0.01/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.12/0.13 % Command : run_portfolio.sh /export/starexec/sandbox/benchmark/theBenchmark.p /export/starexec/sandbox/tmp/tmp.XPZBSjJ1BE 0.12/0.34 % Computer : n004.cluster.edu 0.12/0.34 % Model : x86_64 x86_64 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.34 % Memory : 8042.1875MB 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.34 % CPULimit : 960 0.12/0.34 % DateTime : Thu Jul 2 08:35:43 EDT 2020 0.12/0.34 % CPUTime : 0.12/0.34 % Running portfolio for 120 s 0.12/0.34 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 0.12/0.34 % Number of cores: 8 0.12/0.35 % Python version: Python 3.6.8 0.12/0.35 % Running in FO mode 25.83/26.08 % Running /export/starexec/sandbox/solver/bin/fo/fo7.sh for 25 25.83/26.08 % Running /export/starexec/sandbox/solver/bin/fo/fo8.sh for 20 25.83/26.08 % Solved by: fo/fo8.sh 25.83/26.08 To remain in the chosen logic fragment, unification with booleans has been disabled. 25.83/26.08 % done 1666 iterations in 0.800s 25.83/26.08 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 25.83/26.08 % SZS output start Refutation 25.83/26.08 tff(alpha_morphism, axiom, (morphism(alpha,a,b))). 25.83/26.08 tff('0', plain, morphism(alpha, a, b), 25.83/26.08 inference('cnf', [status(esa)], [alpha_morphism])). 25.83/26.08 tff(morphism, axiom, 25.83/26.08 (![Morphism,Dom,Cod]: 25.83/26.08 (morphism(Morphism,Dom,Cod) => 25.83/26.08 ((zero(Cod) = apply(Morphism,zero(Dom))) & 25.83/26.08 (![El]: (element(El,Dom) => element(apply(Morphism,El),Cod))))))). 25.83/26.08 tff('1', plain, 25.83/26.08 ![X13, X14, X15]: 25.83/26.08 (zero(X15) = apply(X13, zero(X14)) | ~ morphism(X13, X14, X15)), 25.83/26.08 inference('cnf', [status(esa)], [morphism])). 25.83/26.08 tff('2', plain, zero(b) = apply(alpha, zero(a)), 25.83/26.08 inference('sup-', [status(thm)], ['0', '1'])). 25.83/26.08 tff(g_morphism, axiom, (morphism(g,b,e))). 25.83/26.08 tff('3', plain, morphism(g, b, e), 25.83/26.08 inference('cnf', [status(esa)], [g_morphism])). 25.83/26.08 tff(properties_for_injection_2, axiom, 25.83/26.08 (![Morphism,Dom,Cod]: 25.83/26.08 (((![El]: 25.83/26.08 ((element(El,Dom) & (apply(Morphism,El) = zero(Cod))) => 25.83/26.08 (zero(Dom) = El))) & 25.83/26.08 morphism(Morphism,Dom,Cod)) => 25.83/26.08 injection(Morphism)))). 25.83/26.08 tff('4', plain, 25.83/26.08 ![X62, X63, X64]: 25.83/26.08 ( injection(X62) 25.83/26.08 | element(sk_El(X63, X64, X62), X64) 25.83/26.08 | ~ morphism(X62, X64, X63)), 25.83/26.08 inference('cnf', [status(esa)], [properties_for_injection_2])). 25.83/26.08 tff('5', plain, ( element(sk_El(e, b, g), b) | injection(g)), 25.83/26.08 inference('sup-', [status(thm)], ['3', '4'])). 25.83/26.08 tff(g_injection, conjecture, (injection(g))). 25.83/26.08 tff(zf_stmt_0, negated_conjecture, (~injection(g))). 25.83/26.08 tff('6', plain, ~ injection(g), inference('cnf', [status(esa)], [zf_stmt_0])). 