0.00/0.10 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.96/1.03 % Command : run_portfolio.sh /export/starexec/sandbox2/benchmark/theBenchmark.p /export/starexec/sandbox2/tmp/tmp.z3Sce3n8Mt 1.02/1.22 % Computer : n007.cluster.edu 1.02/1.22 % Model : x86_64 x86_64 1.02/1.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 1.02/1.22 % Memory : 8042.1875MB 1.02/1.22 % OS : Linux 3.10.0-693.el7.x86_64 1.02/1.22 % CPULimit : 960 1.02/1.22 % DateTime : Thu Jul 2 08:30:57 EDT 2020 1.02/1.23 % CPUTime : 1.02/1.23 % Running portfolio for 120 s 1.02/1.23 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 1.02/1.23 % Number of cores: 8 1.02/1.23 % Python version: Python 3.6.8 1.02/1.23 % Running in FO mode 27.75/28.20 % Running /export/starexec/sandbox2/solver/bin/fo/fo7.sh for 25 27.75/28.20 % Warning: 27.75/28.20 % To remain in the chosen logic fragment, unification with booleans has been disabled. 27.75/28.20 % 27.75/28.20 % Running /export/starexec/sandbox2/solver/bin/fo/fo8.sh for 20 27.75/28.20 % Solved by: fo/fo8.sh 27.75/28.20 To remain in the chosen logic fragment, unification with booleans has been disabled. 27.75/28.20 % done 1803 iterations in 1.847s 27.75/28.20 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 27.75/28.20 % SZS output start Refutation 27.75/28.20 tff(conj_0, conjecture, 27.75/28.20 (zero_zero_int != 27.75/28.20 hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int, 27.75/28.20 hAPP_int_int(hAPP_int_fun_int_int( 27.75/28.20 plus_plus_int,one_one_int), 27.75/28.20 hAPP_nat_int(semiri1621563631at_int, 27.75/28.20 n))), 27.75/28.20 hAPP_int_nat(number_number_of_nat, 27.75/28.20 hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))). 27.75/28.20 tff(zf_stmt_0, negated_conjecture, 27.75/28.20 (zero_zero_int = 27.75/28.20 hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int, 27.75/28.20 hAPP_int_int(hAPP_int_fun_int_int( 27.75/28.20 plus_plus_int,one_one_int), 27.75/28.20 hAPP_nat_int(semiri1621563631at_int, 27.75/28.20 n))), 27.75/28.20 hAPP_int_nat(number_number_of_nat, 27.75/28.20 hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))). 27.75/28.20 tff('0', plain, 27.75/28.20 zero_zero_int 27.75/28.20 = hAPP_nat_int( 27.75/28.20 hAPP_int_fun_nat_int(power_power_int, 27.75/28.20 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int, one_one_int), 27.75/28.20 hAPP_nat_int(semiri1621563631at_int, n))), 27.75/28.20 hAPP_int_nat(number_number_of_nat, 27.75/28.20 hAPP_int_int(bit0, hAPP_int_int(bit1, pls)))), 27.75/28.20 inference('cnf', [status(esa)], [zf_stmt_0])). 27.75/28.20 tff(fact_151_Pls__def, axiom, (zero_zero_int = pls)). 27.75/28.20 tff('1', plain, zero_zero_int = pls, 27.75/28.20 inference('cnf', [status(esa)], [fact_151_Pls__def])). 27.75/28.20 tff(fact_3460_minus__Pls, axiom, (pls = hAPP_int_int(uminus_uminus_int,pls))). 27.75/28.20 tff('2', plain, pls = hAPP_int_int(uminus_uminus_int, pls), 27.75/28.20 inference('cnf', [status(esa)], [fact_3460_minus__Pls])). 