%------------------------------------------------------------------------------ % File : Z3---4.15.1 % Problem : CAT002-2 : TPTP v9.0.0. Released v1.0.0. % Transfm : none % Format : tptp % Command : run_E %s %d THM % Computer : n015.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Sat Jun 21 05:00:18 AM UTC 2025 % Result : Satisfiable 1.41s 1.61s % Output : Model 1.41s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.11 % Problem : CAT002-2 : TPTP v9.0.0. Released v1.0.0. % 0.06/0.11 % Command : run_E %s %d THM % 0.12/0.33 % Computer : n015.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Thu Jun 19 11:51:26 EDT 2025 % 0.12/0.33 % CPUTime : % 1.41/1.61 % SZS status Satisfiable % 1.41/1.61 % SZS output start Model % 1.41/1.61 tff(tptp_fun__i_val_3_type, type, ( % 1.41/1.61 tptp_fun__i_val_3: $i)). % 1.41/1.61 tff(h_type, type, ( % 1.41/1.61 h: $i)). % 1.41/1.61 tff(tptp_fun__i_val_1_type, type, ( % 1.41/1.61 tptp_fun__i_val_1: $i)). % 1.41/1.61 tff(b_type, type, ( % 1.41/1.61 b: $i)). % 1.41/1.61 tff(tptp_fun__i_val_0_type, type, ( % 1.41/1.61 tptp_fun__i_val_0: $i)). % 1.41/1.61 tff(a_type, type, ( % 1.41/1.61 a: $i)). % 1.41/1.61 tff(tptp_fun__i_val_6_type, type, ( % 1.41/1.61 tptp_fun__i_val_6: $i)). % 1.41/1.61 tff(g_type, type, ( % 1.41/1.61 g: $i)). % 1.41/1.61 tff(tptp_fun__i_val_11_type, type, ( % 1.41/1.61 tptp_fun__i_val_11: $i)). % 1.41/1.61 tff(tptp_fun__i_val_2_type, type, ( % 1.41/1.61 tptp_fun__i_val_2: $i)). % 1.41/1.61 tff(k!36_type, type, ( % 1.41/1.61 k!36: $i > $i)). % 1.41/1.61 tff(tptp_fun__i_val_5_type, type, ( % 1.41/1.61 tptp_fun__i_val_5: $i)). % 1.41/1.61 tff(tptp_fun__i_val_12_type, type, ( % 1.41/1.61 tptp_fun__i_val_12: $i)). % 1.41/1.61 tff(tptp_fun__i_val_22_type, type, ( % 1.41/1.61 tptp_fun__i_val_22: $i)). % 1.41/1.61 tff(tptp_fun__i_val_21_type, type, ( % 1.41/1.61 tptp_fun__i_val_21: $i)). % 1.41/1.61 tff(tptp_fun__i_val_32_type, type, ( % 1.41/1.61 tptp_fun__i_val_32: $i)). % 1.41/1.61 tff(tptp_fun__i_val_10_type, type, ( % 1.41/1.61 tptp_fun__i_val_10: $i)). % 1.41/1.61 tff(tptp_fun__i_val_33_type, type, ( % 1.41/1.61 tptp_fun__i_val_33: $i)). % 1.41/1.61 tff(tptp_fun__i_val_9_type, type, ( % 1.41/1.61 tptp_fun__i_val_9: $i)). % 1.41/1.61 tff(tptp_fun__i_val_39_type, type, ( % 1.41/1.61 tptp_fun__i_val_39: $i)). % 1.41/1.61 tff(tptp_fun__i_val_15_type, type, ( % 1.41/1.61 tptp_fun__i_val_15: $i)). % 1.41/1.61 tff(tptp_fun__i_val_40_type, type, ( % 1.41/1.61 tptp_fun__i_val_40: $i)). % 1.41/1.61 tff(tptp_fun__i_val_20_type, type, ( % 1.41/1.61 tptp_fun__i_val_20: $i)). % 1.41/1.61 tff(tptp_fun__i_val_44_type, type, ( % 1.41/1.61 tptp_fun__i_val_44: $i)). % 1.41/1.61 tff(tptp_fun__i_val_23_type, type, ( % 1.41/1.61 tptp_fun__i_val_23: $i)). % 1.41/1.61 tff(tptp_fun__i_val_30_type, type, ( % 1.41/1.61 tptp_fun__i_val_30: $i)). % 1.41/1.61 tff(tptp_fun__i_val_29_type, type, ( % 1.41/1.61 tptp_fun__i_val_29: $i)). % 1.41/1.61 tff(tptp_fun__i_val_42_type, type, ( % 1.41/1.61 tptp_fun__i_val_42: $i)). % 1.41/1.61 tff(tptp_fun__i_val_37_type, type, ( % 1.41/1.61 tptp_fun__i_val_37: $i)). % 1.41/1.61 tff(tptp_fun__i_val_36_type, type, ( % 1.41/1.61 tptp_fun__i_val_36: $i)). % 1.41/1.61 tff(tptp_fun__i_val_60_type, type, ( % 1.41/1.61 tptp_fun__i_val_60: $i)). % 1.41/1.61 tff(tptp_fun__i_val_35_type, type, ( % 1.41/1.61 tptp_fun__i_val_35: $i)). % 1.41/1.61 tff(tptp_fun__i_val_43_type, type, ( % 1.41/1.61 tptp_fun__i_val_43: $i)). % 1.41/1.61 tff(codomain_type, type, ( % 1.41/1.61 codomain: $i > $i)). % 1.41/1.61 tff(tptp_fun__i_val_4_type, type, ( % 1.41/1.61 tptp_fun__i_val_4: $i)). % 1.41/1.61 tff(tptp_fun__i_val_7_type, type, ( % 1.41/1.61 tptp_fun__i_val_7: $i)). % 1.41/1.61 tff(compose_type, type, ( % 1.41/1.61 compose: ( $i * $i ) > $i)). % 1.41/1.61 tff(tptp_fun__i_val_8_type, type, ( % 1.41/1.61 tptp_fun__i_val_8: $i)). % 1.41/1.61 tff(tptp_fun__i_val_13_type, type, ( % 1.41/1.61 tptp_fun__i_val_13: $i)). % 1.41/1.61 tff(tptp_fun__i_val_14_type, type, ( % 1.41/1.61 tptp_fun__i_val_14: $i)). % 1.41/1.61 tff(tptp_fun__i_val_16_type, type, ( % 1.41/1.61 tptp_fun__i_val_16: $i)). % 1.41/1.61 tff(tptp_fun__i_val_17_type, type, ( % 1.41/1.61 tptp_fun__i_val_17: $i)). % 1.41/1.61 tff(tptp_fun__i_val_18_type, type, ( % 1.41/1.61 tptp_fun__i_val_18: $i)). % 1.41/1.61 tff(tptp_fun__i_val_19_type, type, ( % 1.41/1.61 tptp_fun__i_val_19: $i)). % 1.41/1.61 tff(tptp_fun__i_val_24_type, type, ( % 1.41/1.61 tptp_fun__i_val_24: $i)). % 1.41/1.61 tff(tptp_fun__i_val_25_type, type, ( % 1.41/1.61 tptp_fun__i_val_25: $i)). % 1.41/1.61 tff(tptp_fun__i_val_26_type, type, ( % 1.41/1.61 tptp_fun__i_val_26: $i)). % 1.41/1.61 tff(tptp_fun__i_val_27_type, type, ( % 1.41/1.61 tptp_fun__i_val_27: $i)). % 1.41/1.61 tff(tptp_fun__i_val_28_type, type, ( % 1.41/1.61 tptp_fun__i_val_28: $i)). % 1.41/1.61 tff(tptp_fun__i_val_31_type, type, ( % 1.41/1.61 tptp_fun__i_val_31: $i)). % 1.41/1.61 tff(tptp_fun__i_val_34_type, type, ( % 1.41/1.61 tptp_fun__i_val_34: $i)). % 1.41/1.61 tff(tptp_fun__i_val_38_type, type, ( % 1.41/1.61 tptp_fun__i_val_38: $i)). % 1.41/1.61 tff(tptp_fun__i_val_41_type, type, ( % 1.41/1.61 tptp_fun__i_val_41: $i)). % 1.41/1.61 tff(tptp_fun__i_val_45_type, type, ( % 1.41/1.61 tptp_fun__i_val_45: $i)). % 1.41/1.61 tff(tptp_fun__i_val_46_type, type, ( % 