25.83/26.08 tff('7', plain, element(sk_El(e, b, g), b), 25.83/26.08 inference('clc', [status(thm)], ['5', '6'])). 25.83/26.08 tff(beta_morphism, axiom, (morphism(beta,b,c))). 25.83/26.08 tff('8', plain, morphism(beta, b, c), 25.83/26.08 inference('cnf', [status(esa)], [beta_morphism])). 25.83/26.08 tff('9', plain, morphism(alpha, a, b), 25.83/26.08 inference('cnf', [status(esa)], [alpha_morphism])). 25.83/26.08 tff(exact_properties, axiom, 25.83/26.08 (![Morphism1,Morphism2,Dom,CodDom,Cod]: 25.83/26.08 ((morphism(Morphism2,CodDom,Cod) & morphism(Morphism1,Dom,CodDom) & 25.83/26.08 exact(Morphism1,Morphism2)) => 25.83/26.08 (![ElCodDom]: 25.83/26.08 (((zero(Cod) = apply(Morphism2,ElCodDom)) & element(ElCodDom,CodDom)) <=> 25.83/26.08 (?[ElDom]: 25.83/26.08 (element(ElDom,Dom) & (ElCodDom = apply(Morphism1,ElDom))))))))). 25.83/26.08 tff('10', plain, 25.83/26.08 ![X17, X18, X19, X20, X21, X24]: 25.83/26.08 (~ exact(X17, X18) 25.83/26.08 | ~ morphism(X17, X19, X20) 25.83/26.08 | ~ morphism(X18, X20, X21) 25.83/26.08 | X24 = apply(X17, sk_ElDom_1(X24, X19, X17)) 25.83/26.08 | ~ element(X24, X20) 25.83/26.08 | zero(X21) != apply(X18, X24)), 25.83/26.08 inference('cnf', [status(esa)], [exact_properties])). 25.83/26.08 tff('11', plain, 25.83/26.08 ![X0, X1, X2]: 25.83/26.08 (zero(X0) != apply(X2, X1) 25.83/26.08 | ~ element(X1, b) 25.83/26.08 | X1 = apply(alpha, sk_ElDom_1(X1, a, alpha)) 25.83/26.08 | ~ morphism(X2, b, X0) 25.83/26.08 | ~ exact(alpha, X2)), 25.83/26.08 inference('sup-', [status(thm)], ['9', '10'])). 25.83/26.08 tff('12', plain, 25.83/26.08 ![X0]: 25.83/26.08 (~ exact(alpha, beta) 25.83/26.08 | X0 = apply(alpha, sk_ElDom_1(X0, a, alpha)) 25.83/26.08 | ~ element(X0, b) 25.83/26.08 | zero(c) != apply(beta, X0)), 25.83/26.08 inference('sup-', [status(thm)], ['8', '11'])). 25.83/26.08 tff(alpha_beta_exact, axiom, (exact(alpha,beta))). 25.83/26.08 tff('13', plain, exact(alpha, beta), 25.83/26.08 inference('cnf', [status(esa)], [alpha_beta_exact])). 25.83/26.08 tff('14', plain, 25.83/26.08 ![X0]: 25.83/26.08 (X0 = apply(alpha, sk_ElDom_1(X0, a, alpha)) 25.83/26.08 | ~ element(X0, b) 25.83/26.08 | zero(c) != apply(beta, X0)), 25.83/26.08 inference('demod', [status(thm)], ['12', '13'])). 25.83/26.08 tff('15', plain, 25.83/26.08 (zero(c) != apply(beta, sk_El(e, b, g)) 25.83/26.08 | sk_El(e, b, g) = apply(alpha, sk_ElDom_1(sk_El(e, b, g), a, alpha))), 25.83/26.08 inference('sup-', [status(thm)], ['7', '14'])). 25.83/26.08 tff('16', plain, element(sk_El(e, b, g), b), 25.83/26.08 inference('clc', [status(thm)], ['5', '6'])). 25.83/26.08 tff('17', plain, morphism(beta, b, c), 25.83/26.08 inference('cnf', [status(esa)], [beta_morphism])). 25.83/26.08 tff('18', plain, 25.83/26.08 ![X13, X14, X15, X16]: 25.83/26.08 (~ element(X16, X14) 25.83/26.08 | element(apply(X13, X16), X15) 25.83/26.08 | ~ morphism(X13, X14, X15)), 25.83/26.08 inference('cnf', [status(esa)], [morphism])). 