27.75/28.20 tff(fact_4427_floor__minus__real__of__int, axiom, 27.75/28.20 (![N]: 27.75/28.20 (hAPP_int_int(uminus_uminus_int,N) = 27.75/28.20 archim1246769320r_real(hAPP_real_real(uminus_uminus_real, 27.75/28.20 hAPP_int_real(real_int,N)))))). 27.75/28.20 tff('3', plain, 27.75/28.20 ![X2172]: 27.75/28.20 hAPP_int_int(uminus_uminus_int, X2172) 27.75/28.20 = archim1246769320r_real( 27.75/28.20 hAPP_real_real(uminus_uminus_real, hAPP_int_real(real_int, X2172))), 27.75/28.20 inference('cnf', [status(esa)], [fact_4427_floor__minus__real__of__int])). 27.75/28.20 tff(fact_4379_real__of__int__zero, axiom, 27.75/28.20 (hAPP_int_real(real_int,zero_zero_int) = zero_zero_real)). 27.75/28.20 tff('4', plain, hAPP_int_real(real_int, zero_zero_int) = zero_zero_real, 27.75/28.20 inference('cnf', [status(esa)], [fact_4379_real__of__int__zero])). 27.75/28.20 tff('5', plain, zero_zero_int = pls, 27.75/28.20 inference('cnf', [status(esa)], [fact_151_Pls__def])). 27.75/28.20 tff('6', plain, hAPP_int_real(real_int, pls) = zero_zero_real, 27.75/28.20 inference('demod', [status(thm)], ['4', '5'])). 27.75/28.20 tff('7', plain, 27.75/28.20 pls 27.75/28.20 = archim1246769320r_real( 27.75/28.20 hAPP_real_real(uminus_uminus_real, zero_zero_real)), 27.75/28.20 inference('demod', [status(thm)], ['2', '3', '6'])). 27.75/28.20 tff('8', plain, hAPP_int_real(real_int, pls) = zero_zero_real, 27.75/28.20 inference('demod', [status(thm)], ['4', '5'])). 27.75/28.20 tff(fact_4398_real__of__int__minus, axiom, 27.75/28.20 (![X]: 27.75/28.20 (hAPP_real_real(uminus_uminus_real,hAPP_int_real(real_int,X)) = 27.75/28.20 hAPP_int_real(real_int,hAPP_int_int(uminus_uminus_int,X))))). 27.75/28.20 tff('9', plain, 27.75/28.20 ![X1054]: 27.75/28.20 hAPP_real_real(uminus_uminus_real, hAPP_int_real(real_int, X1054)) 27.75/28.20 = hAPP_int_real(real_int, hAPP_int_int(uminus_uminus_int, X1054)), 27.75/28.20 inference('cnf', [status(esa)], [fact_4398_real__of__int__minus])). 27.75/28.20 tff('10', plain, 27.75/28.20 ![X2172]: 27.75/28.20 hAPP_int_int(uminus_uminus_int, X2172) 27.75/28.20 = archim1246769320r_real( 27.75/28.20 hAPP_real_real(uminus_uminus_real, hAPP_int_real(real_int, X2172))), 27.75/28.20 inference('cnf', [status(esa)], [fact_4427_floor__minus__real__of__int])). 27.75/28.20 tff('11', plain, 27.75/28.20 ![X1054]: 27.75/28.20 hAPP_real_real(uminus_uminus_real, hAPP_int_real(real_int, X1054)) 27.75/28.20 = hAPP_int_real(real_int, 27.75/28.20 archim1246769320r_real( 27.75/28.20 hAPP_real_real(uminus_uminus_real, 27.75/28.20 hAPP_int_real(real_int, X1054)))), 27.75/28.20 inference('demod', [status(thm)], ['9', '10'])). 27.75/28.20 tff('12', plain, 27.75/28.20 hAPP_real_real(uminus_uminus_real, hAPP_int_real(real_int, pls)) 27.75/28.20 = hAPP_int_real(real_int, 27.75/28.20 archim1246769320r_real( 27.75/28.20 hAPP_real_real(uminus_uminus_real, zero_zero_real))), 27.75/28.20 inference('sup+', [status(thm)], ['8', '11'])). 27.75/28.20 tff('13', plain, hAPP_int_real(real_int, pls) = zero_zero_real, 27.75/28.20 inference('demod', [status(thm)], ['4', '5'])). 27.75/28.20 tff('14', plain, 27.75/28.20 pls 27.75/28.20 = archim1246769320r_real( 27.75/28.20 hAPP_real_real(uminus_uminus_real, zero_zero_real)), 27.75/28.20 inference('demod', [status(thm)], ['2', '3', '6'])). 