1.41/1.61 tptp_fun__i_val_46: $i)). % 1.41/1.61 tff(tptp_fun__i_val_47_type, type, ( % 1.41/1.61 tptp_fun__i_val_47: $i)). % 1.41/1.61 tff(tptp_fun__i_val_48_type, type, ( % 1.41/1.61 tptp_fun__i_val_48: $i)). % 1.41/1.61 tff(tptp_fun__i_val_49_type, type, ( % 1.41/1.61 tptp_fun__i_val_49: $i)). % 1.41/1.61 tff(tptp_fun__i_val_50_type, type, ( % 1.41/1.61 tptp_fun__i_val_50: $i)). % 1.41/1.61 tff(tptp_fun__i_val_51_type, type, ( % 1.41/1.61 tptp_fun__i_val_51: $i)). % 1.41/1.61 tff(tptp_fun__i_val_52_type, type, ( % 1.41/1.61 tptp_fun__i_val_52: $i)). % 1.41/1.61 tff(tptp_fun__i_val_53_type, type, ( % 1.41/1.61 tptp_fun__i_val_53: $i)). % 1.41/1.61 tff(tptp_fun__i_val_54_type, type, ( % 1.41/1.61 tptp_fun__i_val_54: $i)). % 1.41/1.61 tff(tptp_fun__i_val_55_type, type, ( % 1.41/1.61 tptp_fun__i_val_55: $i)). % 1.41/1.61 tff(tptp_fun__i_val_56_type, type, ( % 1.41/1.61 tptp_fun__i_val_56: $i)). % 1.41/1.61 tff(tptp_fun__i_val_57_type, type, ( % 1.41/1.61 tptp_fun__i_val_57: $i)). % 1.41/1.61 tff(tptp_fun__i_val_58_type, type, ( % 1.41/1.61 tptp_fun__i_val_58: $i)). % 1.41/1.61 tff(tptp_fun__i_val_59_type, type, ( % 1.41/1.61 tptp_fun__i_val_59: $i)). % 1.41/1.61 tff(tptp_fun__i_val_61_type, type, ( % 1.41/1.61 tptp_fun__i_val_61: $i)). % 1.41/1.61 tff(tptp_fun__i_val_62_type, type, ( % 1.41/1.61 tptp_fun__i_val_62: $i)). % 1.41/1.61 tff(tptp_fun__i_val_63_type, type, ( % 1.41/1.61 tptp_fun__i_val_63: $i)). % 1.41/1.61 tff(tptp_fun__i_val_64_type, type, ( % 1.41/1.61 tptp_fun__i_val_64: $i)). % 1.41/1.61 tff(tptp_fun__i_val_65_type, type, ( % 1.41/1.61 tptp_fun__i_val_65: $i)). % 1.41/1.61 tff(tptp_fun__i_val_66_type, type, ( % 1.41/1.61 tptp_fun__i_val_66: $i)). % 1.41/1.61 tff(domain_type, type, ( % 1.41/1.61 domain: $i > $i)). % 1.41/1.61 tff(formula1, axiom, % 1.41/1.61 h = $i!val!3). % 1.41/1.61 tff(formula2, axiom, % 1.41/1.61 b = $i!val!1). % 1.41/1.61 tff(formula3, axiom, % 1.41/1.61 a = $i!val!0). % 1.41/1.61 tff(formula4, axiom, % 1.41/1.61 g = $i!val!6). % 1.41/1.61 tff(formula5, axiom, % 1.41/1.61 ![X0: $i] : (codomain(X0) = ite_t((k!36(X0) = $i!val!43), $i!val!43, ite_t((k!36(X0) = $i!val!40), $i!val!40, ite_t(((k!36(X0) = $i!val!60) | (k!36(X0) = $i!val!35)), $i!val!60, ite_t((k!36(X0) = $i!val!36), $i!val!36, ite_t((k!36(X0) = $i!val!39), $i!val!39, ite_t((k!36(X0) = $i!val!37), $i!val!37, ite_t((k!36(X0) = $i!val!42), $i!val!42, ite_t((k!36(X0) = $i!val!33), $i!val!33, ite_t((k!36(X0) = $i!val!44), $i!val!44, ite_t((k!36(X0) = $i!val!29), $i!val!29, ite_t((k!36(X0) = $i!val!32), $i!val!32, ite_t((k!36(X0) = $i!val!30), $i!val!30, ite_t((k!36(X0) = $i!val!23), $i!val!44, ite_t((k!36(X0) = $i!val!20), $i!val!40, ite_t((k!36(X0) = $i!val!15), $i!val!39, ite_t((k!36(X0) = $i!val!9), $i!val!33, ite_t((k!36(X0) = $i!val!10), $i!val!32, ite_t(((k!36(X0) = $i!val!21) | (k!36(X0) = $i!val!22)), $i!val!2, ite_t((k!36(X0) = $i!val!12), $i!val!12, ite_t((k!36(X0) = $i!val!5), $i!val!5, ite_t((k!36(X0) = $i!val!2), $i!val!2, ite_t(((k!36(X0) = $i!val!6) | (k!36(X0) = $i!val!3)), $i!val!5, ite_t((k!36(X0) = $i!val!0), $i!val!2, $i!val!11))))))))))))))))))))))))). % 1.41/1.61 tff(formula6, axiom, % 1.41/1.61 k!36($i!val!2) = $i!val!2). % 1.41/1.61 tff(formula7, axiom, % 1.41/1.61 k!36($i!val!60) = $i!val!60). % 1.41/1.61 tff(formula8, axiom, % 1.41/1.61 k!36($i!val!30) = $i!val!30). % 1.41/1.61 tff(formula9, axiom, % 1.41/1.61 k!36($i!val!5) = $i!val!5). % 1.41/1.61 tff(formula10, axiom, % 1.41/1.61 k!36($i!val!4) = $i!val!4). % 1.41/1.61 tff(formula11, axiom, % 1.41/1.61 k!36($i!val!42) = $i!val!42). % 1.41/1.61 tff(formula12, axiom, % 1.41/1.61 k!36($i!val!12) = $i!val!12). % 1.41/1.61 tff(formula13, axiom, % 1.41/1.61 k!36($i!val!22) = $i!val!22). % 1.41/1.61 tff(formula14, axiom, % 1.41/1.61 k!36($i!val!6) = $i!val!6). % 1.41/1.61 tff(formula15, axiom, % 1.41/1.61 k!36($i!val!23) = $i!val!23). % 1.41/1.61 tff(formula16, axiom, % 1.41/1.61 k!36($i!val!11) = $i!val!11). % 1.41/1.61 tff(formula17, axiom, % 1.41/1.61 k!36($i!val!21) = $i!val!21). % 1.41/1.61 tff(formula18, axiom, % 1.41/1.61 k!36($i!val!40) = $i!val!40). % 1.41/1.61 tff(formula19, axiom, % 1.41/1.61 k!36($i!val!29) = $i!val!29). % 1.41/1.61 tff(formula20, axiom, % 1.41/1.61 k!36($i!val!36) = $i!val!36). % 1.41/1.61 tff(formula21, axiom, % 1.41/1.61 k!36($i!val!39) = $i!val!39). % 1.41/1.61 tff(formula22, axiom, % 1.41/1.61 k!36($i!val!10) = $i!val!10). % 1.41/1.61 tff(formula23, axiom, % 1.41/1.61 k!36($i!val!20) = $i!val!20). % 1.41/1.61 tff(formula24, axiom, % 1.41/1.61 k!36($i!val!3) = $i!val!3). % 1.41/1.61 tff(formula25, axiom, % 1.41/1.61 k!36($i!val!9) = $i!val!9). % 1.41/1.61 tff(formula26, axiom, % 1.41/1.61 k!36($i!val!1) = $i!val!1). % 1.41/1.61 tff(formula27, axiom, % 1.41/1.61 k!36($i!val!37) = $i!val!37). % 1.41/1.61 tff(formula28, axiom, % 1.41/1.61 k!36($i!val!33) = $i!val!33). % 1.41/1.61 tff(formula29, axiom, % 1.41/1.61 k!36($i!val!35) = $i!val!35). % 1.41/1.61 tff(formula30, axiom, % 1.41/1.61 k!36($i!val!32) = $i!val!32). % 1.41/1.61 tff(formula31, axiom, % 1.41/1.61 k!36($i!val!43) = $i!val!43). % 1.41/1.61 tff(formula32, axiom, % 1.41/1.61 k!36($i!val!15) = $i!val!15). % 1.41/1.61 tff(formula33, axiom, % 1.41/1.61 k!36($i!val!44) = $i!val!44). % 1.41/1.61 tff(formula34, axiom, % 1.41/1.61 