25.83/26.08 tff('19', plain, ![X0]: ( element(apply(beta, X0), c) | ~ element(X0, b)), 25.83/26.08 inference('sup-', [status(thm)], ['17', '18'])). 25.83/26.08 tff('20', plain, element(apply(beta, sk_El(e, b, g)), c), 25.83/26.08 inference('sup-', [status(thm)], ['16', '19'])). 25.83/26.08 tff(h_morphism, axiom, (morphism(h,c,r))). 25.83/26.08 tff('21', plain, morphism(h, c, r), 25.83/26.08 inference('cnf', [status(esa)], [h_morphism])). 25.83/26.08 tff(injection_properties_2, axiom, 25.83/26.08 (![Morphism,Dom,Cod]: 25.83/26.08 ((morphism(Morphism,Dom,Cod) & injection(Morphism)) => 25.83/26.08 (![El]: 25.83/26.08 ((element(El,Dom) & (zero(Cod) = apply(Morphism,El))) => 25.83/26.08 (El = zero(Dom))))))). 25.83/26.08 tff('22', plain, 25.83/26.08 ![X58, X59, X60, X61]: 25.83/26.08 (~ injection(X58) 25.83/26.08 | ~ morphism(X58, X59, X60) 25.83/26.08 | X61 = zero(X59) 25.83/26.08 | zero(X60) != apply(X58, X61) 25.83/26.08 | ~ element(X61, X59)), 25.83/26.08 inference('cnf', [status(esa)], [injection_properties_2])). 25.83/26.08 tff('23', plain, 25.83/26.08 ![X0]: 25.83/26.08 (~ element(X0, c) 25.83/26.08 | zero(r) != apply(h, X0) 25.83/26.08 | X0 = zero(c) 25.83/26.08 | ~ injection(h)), 25.83/26.08 inference('sup-', [status(thm)], ['21', '22'])). 25.83/26.08 tff(h_injection, axiom, (injection(h))). 25.83/26.08 tff('24', plain, injection(h), 25.83/26.08 inference('cnf', [status(esa)], [h_injection])). 25.83/26.08 tff('25', plain, 25.83/26.08 ![X0]: (~ element(X0, c) | zero(r) != apply(h, X0) | X0 = zero(c)), 25.83/26.08 inference('demod', [status(thm)], ['23', '24'])). 25.83/26.08 tff('26', plain, 25.83/26.08 (apply(beta, sk_El(e, b, g)) = zero(c) 25.83/26.08 | zero(r) != apply(h, apply(beta, sk_El(e, b, g)))), 25.83/26.08 inference('sup-', [status(thm)], ['20', '25'])). 25.83/26.08 tff('27', plain, element(sk_El(e, b, g), b), 25.83/26.08 inference('clc', [status(thm)], ['5', '6'])). 25.83/26.08 tff('28', plain, morphism(beta, b, c), 25.83/26.08 inference('cnf', [status(esa)], [beta_morphism])). 25.83/26.08 tff(delta_morphism, axiom, (morphism(delta,e,r))). 25.83/26.08 tff('29', plain, morphism(delta, e, r), 25.83/26.08 inference('cnf', [status(esa)], [delta_morphism])). 25.83/26.08 tff(beta_h_g_delta_commute, axiom, (commute(beta,h,g,delta))). 25.83/26.08 tff('30', plain, commute(beta, h, g, delta), 25.83/26.08 inference('cnf', [status(esa)], [beta_h_g_delta_commute])). 25.83/26.08 tff(commute_properties, axiom, 25.83/26.08 (![M1,M2,M3,M4,Dom,DomCod1,DomCod2,Cod]: 25.83/26.08 ((morphism(M2,DomCod1,Cod) & morphism(M3,Dom,DomCod2) & 25.83/26.08 commute(M1,M2,M3,M4) & morphism(M4,DomCod2,Cod) & 25.83/26.08 morphism(M1,Dom,DomCod1)) => 25.83/26.08 (![ElDom]: 25.83/26.08 (element(ElDom,Dom) => 25.83/26.08 (apply(M2,apply(M1,ElDom)) = apply(M4,apply(M3,ElDom)))))))). 