27.75/28.20 tff('15', plain, hAPP_int_real(real_int, pls) = zero_zero_real, 27.75/28.20 inference('demod', [status(thm)], ['4', '5'])). 27.75/28.20 tff('16', plain, 27.75/28.20 hAPP_real_real(uminus_uminus_real, zero_zero_real) = zero_zero_real, 27.75/28.20 inference('demod', [status(thm)], ['12', '13', '14', '15'])). 27.75/28.20 tff('17', plain, pls = archim1246769320r_real(zero_zero_real), 27.75/28.20 inference('demod', [status(thm)], ['7', '16'])). 27.75/28.20 tff('18', plain, zero_zero_int = archim1246769320r_real(zero_zero_real), 27.75/28.20 inference('demod', [status(thm)], ['1', '17'])). 27.75/28.20 tff(gsy_c_Groups_Oone__class_Oone_000tc__Int__Oint, axiom, 27.75/28.20 (is_int(one_one_int))). 27.75/28.20 tff('19', plain, is_int(one_one_int), 27.75/28.20 inference('cnf', [status(esa)], 27.75/28.20 [gsy_c_Groups_Oone__class_Oone_000tc__Int__Oint])). 27.75/28.20 tff(fact_4383_floor__real__of__int, axiom, 27.75/28.20 (![N]: 27.75/28.20 (is_int(N) => (archim1246769320r_real(hAPP_int_real(real_int,N)) = N)))). 27.75/28.20 tff('20', plain, 27.75/28.20 ![X4961]: 27.75/28.20 (archim1246769320r_real(hAPP_int_real(real_int, X4961)) = X4961 27.75/28.20 | ~ is_int(X4961)), 27.75/28.20 inference('cnf', [status(esa)], [fact_4383_floor__real__of__int])). 27.75/28.20 tff('21', plain, 27.75/28.20 archim1246769320r_real(hAPP_int_real(real_int, one_one_int)) 27.75/28.20 = one_one_int, 27.75/28.20 inference('sup-', [status(thm)], ['19', '20'])). 27.75/28.20 tff(fact_4389_real__of__one, axiom, 27.75/28.20 (hAPP_int_real(real_int,one_one_int) = one_one_real)). 27.75/28.20 tff('22', plain, hAPP_int_real(real_int, one_one_int) = one_one_real, 27.75/28.20 inference('cnf', [status(esa)], [fact_4389_real__of__one])). 27.75/28.20 tff('23', plain, archim1246769320r_real(one_one_real) = one_one_int, 27.75/28.20 inference('demod', [status(thm)], ['21', '22'])). 27.75/28.20 tff(fact_3105_int__Suc, axiom, 27.75/28.20 (![M]: 27.75/28.20 (hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int), 27.75/28.20 hAPP_nat_int(semiri1621563631at_int,M)) = 27.75/28.20 hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,M))))). 27.75/28.20 tff('24', plain, 27.75/28.20 ![X1996]: 27.75/28.20 hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int, one_one_int), 27.75/28.20 hAPP_nat_int(semiri1621563631at_int, X1996)) 27.75/28.20 = hAPP_nat_int(semiri1621563631at_int, hAPP_nat_nat(suc, X1996)), 27.75/28.20 inference('cnf', [status(esa)], [fact_3105_int__Suc])). 27.75/28.20 tff('25', plain, archim1246769320r_real(one_one_real) = one_one_int, 27.75/28.20 inference('demod', [status(thm)], ['21', '22'])). 27.75/28.20 tff('26', plain, 27.75/28.20 ![X1996]: 27.75/28.20 hAPP_int_int( 27.75/28.20 hAPP_int_fun_int_int(plus_plus_int, 27.75/28.20 archim1246769320r_real(one_one_real)), 27.75/28.20 hAPP_nat_int(semiri1621563631at_int, X1996)) 27.75/28.20 = hAPP_nat_int(semiri1621563631at_int, hAPP_nat_nat(suc, X1996)), 27.75/28.20 inference('demod', [status(thm)], ['24', '25'])). 