1 @ C) @ B)))))))))),inference(rewrite,[status(thm)],[4040,26])). 118.01/40.54 thf(16,plain,(! [B:'type/nums/num',A:('type/nums/num' > $o)] : ((~ (A @ ('const/nums/SUC' @ (sk3 @ (A))))) | (~ (A @ ('const/nums/NUMERAL' @ 'const/nums/_0'))) | (A @ B))),inference(cnfConj,[status(thm)],[14])). 118.01/40.54 thf(4124,plain,(! [B:'type/nums/num',A:('type/nums/num' > $o)] : (~ (($true)) | (~ (A @ ('const/nums/NUMERAL' @ 'const/nums/_0'))) | (A @ B) | (('const/iterate/polynomial_function' @ (^ [C:'type/realax/real']: ('const/realax/real_pow' @ (sk1 @ C) @ ('const/nums/SUC' @ (sk3 @ (^ [D:'type/nums/num']: ('const/iterate/polynomial_function' @ (^ [E:'type/realax/real']: ('const/realax/real_pow' @ (sk1 @ E) @ D))))))))) != (A @ ('const/nums/SUC' @ (sk3 @ (A))))))),inference(paramod_ordered,[status(thm)],[4086,16])). 118.01/40.54 thf(4125,plain,(! [B:'type/nums/num',A:('type/nums/num' > $o)] : ((~ (A @ ('const/nums/NUMERAL' @ 'const/nums/_0'))) | (A @ B) | (('const/iterate/polynomial_function' @ (^ [C:'type/realax/real']: ('const/realax/real_pow' @ (sk1 @ C) @ ('const/nums/SUC' @ (sk3 @ (^ [D:'type/nums/num']: ('const/iterate/polynomial_function' @ (^ [E:'type/realax/real']: ('const/realax/real_pow' @ (sk1 @ E) @ D))))))))) != (A @ ('const/nums/SUC' @ (sk3 @ (A))))))),inference(simp,[status(thm)],[4124])). 118.01/40.54 thf(4144,plain,(! [A:'type/nums/num'] : ((~ ('const/iterate/polynomial_function' @ (^ [B:'type/realax/real']: ('const/realax/real_pow' @ (sk1 @ B) @ ('const/nums/NUMERAL' @ 'const/nums/_0'))))) | ('const/iterate/polynomial_function' @ (^ [B:'type/realax/real']: ('const/realax/real_pow' @ (sk1 @ B) @ A))))),inference(pre_uni,[status(thm)],[4125:[bind(A, $thf(^ [C:'type/nums/num']: ('const/iterate/polynomial_function' @ (^ [D:'type/realax/real']: ('const/realax/real_pow' @ (sk1 @ D) @ C))))),bind(B, $thf(B))]])). 118.01/40.54 thf(4150,plain,(! [A:'type/nums/num'] : ((~ ('const/iterate/polynomial_function' @ (^ [B:'type/realax/real']: ('const/realax/real_pow' @ (sk1 @ B) @ ('const/nums/NUMERAL' @ 'const/nums/_0'))))) | ('const/iterate/polynomial_function' @ (^ [B:'type/realax/real']: ('const/realax/real_pow' @ (sk1 @ B) @ A))))),inference(simp,[status(thm)],[4144])). 118.01/40.54 thf(13417,plain,(! [A:'type/nums/num'] : ((~ ('const/iterate/polynomial_function' @ (^ [B:'type/realax/real']: ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')))))) | ('const/iterate/polynomial_function' @ (^ [B:'type/realax/real']: ('const/realax/real_pow' @ (sk1 @ B) @ A))))),inference(rewrite,[status(thm)],[4150,29])). 118.01/40.54 thf(13536,plain,(! [A:'type/nums/num'] : ((~ ('const/iterate/polynomial_function' @ (^ [B:'type/realax/real']: ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')))))) | ~ (($true)) | (('const/iterate/polynomial_function' @ (^ [B:'type/realax/real']: ('const/realax/real_pow' @ (sk1 @ B) @ A))) != ('const/iterate/polynomial_function' @ (^ [B:'type/realax/real']: ('const/realax/real_pow' @ (sk1 @ B) @ sk2)))))),inference(paramod_ordered,[status(thm)],[13417,12])). 118.01/40.54 thf(13537,plain,(! [A:'type/nums/num'] : ((~ ('const/iterate/polynomial_function' @ (^ [B:'type/realax/real']: ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')))))) | (('const/iterate/polynomial_function' @ (^ [B:'type/realax/real']: ('const/realax/real_pow' @ (sk1 @ B) @ A))) != ('const/iterate/polynomial_function' @ (^ [B:'type/realax/real']: ('const/realax/real_pow' @ (sk1 @ B) @ sk2)))))),inference(simp,[status(thm)],[13536])). 118.01/40.54 thf(13538,plain,((~ ('const/iterate/polynomial_function' @ (^ [A:'type/realax/real']: ('const/realax/real_of_num' @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))))))),inference(pattern_uni,[status(thm)],[13537:[bind(A, $thf(sk2))]])). 118.01/40.54 thf(13958,plain,(~ (($true))),inference(rewrite,[status(thm)],[13538,23])). 118.01/40.54 thf(13959,plain,(($false)),inference(simp,[status(thm)],[13958])). 118.01/40.54 % SZS output end Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p 118.01/40.54 % [INFO] Killing All external provers ... 0.28/40.76 EOF