25.83/26.08 tff('31', plain, 25.83/26.08 ![X29, X30, X31, X32, X33, X34, X35, X36, X37]: 25.83/26.08 (~ element(X29, X30) 25.83/26.08 | apply(X33, apply(X34, X29)) = apply(X31, apply(X32, X29)) 25.83/26.08 | ~ morphism(X34, X30, X35) 25.83/26.08 | ~ commute(X34, X33, X32, X31) 25.83/26.08 | ~ morphism(X32, X30, X36) 25.83/26.08 | ~ morphism(X33, X35, X37) 25.83/26.08 | ~ morphism(X31, X36, X37)), 25.83/26.08 inference('cnf', [status(esa)], [commute_properties])). 25.83/26.08 tff('32', plain, 25.83/26.08 ![X0, X1, X2, X3, X4]: 25.83/26.08 (~ morphism(delta, X1, X0) 25.83/26.08 | ~ morphism(h, X2, X0) 25.83/26.08 | ~ morphism(g, X3, X1) 25.83/26.08 | ~ morphism(beta, X3, X2) 25.83/26.08 | apply(h, apply(beta, X4)) = apply(delta, apply(g, X4)) 25.83/26.08 | ~ element(X4, X3)), 25.83/26.08 inference('sup-', [status(thm)], ['30', '31'])). 25.83/26.08 tff('33', plain, 25.83/26.08 ![X0, X1, X2]: 25.83/26.08 (~ element(X1, X0) 25.83/26.08 | apply(h, apply(beta, X1)) = apply(delta, apply(g, X1)) 25.83/26.08 | ~ morphism(beta, X0, X2) 25.83/26.08 | ~ morphism(g, X0, e) 25.83/26.08 | ~ morphism(h, X2, r)), 25.83/26.08 inference('sup-', [status(thm)], ['29', '32'])). 25.83/26.08 tff('34', plain, 25.83/26.08 ![X0]: 25.83/26.08 (~ morphism(h, c, r) 25.83/26.08 | ~ morphism(g, b, e) 25.83/26.08 | apply(h, apply(beta, X0)) = apply(delta, apply(g, X0)) 25.83/26.08 | ~ element(X0, b)), 25.83/26.08 inference('sup-', [status(thm)], ['28', '33'])). 25.83/26.08 tff('35', plain, morphism(h, c, r), 25.83/26.08 inference('cnf', [status(esa)], [h_morphism])). 25.83/26.08 tff('36', plain, morphism(g, b, e), 25.83/26.08 inference('cnf', [status(esa)], [g_morphism])). 25.83/26.08 tff('37', plain, 25.83/26.08 ![X0]: 25.83/26.08 (apply(h, apply(beta, X0)) = apply(delta, apply(g, X0)) 25.83/26.08 | ~ element(X0, b)), 25.83/26.08 inference('demod', [status(thm)], ['34', '35', '36'])). 25.83/26.08 tff('38', plain, 25.83/26.08 apply(h, apply(beta, sk_El(e, b, g))) 25.83/26.08 = apply(delta, apply(g, sk_El(e, b, g))), 25.83/26.08 inference('sup-', [status(thm)], ['27', '37'])). 25.83/26.08 tff('39', plain, morphism(g, b, e), 25.83/26.08 inference('cnf', [status(esa)], [g_morphism])). 25.83/26.08 tff('40', plain, 25.83/26.08 ![X62, X63, X64]: 25.83/26.08 ( injection(X62) 25.83/26.08 | apply(X62, sk_El(X63, X64, X62)) = zero(X63) 25.83/26.08 | ~ morphism(X62, X64, X63)), 25.83/26.08 inference('cnf', [status(esa)], [properties_for_injection_2])). 25.83/26.08 tff('41', plain, (apply(g, sk_El(e, b, g)) = zero(e) | injection(g)), 25.83/26.08 inference('sup-', [status(thm)], ['39', '40'])). 25.83/26.08 tff('42', plain, ~ injection(g), inference('cnf', [status(esa)], [zf_stmt_0])). 25.83/26.08 tff('43', plain, apply(g, sk_El(e, b, g)) = zero(e), 25.83/26.08 inference('clc', [status(thm)], ['41', '42'])). 25.83/26.08 tff('44', plain, morphism(delta, e, r), 25.83/26.08 inference('cnf', [status(esa)], [delta_morphism])). 25.83/26.08 tff('45', plain, 25.83/26.08 ![X13, X14, X15]: 25.83/26.08 (zero(X15) = apply(X13, zero(X14)) | ~ morphism(X13, X14, X15)), 25.83/26.08 inference('cnf', [status(esa)], [morphism])). 