27.75/28.20 tff('27', plain, pls = archim1246769320r_real(zero_zero_real), 27.75/28.20 inference('demod', [status(thm)], ['7', '16'])). 27.75/28.20 tff(fact_3484_minus__Min, axiom, 27.75/28.20 (hAPP_int_int(uminus_uminus_int,min) = hAPP_int_int(bit1,pls))). 27.75/28.20 tff('28', plain, 27.75/28.20 hAPP_int_int(uminus_uminus_int, min) = hAPP_int_int(bit1, pls), 27.75/28.20 inference('cnf', [status(esa)], [fact_3484_minus__Min])). 27.75/28.20 tff(fact_51_semiring__norm_I110_J, axiom, 27.75/28.20 (one_one_int = hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls)))). 27.75/28.20 tff('29', plain, 27.75/28.20 one_one_int = hAPP_int_int(number_number_of_int, hAPP_int_int(bit1, pls)), 27.75/28.20 inference('cnf', [status(esa)], [fact_51_semiring__norm_I110_J])). 27.75/28.20 tff('30', plain, 27.75/28.20 hAPP_int_int(uminus_uminus_int, min) = hAPP_int_int(bit1, pls), 27.75/28.20 inference('cnf', [status(esa)], [fact_3484_minus__Min])). 27.75/28.20 tff('31', plain, 27.75/28.20 one_one_int 27.75/28.20 = hAPP_int_int(number_number_of_int, 27.75/28.20 hAPP_int_int(uminus_uminus_int, min)), 27.75/28.20 inference('demod', [status(thm)], ['29', '30'])). 27.75/28.20 tff('32', plain, is_int(one_one_int), 27.75/28.20 inference('cnf', [status(esa)], 27.75/28.20 [gsy_c_Groups_Oone__class_Oone_000tc__Int__Oint])). 27.75/28.20 tff(fact_87_eq__number__of, axiom, 27.75/28.20 (![Xa,Ya]: 27.75/28.20 ((is_int(Ya) & is_int(Xa)) => 27.75/28.20 ((hAPP_int_int(number_number_of_int,Xa) = 27.75/28.20 hAPP_int_int(number_number_of_int,Ya)) <=> 27.75/28.20 (Xa = Ya))))). 27.75/28.20 tff('33', plain, 27.75/28.20 ![X17, X18]: 27.75/28.20 (~ is_int(X17) 27.75/28.20 | ~ is_int(X18) 27.75/28.20 | X17 = X18 27.75/28.20 | hAPP_int_int(number_number_of_int, X17) 27.75/28.20 != hAPP_int_int(number_number_of_int, X18)), 27.75/28.20 inference('cnf', [status(esa)], [fact_87_eq__number__of])). 27.75/28.20 tff('34', plain, 27.75/28.20 ![X0]: 27.75/28.20 (hAPP_int_int(number_number_of_int, one_one_int) 27.75/28.20 != hAPP_int_int(number_number_of_int, X0) 27.75/28.20 | one_one_int = X0 27.75/28.20 | ~ is_int(X0)), 27.75/28.20 inference('sup-', [status(thm)], ['32', '33'])). 27.75/28.20 tff('35', plain, is_int(one_one_int), 27.75/28.20 inference('cnf', [status(esa)], 27.75/28.20 [gsy_c_Groups_Oone__class_Oone_000tc__Int__Oint])). 27.75/28.20 tff(fact_279_number__of__is__id, axiom, 27.75/28.20 (![K_2]: (is_int(K_2) => (K_2 = hAPP_int_int(number_number_of_int,K_2))))). 27.75/28.20 tff('36', plain, 27.75/28.20 ![X1115]: 27.75/28.20 (X1115 = hAPP_int_int(number_number_of_int, X1115) | ~ is_int(X1115)), 27.75/28.20 inference('cnf', [status(esa)], [fact_279_number__of__is__id])). 27.75/28.20 tff('37', plain, 27.75/28.20 one_one_int = hAPP_int_int(number_number_of_int, one_one_int), 27.75/28.20 inference('sup-', [status(thm)], ['35', '36'])). 27.75/28.20 tff('38', plain, 27.75/28.20 ![X0]: 27.75/28.20 (one_one_int != hAPP_int_int(number_number_of_int, X0) 27.75/28.20 | one_one_int = X0 27.75/28.20 | ~ is_int(X0)), 27.75/28.20 inference('demod', [status(thm)], ['34', '37'])). 27.75/28.20 tff('39', plain, 27.75/28.20 (one_one_int != one_one_int 27.75/28.20 | ~ is_int(hAPP_int_int(uminus_uminus_int, min)) 27.75/28.20 | one_one_int = hAPP_int_int(uminus_uminus_int, min)), 27.75/28.20 inference('sup-', [status(thm)], ['31', '38'])). 27.75/28.20 tff(gsy_c_Int_OMin, axiom, (is_int(min))). 27.75/28.20 tff('40', plain, is_int(min), 27.75/28.20 inference('cnf', [status(esa)], [gsy_c_Int_OMin])). 27.75/28.20 tff(gsy_c_hAPP_000tc__Int__Oint_000tc__Int__Oint, axiom, 27.75/28.20 (![B_1_1,B_2_1]: (is_int(B_2_1) => is_int(hAPP_int_int(B_1_1,B_2_1))))). 27.75/28.20 tff('41', plain, 27.75/28.20 ![X1867, X1868]: ( is_int(hAPP_int_int(X1867, X1868)) | ~ is_int(X1868)), 27.75/28.20 inference('cnf', [status(esa)], 27.75/28.20 [gsy_c_hAPP_000tc__Int__Oint_000tc__Int__Oint])). 27.75/28.20 tff('42', plain, ![X0]: is_int(hAPP_int_int(X0, min)), 27.75/28.20 inference('sup-', [status(thm)], ['40', '41'])). 27.75/28.20 tff('43', plain, 27.75/28.20 (one_one_int != one_one_int 27.75/28.20 | one_one_int = hAPP_int_int(uminus_uminus_int, min)), 27.75/28.20 inference('demod', [status(thm)], ['39', '42'])). 27.75/28.20 tff('44', plain, one_one_int = hAPP_int_int(uminus_uminus_int, min), 27.75/28.20 inference('simplify', [status(thm)], ['43'])). 27.75/28.20 tff('45', plain, one_one_int = hAPP_int_int(bit1, pls), 27.75/28.20 inference('demod', [status(thm)], ['28', '44'])). 27.75/28.20 tff('46', plain, pls = archim1246769320r_real(zero_zero_real), 27.75/28.20 inference('demod', [status(thm)], ['7', '16'])). 27.75/28.20 tff('47', plain, 27.75/28.20 one_one_int = hAPP_int_int(bit1, archim1246769320r_real(zero_zero_real)), 27.75/28.20 inference('demod', [status(thm)], ['45', '46'])). 27.75/28.20 tff('48', plain, archim1246769320r_real(one_one_real) = one_one_int, 27.75/28.20 inference('demod', [status(thm)], ['21', '22'])). 27.75/28.20 tff('49', plain, 27.75/28.20 archim1246769320r_real(one_one_real) 27.75/28.20 = hAPP_int_int(bit1, archim1246769320r_real(zero_zero_real)), 27.75/28.20 inference('demod', [status(thm)], ['47', '48'])). 27.75/28.20 tff(fact_73_nat__1__add__1, axiom, 27.75/28.20 (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),one_one_nat) = 27.75/28.20 hAPP_int_nat(number_number_of_nat, 27.75/28.20 hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))). 27.75/28.20 tff('50', plain, 27.75/28.20 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat, one_one_nat), 27.75/28.20 one_one_nat) 27.75/28.20 = hAPP_int_nat(number_number_of_nat, 27.75/28.20 hAPP_int_int(bit0, hAPP_int_int(bit1, pls))), 27.75/28.20 inference('cnf', [status(esa)], [fact_73_nat__1__add__1])). 27.75/28.20 tff(fact_118_int__0__less__1, axiom, 27.75/28.20 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int), 27.75/28.20 one_one_int)))). 27.75/28.20 tff('51', plain, 27.75/28.20 hBOOL( 27.75/28.20 hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int, zero_zero_int), 27.75/28.20 one_one_int)), 27.75/28.20 inference('cnf', [status(esa)], [fact_118_int__0__less__1])). 