25.83/26.08 tff('46', plain, zero(r) = apply(delta, zero(e)), 25.83/26.08 inference('sup-', [status(thm)], ['44', '45'])). 25.83/26.08 tff('47', plain, apply(h, apply(beta, sk_El(e, b, g))) = zero(r), 25.83/26.08 inference('demod', [status(thm)], ['38', '43', '46'])). 25.83/26.08 tff('48', plain, 25.83/26.08 (apply(beta, sk_El(e, b, g)) = zero(c) | zero(r) != zero(r)), 25.83/26.08 inference('demod', [status(thm)], ['26', '47'])). 25.83/26.08 tff('49', plain, apply(beta, sk_El(e, b, g)) = zero(c), 25.83/26.08 inference('simplify', [status(thm)], ['48'])). 25.83/26.08 tff('50', plain, 25.83/26.08 (zero(c) != zero(c) 25.83/26.08 | sk_El(e, b, g) = apply(alpha, sk_ElDom_1(sk_El(e, b, g), a, alpha))), 25.83/26.08 inference('demod', [status(thm)], ['15', '49'])). 25.83/26.08 tff('51', plain, 25.83/26.08 sk_El(e, b, g) = apply(alpha, sk_ElDom_1(sk_El(e, b, g), a, alpha)), 25.83/26.08 inference('simplify', [status(thm)], ['50'])). 25.83/26.08 tff('52', plain, element(sk_El(e, b, g), b), 25.83/26.08 inference('clc', [status(thm)], ['5', '6'])). 25.83/26.08 tff('53', plain, morphism(beta, b, c), 25.83/26.08 inference('cnf', [status(esa)], [beta_morphism])). 25.83/26.08 tff('54', plain, morphism(alpha, a, b), 25.83/26.08 inference('cnf', [status(esa)], [alpha_morphism])). 25.83/26.08 tff('55', plain, 25.83/26.08 ![X17, X18, X19, X20, X21, X24]: 25.83/26.08 (~ exact(X17, X18) 25.83/26.08 | ~ morphism(X17, X19, X20) 25.83/26.08 | ~ morphism(X18, X20, X21) 25.83/26.08 | element(sk_ElDom_1(X24, X19, X17), X19) 25.83/26.08 | ~ element(X24, X20) 25.83/26.08 | zero(X21) != apply(X18, X24)), 25.83/26.08 inference('cnf', [status(esa)], [exact_properties])). 25.83/26.08 tff('56', plain, 25.83/26.08 ![X0, X1, X2]: 25.83/26.08 (zero(X0) != apply(X2, X1) 25.83/26.08 | ~ element(X1, b) 25.83/26.08 | element(sk_ElDom_1(X1, a, alpha), a) 25.83/26.08 | ~ morphism(X2, b, X0) 25.83/26.08 | ~ exact(alpha, X2)), 25.83/26.08 inference('sup-', [status(thm)], ['54', '55'])). 25.83/26.08 tff('57', plain, 25.83/26.08 ![X0]: 25.83/26.08 (~ exact(alpha, beta) 25.83/26.08 | element(sk_ElDom_1(X0, a, alpha), a) 25.83/26.08 | ~ element(X0, b) 25.83/26.08 | zero(c) != apply(beta, X0)), 25.83/26.08 inference('sup-', [status(thm)], ['53', '56'])). 25.83/26.08 tff('58', plain, exact(alpha, beta), 25.83/26.08 inference('cnf', [status(esa)], [alpha_beta_exact])). 25.83/26.08 tff('59', plain, 25.83/26.08 ![X0]: 25.83/26.08 ( element(sk_ElDom_1(X0, a, alpha), a) 25.83/26.08 | ~ element(X0, b) 25.83/26.08 | zero(c) != apply(beta, X0)), 25.83/26.08 inference('demod', [status(thm)], ['57', '58'])). 25.83/26.08 tff('60', plain, 25.83/26.08 (zero(c) != apply(beta, sk_El(e, b, g)) 25.83/26.08 | element(sk_ElDom_1(sk_El(e, b, g), a, alpha), a)), 25.83/26.08 inference('sup-', [status(thm)], ['52', '59'])). 25.83/26.08 tff('61', plain, apply(beta, sk_El(e, b, g)) = zero(c), 25.83/26.08 inference('simplify', [status(thm)], ['48'])). 