27.75/28.20 tff('52', plain, zero_zero_int = pls, 27.75/28.20 inference('cnf', [status(esa)], [fact_151_Pls__def])). 27.75/28.20 tff('53', plain, 27.75/28.20 hBOOL( 27.75/28.20 hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int, pls), one_one_int)), 27.75/28.20 inference('demod', [status(thm)], ['51', '52'])). 27.75/28.20 tff(fact_473_zero__less__imp__eq__int, axiom, 27.75/28.20 (![K_2]: 27.75/28.20 (is_int(K_2) => 27.75/28.20 (hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int), 27.75/28.20 K_2)) => 27.75/28.20 (?[N_1]: 27.75/28.20 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat, 27.75/28.20 zero_zero_nat), 27.75/28.20 N_1)) & 27.75/28.20 (K_2 = hAPP_nat_int(semiri1621563631at_int,N_1)))))))). 27.75/28.20 tff('54', plain, 27.75/28.20 ![X41]: 27.75/28.20 (~ hBOOL( 27.75/28.20 hAPP_int_bool( 27.75/28.20 hAPP_i1948725293t_bool(ord_less_int, zero_zero_int), X41)) 27.75/28.20 | X41 = hAPP_nat_int(semiri1621563631at_int, sk_N_1(X41)) 27.75/28.20 | ~ is_int(X41)), 27.75/28.20 inference('cnf', [status(esa)], [fact_473_zero__less__imp__eq__int])). 27.75/28.20 tff('55', plain, zero_zero_int = pls, 27.75/28.20 inference('cnf', [status(esa)], [fact_151_Pls__def])). 27.75/28.20 tff('56', plain, 27.75/28.20 ![X41]: 27.75/28.20 (~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int, pls), X41)) 27.75/28.20 | X41 = hAPP_nat_int(semiri1621563631at_int, sk_N_1(X41)) 27.75/28.20 | ~ is_int(X41)), 27.75/28.20 inference('demod', [status(thm)], ['54', '55'])). 27.75/28.20 tff('57', plain, 27.75/28.20 (~ is_int(one_one_int) 27.75/28.20 | one_one_int 27.75/28.20 = hAPP_nat_int(semiri1621563631at_int, sk_N_1(one_one_int))), 27.75/28.20 inference('sup-', [status(thm)], ['53', '56'])). 27.75/28.20 tff('58', plain, is_int(one_one_int), 27.75/28.20 inference('cnf', [status(esa)], 27.75/28.20 [gsy_c_Groups_Oone__class_Oone_000tc__Int__Oint])). 27.75/28.20 tff('59', plain, 27.75/28.20 one_one_int = hAPP_nat_int(semiri1621563631at_int, sk_N_1(one_one_int)), 27.75/28.20 inference('demod', [status(thm)], ['57', '58'])). 27.75/28.20 tff(fact_2703_nat__int, axiom, 27.75/28.20 (![N]: (N = hAPP_int_nat(nat,hAPP_nat_int(semiri1621563631at_int,N))))). 27.75/28.20 tff('60', plain, 27.75/28.20 ![X2876]: 27.75/28.20 X2876 = hAPP_int_nat(nat, hAPP_nat_int(semiri1621563631at_int, X2876)), 27.75/28.20 inference('cnf', [status(esa)], [fact_2703_nat__int])). 27.75/28.20 tff('61', plain, sk_N_1(one_one_int) = hAPP_int_nat(nat, one_one_int), 27.75/28.20 inference('sup+', [status(thm)], ['59', '60'])). 27.75/28.20 tff(fact_2747_transfer__nat__int__numerals_I2_J, axiom, 27.75/28.20 (one_one_nat = hAPP_int_nat(nat,one_one_int))). 27.75/28.20 tff('62', plain, one_one_nat = hAPP_int_nat(nat, one_one_int), 27.75/28.20 inference('cnf', [status(esa)], 27.75/28.20 [fact_2747_transfer__nat__int__numerals_I2_J])). 27.75/28.20 tff('63', plain, one_one_nat = sk_N_1(one_one_int), 27.75/28.20 inference('sup+', [status(thm)], ['61', '62'])). 27.75/28.20 tff('64', plain, archim1246769320r_real(one_one_real) = one_one_int, 27.75/28.20 inference('demod', [status(thm)], ['21', '22'])). 