25.83/26.08 tff('62', plain, 25.83/26.08 (zero(c) != zero(c) | element(sk_ElDom_1(sk_El(e, b, g), a, alpha), a)), 25.83/26.08 inference('demod', [status(thm)], ['60', '61'])). 25.83/26.08 tff('63', plain, element(sk_ElDom_1(sk_El(e, b, g), a, alpha), a), 25.83/26.08 inference('simplify', [status(thm)], ['62'])). 25.83/26.08 tff(f_morphism, axiom, (morphism(f,a,d))). 25.83/26.08 tff('64', plain, morphism(f, a, d), 25.83/26.08 inference('cnf', [status(esa)], [f_morphism])). 25.83/26.08 tff('65', plain, 25.83/26.08 ![X58, X59, X60, X61]: 25.83/26.08 (~ injection(X58) 25.83/26.08 | ~ morphism(X58, X59, X60) 25.83/26.08 | X61 = zero(X59) 25.83/26.08 | zero(X60) != apply(X58, X61) 25.83/26.08 | ~ element(X61, X59)), 25.83/26.08 inference('cnf', [status(esa)], [injection_properties_2])). 25.83/26.08 tff('66', plain, 25.83/26.08 ![X0]: 25.83/26.08 (~ element(X0, a) 25.83/26.08 | zero(d) != apply(f, X0) 25.83/26.08 | X0 = zero(a) 25.83/26.08 | ~ injection(f)), 25.83/26.08 inference('sup-', [status(thm)], ['64', '65'])). 25.83/26.08 tff(f_injection, axiom, (injection(f))). 25.83/26.08 tff('67', plain, injection(f), 25.83/26.08 inference('cnf', [status(esa)], [f_injection])). 25.83/26.08 tff('68', plain, 25.83/26.08 ![X0]: (~ element(X0, a) | zero(d) != apply(f, X0) | X0 = zero(a)), 25.83/26.08 inference('demod', [status(thm)], ['66', '67'])). 25.83/26.08 tff('69', plain, 25.83/26.08 (sk_ElDom_1(sk_El(e, b, g), a, alpha) = zero(a) 25.83/26.08 | zero(d) != apply(f, sk_ElDom_1(sk_El(e, b, g), a, alpha))), 25.83/26.08 inference('sup-', [status(thm)], ['63', '68'])). 25.83/26.08 tff('70', plain, element(sk_ElDom_1(sk_El(e, b, g), a, alpha), a), 25.83/26.08 inference('simplify', [status(thm)], ['62'])). 25.83/26.08 tff('71', plain, morphism(f, a, d), 25.83/26.08 inference('cnf', [status(esa)], [f_morphism])). 25.83/26.08 tff('72', plain, 25.83/26.08 ![X13, X14, X15, X16]: 25.83/26.08 (~ element(X16, X14) 25.83/26.08 | element(apply(X13, X16), X15) 25.83/26.08 | ~ morphism(X13, X14, X15)), 25.83/26.08 inference('cnf', [status(esa)], [morphism])). 25.83/26.08 tff('73', plain, ![X0]: ( element(apply(f, X0), d) | ~ element(X0, a)), 25.83/26.08 inference('sup-', [status(thm)], ['71', '72'])). 25.83/26.08 tff('74', plain, element(apply(f, sk_ElDom_1(sk_El(e, b, g), a, alpha)), d), 25.83/26.08 inference('sup-', [status(thm)], ['70', '73'])). 25.83/26.08 tff(gamma_morphism, axiom, (morphism(gamma,d,e))). 25.83/26.08 tff('75', plain, morphism(gamma, d, e), 25.83/26.08 inference('cnf', [status(esa)], [gamma_morphism])). 25.83/26.08 tff('76', plain, 25.83/26.08 ![X58, X59, X60, X61]: 25.83/26.08 (~ injection(X58) 25.83/26.08 | ~ morphism(X58, X59, X60) 25.83/26.08 | X61 = zero(X59) 25.83/26.08 | zero(X60) != apply(X58, X61) 25.83/26.08 | ~ element(X61, X59)), 25.83/26.08 inference('cnf', [status(esa)], [injection_properties_2])). 25.83/26.08 tff('77', plain, 25.83/26.08 ![X0]: 25.83/26.08 (~ element(X0, d) 25.83/26.08 | zero(e) != apply(gamma, X0) 25.83/26.08 | X0 = zero(d) 25.83/26.08 | ~ injection(gamma)), 25.83/26.08 inference('sup-', [status(thm)], ['75', '76'])). 25.83/26.08 tff(gamma_injection, axiom, (injection(gamma))). 25.83/26.08 tff('78', plain, injection(gamma), 25.83/26.08 inference('cnf', [status(esa)], [gamma_injection])). 25.83/26.08 tff('79', plain, 25.83/26.08 ![X0]: (~ element(X0, d) | zero(e) != apply(gamma, X0) | X0 = zero(d)), 25.83/26.08 inference('demod', [status(thm)], ['77', '78'])). 25.83/26.08 tff('80', plain, 25.83/26.08 (apply(f, sk_ElDom_1(sk_El(e, b, g), a, alpha)) = zero(d) 25.83/26.08 | zero(e) 25.83/26.08 != apply(gamma, apply(f, sk_ElDom_1(sk_El(e, b, g), a, alpha)))), 25.83/26.08 inference('sup-', [status(thm)], ['74', '79'])). 25.83/26.08 tff('81', plain, element(sk_ElDom_1(sk_El(e, b, g), a, alpha), a), 25.83/26.08 inference('simplify', [status(thm)], ['62'])). 25.83/26.08 tff('82', plain, morphism(alpha, a, b), 25.83/26.08 inference('cnf', [status(esa)], [alpha_morphism])). 25.83/26.08 tff('83', plain, morphism(gamma, d, e), 25.83/26.08 inference('cnf', [status(esa)], [gamma_morphism])). 25.83/26.08 tff(alpha_g_f_gamma_commute, axiom, (commute(alpha,g,f,gamma))). 25.83/26.08 tff('84', plain, commute(alpha, g, f, gamma), 25.83/26.08 inference('cnf', [status(esa)], [alpha_g_f_gamma_commute])). 25.83/26.08 tff('85', plain, 25.83/26.08 ![X29, X30, X31, X32, X33, X34, X35, X36, X37]: 25.83/26.08 (~ element(X29, X30) 25.83/26.08 | apply(X33, apply(X34, X29)) = apply(X31, apply(X32, X29)) 25.83/26.08 | ~ morphism(X34, X30, X35) 25.83/26.08 | ~ commute(X34, X33, X32, X31) 25.83/26.08 | ~ morphism(X32, X30, X36) 25.83/26.08 | ~ morphism(X33, X35, X37) 25.83/26.08 | ~ morphism(X31, X36, X37)), 25.83/26.08 inference('cnf', [status(esa)], [commute_properties])). 25.83/26.08 tff('86', plain, 25.83/26.08 ![X0, X1, X2, X3, X4]: 25.83/26.08 (~ morphism(gamma, X1, X0) 25.83/26.08 | ~ morphism(g, X2, X0) 25.83/26.08 | ~ morphism(f, X3, X1) 25.83/26.08 | ~ morphism(alpha, X3, X2) 25.83/26.08 | apply(g, apply(alpha, X4)) = apply(gamma, apply(f, X4)) 25.83/26.08 | ~ element(X4, X3)), 25.83/26.08 inference('sup-', [status(thm)], ['84', '85'])). 25.83/26.08 tff('87', plain, 25.83/26.08 ![X0, X1, X2]: 25.83/26.08 (~ element(X1, X0) 25.83/26.08 | apply(g, apply(alpha, X1)) = apply(gamma, apply(f, X1)) 25.83/26.08 | ~ morphism(alpha, X0, X2) 25.83/26.08 | ~ morphism(f, X0, d) 25.83/26.08 | ~ morphism(g, X2, e)), 25.83/26.08 inference('sup-', [status(thm)], ['83', '86'])). 25.83/26.08 tff('88', plain, 25.83/26.08 ![X0]: 25.83/26.08 (~ morphism(g, b, e) 25.83/26.08 | ~ morphism(f, a, d) 25.83/26.08 | apply(g, apply(alpha, X0)) = apply(gamma, apply(f, X0)) 25.83/26.08 | ~ element(X0, a)), 25.83/26.08 inference('sup-', [status(thm)], ['82', '87'])). 25.83/26.08 tff('89', plain, morphism(g, b, e), 25.83/26.08 inference('cnf', [status(esa)], [g_morphism])). 25.83/26.08 tff('90', plain, morphism(f, a, d), 25.83/26.08 inference('cnf', [status(esa)], [f_morphism])). 