27.75/28.20 tff('65', plain, one_one_nat = sk_N_1(archim1246769320r_real(one_one_real)), 27.75/28.20 inference('demod', [status(thm)], ['63', '64'])). 27.75/28.20 tff('66', plain, one_one_nat = sk_N_1(archim1246769320r_real(one_one_real)), 27.75/28.20 inference('demod', [status(thm)], ['63', '64'])). 27.75/28.20 tff('67', plain, pls = archim1246769320r_real(zero_zero_real), 27.75/28.20 inference('demod', [status(thm)], ['7', '16'])). 27.75/28.20 tff('68', plain, 27.75/28.20 archim1246769320r_real(one_one_real) 27.75/28.20 = hAPP_int_int(bit1, archim1246769320r_real(zero_zero_real)), 27.75/28.20 inference('demod', [status(thm)], ['47', '48'])). 27.75/28.20 tff('69', plain, 27.75/28.20 hAPP_nat_nat( 27.75/28.20 hAPP_nat_fun_nat_nat(plus_plus_nat, 27.75/28.20 sk_N_1(archim1246769320r_real(one_one_real))), 27.75/28.20 sk_N_1(archim1246769320r_real(one_one_real))) 27.75/28.20 = hAPP_int_nat(number_number_of_nat, 27.75/28.20 hAPP_int_int(bit0, archim1246769320r_real(one_one_real))), 27.75/28.20 inference('demod', [status(thm)], ['50', '65', '66', '67', '68'])). 27.75/28.20 tff('70', plain, 27.75/28.20 archim1246769320r_real(zero_zero_real) 27.75/28.20 = hAPP_nat_int( 27.75/28.20 hAPP_int_fun_nat_int(power_power_int, 27.75/28.20 hAPP_nat_int(semiri1621563631at_int, hAPP_nat_nat(suc, n))), 27.75/28.20 hAPP_nat_nat( 27.75/28.20 hAPP_nat_fun_nat_nat(plus_plus_nat, 27.75/28.20 sk_N_1(archim1246769320r_real(one_one_real))), 27.75/28.20 sk_N_1(archim1246769320r_real(one_one_real)))), 27.75/28.20 inference('demod', [status(thm)], 27.75/28.20 ['0', '18', '23', '26', '27', '49', '69'])). 27.75/28.20 tff(fact_347_field__power__not__zero, axiom, 27.75/28.20 (![N_52,A_197]: 27.75/28.20 (is_int(A_197) => 27.75/28.20 ((zero_zero_int != A_197) => 27.75/28.20 (zero_zero_int != 27.75/28.20 hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_197),N_52)))))). 27.75/28.20 tff('71', plain, 27.75/28.20 ![X5174, X5175]: 27.75/28.20 (zero_zero_int = X5174 27.75/28.20 | zero_zero_int 27.75/28.20 != hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int, X5174), 27.75/28.20 X5175) 27.75/28.20 | ~ is_int(X5174)), 27.75/28.20 inference('cnf', [status(esa)], [fact_347_field__power__not__zero])). 27.75/28.20 tff('72', plain, zero_zero_int = archim1246769320r_real(zero_zero_real), 27.75/28.20 inference('demod', [status(thm)], ['1', '17'])). 27.75/28.20 tff('73', plain, zero_zero_int = archim1246769320r_real(zero_zero_real), 27.75/28.20 inference('demod', [status(thm)], ['1', '17'])). 27.75/28.20 tff('74', plain, 27.75/28.20 ![X5174, X5175]: 27.75/28.20 (archim1246769320r_real(zero_zero_real) = X5174 27.75/28.20 | archim1246769320r_real(zero_zero_real) 27.75/28.20 != hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int, X5174), 27.75/28.20 X5175) 27.75/28.20 | ~ is_int(X5174)), 27.75/28.20 inference('demod', [status(thm)], ['71', '72', '73'])). 27.75/28.20 tff('75', plain, 27.75/28.20 (archim1246769320r_real(zero_zero_real) 27.75/28.20 != archim1246769320r_real(zero_zero_real) 27.75/28.20 | ~ is_int(hAPP_nat_int(semiri1621563631at_int, hAPP_nat_nat(suc, n))) 27.75/28.20 | archim1246769320r_real(zero_zero_real) 27.75/28.20 = hAPP_nat_int(semiri1621563631at_int, hAPP_nat_nat(suc, n))), 27.75/28.20 inference('sup-', [status(thm)], ['70', '74'])). 