25.83/26.08 tff('91', plain, 25.83/26.08 ![X0]: 25.83/26.08 (apply(g, apply(alpha, X0)) = apply(gamma, apply(f, X0)) 25.83/26.08 | ~ element(X0, a)), 25.83/26.08 inference('demod', [status(thm)], ['88', '89', '90'])). 25.83/26.08 tff('92', plain, 25.83/26.08 apply(g, apply(alpha, sk_ElDom_1(sk_El(e, b, g), a, alpha))) 25.83/26.08 = apply(gamma, apply(f, sk_ElDom_1(sk_El(e, b, g), a, alpha))), 25.83/26.08 inference('sup-', [status(thm)], ['81', '91'])). 25.83/26.08 tff('93', plain, 25.83/26.08 sk_El(e, b, g) = apply(alpha, sk_ElDom_1(sk_El(e, b, g), a, alpha)), 25.83/26.08 inference('simplify', [status(thm)], ['50'])). 25.83/26.08 tff('94', plain, 25.83/26.08 apply(g, sk_El(e, b, g)) 25.83/26.08 = apply(gamma, apply(f, sk_ElDom_1(sk_El(e, b, g), a, alpha))), 25.83/26.08 inference('demod', [status(thm)], ['92', '93'])). 25.83/26.08 tff('95', plain, apply(g, sk_El(e, b, g)) = zero(e), 25.83/26.08 inference('clc', [status(thm)], ['41', '42'])). 25.83/26.08 tff('96', plain, 25.83/26.08 zero(e) = apply(gamma, apply(f, sk_ElDom_1(sk_El(e, b, g), a, alpha))), 25.83/26.08 inference('demod', [status(thm)], ['94', '95'])). 25.83/26.08 tff('97', plain, 25.83/26.08 (apply(f, sk_ElDom_1(sk_El(e, b, g), a, alpha)) = zero(d) 25.83/26.08 | zero(e) != zero(e)), 25.83/26.08 inference('demod', [status(thm)], ['80', '96'])). 25.83/26.08 tff('98', plain, apply(f, sk_ElDom_1(sk_El(e, b, g), a, alpha)) = zero(d), 25.83/26.08 inference('simplify', [status(thm)], ['97'])). 25.83/26.08 tff('99', plain, 25.83/26.08 (sk_ElDom_1(sk_El(e, b, g), a, alpha) = zero(a) | zero(d) != zero(d)), 25.83/26.08 inference('demod', [status(thm)], ['69', '98'])). 25.83/26.08 tff('100', plain, sk_ElDom_1(sk_El(e, b, g), a, alpha) = zero(a), 25.83/26.08 inference('simplify', [status(thm)], ['99'])). 25.83/26.08 tff('101', plain, sk_El(e, b, g) = apply(alpha, zero(a)), 25.83/26.08 inference('demod', [status(thm)], ['51', '100'])). 25.83/26.08 tff('102', plain, sk_El(e, b, g) = zero(b), 25.83/26.08 inference('sup+', [status(thm)], ['2', '101'])). 25.83/26.08 tff('103', plain, morphism(g, b, e), 25.83/26.08 inference('cnf', [status(esa)], [g_morphism])). 25.83/26.08 tff('104', plain, 25.83/26.08 ![X62, X63, X64]: 25.83/26.08 ( injection(X62) 25.83/26.08 | zero(X64) != sk_El(X63, X64, X62) 25.83/26.08 | ~ morphism(X62, X64, X63)), 25.83/26.08 inference('cnf', [status(esa)], [properties_for_injection_2])). 25.83/26.08 tff('105', plain, (zero(b) != sk_El(e, b, g) | injection(g)), 25.83/26.08 inference('sup-', [status(thm)], ['103', '104'])). 25.83/26.08 tff('106', plain, ~ injection(g), 25.83/26.08 inference('cnf', [status(esa)], [zf_stmt_0])). 25.83/26.08 tff('107', plain, zero(b) != sk_El(e, b, g), 25.83/26.08 inference('clc', [status(thm)], ['105', '106'])). 25.83/26.08 tff('108', plain, $false, 25.83/26.08 inference('simplify_reflect-', [status(thm)], ['102', '107'])). 25.83/26.08 25.83/26.08 % SZS output end Refutation 25.83/26.08 25.83/26.09 % Zipperpin 1.5 exiting 25.83/26.09 EOF