27.75/28.20 tff(gsy_c_hAPP_000tc__Nat__Onat_000tc__Int__Oint, axiom, 27.75/28.20 (![B_1_1,B_2_1]: is_int(hAPP_nat_int(B_1_1,B_2_1)))). 27.75/28.20 tff('76', plain, ![X2915, X2916]: is_int(hAPP_nat_int(X2915, X2916)), 27.75/28.20 inference('cnf', [status(esa)], 27.75/28.20 [gsy_c_hAPP_000tc__Nat__Onat_000tc__Int__Oint])). 27.75/28.20 tff('77', plain, 27.75/28.20 (archim1246769320r_real(zero_zero_real) 27.75/28.20 != archim1246769320r_real(zero_zero_real) 27.75/28.20 | archim1246769320r_real(zero_zero_real) 27.75/28.20 = hAPP_nat_int(semiri1621563631at_int, hAPP_nat_nat(suc, n))), 27.75/28.20 inference('demod', [status(thm)], ['75', '76'])). 27.75/28.20 tff('78', plain, 27.75/28.20 archim1246769320r_real(zero_zero_real) 27.75/28.20 = hAPP_nat_int(semiri1621563631at_int, hAPP_nat_nat(suc, n)), 27.75/28.20 inference('simplify', [status(thm)], ['77'])). 27.75/28.20 tff(fact_71_int__eq__0__conv, axiom, 27.75/28.20 (![Na]: 27.75/28.20 ((hAPP_nat_int(semiri1621563631at_int,Na) = zero_zero_int) <=> 27.75/28.20 (Na = zero_zero_nat)))). 27.75/28.20 tff('79', plain, 27.75/28.20 ![X291]: 27.75/28.20 (X291 = zero_zero_nat 27.75/28.20 | hAPP_nat_int(semiri1621563631at_int, X291) != zero_zero_int), 27.75/28.20 inference('cnf', [status(esa)], [fact_71_int__eq__0__conv])). 27.75/28.20 tff('80', plain, zero_zero_int = pls, 27.75/28.20 inference('cnf', [status(esa)], [fact_151_Pls__def])). 27.75/28.20 tff('81', plain, 27.75/28.20 ![X291]: 27.75/28.20 (X291 = zero_zero_nat 27.75/28.20 | hAPP_nat_int(semiri1621563631at_int, X291) != pls), 27.75/28.20 inference('demod', [status(thm)], ['79', '80'])). 27.75/28.20 tff('82', plain, pls = archim1246769320r_real(zero_zero_real), 27.75/28.20 inference('demod', [status(thm)], ['7', '16'])). 27.75/28.20 tff('83', plain, 27.75/28.20 ![X291]: 27.75/28.20 (X291 = zero_zero_nat 27.75/28.20 | hAPP_nat_int(semiri1621563631at_int, X291) 27.75/28.20 != archim1246769320r_real(zero_zero_real)), 27.75/28.20 inference('demod', [status(thm)], ['81', '82'])). 27.75/28.20 tff('84', plain, 27.75/28.20 (archim1246769320r_real(zero_zero_real) 27.75/28.20 != archim1246769320r_real(zero_zero_real) 27.75/28.20 | hAPP_nat_nat(suc, n) = zero_zero_nat), 27.75/28.20 inference('sup-', [status(thm)], ['78', '83'])). 27.75/28.20 tff('85', plain, hAPP_nat_nat(suc, n) = zero_zero_nat, 27.75/28.20 inference('simplify', [status(thm)], ['84'])). 27.75/28.20 tff(fact_2996_Zero__neq__Suc, axiom, 27.75/28.20 (![M]: (hAPP_nat_nat(suc,M) != zero_zero_nat))). 27.75/28.20 tff('86', plain, ![X1653]: hAPP_nat_nat(suc, X1653) != zero_zero_nat, 27.75/28.20 inference('cnf', [status(esa)], [fact_2996_Zero__neq__Suc])). 27.75/28.20 tff('87', plain, $false, 27.75/28.20 inference('simplify_reflect-', [status(thm)], ['85', '86'])). 27.75/28.20 27.75/28.20 % SZS output end Refutation 27.75/28.20 27.75/28.21 % Zipperpin 1.5 exiting 27.75/28.21 EOF