k!36($i!val!0) = $i!val!0). % 1.41/1.61 tff(formula35, axiom, % 1.41/1.61 ![X0: $i] : ((~((($i!val!2 = X0)) | (($i!val!60 = X0)) | (($i!val!30 = X0)) | (($i!val!5 = X0)) | (($i!val!4 = X0)) | (($i!val!42 = X0)) | (($i!val!12 = X0)) | (($i!val!22 = X0)) | (($i!val!6 = X0)) | (($i!val!23 = X0)) | (($i!val!11 = X0)) | (($i!val!21 = X0)) | (($i!val!40 = X0)) | (($i!val!29 = X0)) | (($i!val!36 = X0)) | (($i!val!39 = X0)) | (($i!val!10 = X0)) | (($i!val!20 = X0)) | (($i!val!3 = X0)) | (($i!val!9 = X0)) | (($i!val!1 = X0)) | (($i!val!37 = X0)) | (($i!val!33 = X0)) | (($i!val!35 = X0)) | (($i!val!32 = X0)) | (($i!val!43 = X0)) | (($i!val!15 = X0)) | (($i!val!44 = X0)) | (($i!val!0 = X0)))) => (k!36(X0) = $i!val!7))). % 1.41/1.61 tff(formula36, axiom, % 1.41/1.61 compose($i!val!0, $i!val!1) = $i!val!4). % 1.41/1.61 tff(formula37, axiom, % 1.41/1.61 compose($i!val!3, $i!val!4) = $i!val!7). % 1.41/1.61 tff(formula38, axiom, % 1.41/1.61 compose($i!val!6, $i!val!4) = $i!val!7). % 1.41/1.61 tff(formula39, axiom, % 1.41/1.61 compose($i!val!2, $i!val!1) = $i!val!1). % 1.41/1.61 tff(formula40, axiom, % 1.41/1.61 compose($i!val!5, $i!val!4) = $i!val!4). % 1.41/1.61 tff(formula41, axiom, % 1.41/1.61 compose($i!val!3, $i!val!1) = $i!val!8). % 1.41/1.61 tff(formula42, axiom, % 1.41/1.61 compose($i!val!6, $i!val!1) = $i!val!9). % 1.41/1.61 tff(formula43, axiom, % 1.41/1.61 compose($i!val!0, $i!val!0) = $i!val!10). % 1.41/1.61 tff(formula44, axiom, % 1.41/1.61 compose($i!val!3, $i!val!0) = $i!val!22). % 1.41/1.61 tff(formula45, axiom, % 1.41/1.61 compose($i!val!6, $i!val!0) = $i!val!21). % 1.41/1.61 tff(formula46, axiom, % 1.41/1.61 compose($i!val!0, $i!val!2) = $i!val!0). % 1.41/1.61 tff(formula47, axiom, % 1.41/1.61 compose($i!val!3, $i!val!5) = $i!val!3). % 1.41/1.61 tff(formula48, axiom, % 1.41/1.61 compose($i!val!6, $i!val!5) = $i!val!6). % 1.41/1.61 tff(formula49, axiom, % 1.41/1.61 compose($i!val!5, $i!val!1) = $i!val!13). % 1.41/1.61 tff(formula50, axiom, % 1.41/1.61 compose($i!val!4, $i!val!1) = $i!val!14). % 1.41/1.61 tff(formula51, axiom, % 1.41/1.61 compose($i!val!1, $i!val!1) = $i!val!15). % 1.41/1.61 tff(formula52, axiom, % 1.41/1.61 compose($i!val!7, $i!val!1) = $i!val!16). % 1.41/1.61 tff(formula53, axiom, % 1.41/1.61 compose($i!val!2, $i!val!0) = $i!val!17). % 1.41/1.61 tff(formula54, axiom, % 1.41/1.61 compose($i!val!5, $i!val!0) = $i!val!0). % 1.41/1.61 tff(formula55, axiom, % 1.41/1.61 compose($i!val!4, $i!val!0) = $i!val!18). % 1.41/1.61 tff(formula56, axiom, % 1.41/1.61 compose($i!val!1, $i!val!0) = $i!val!19). % 1.41/1.61 tff(formula57, axiom, % 1.41/1.61 compose($i!val!7, $i!val!0) = $i!val!20). % 1.41/1.61 tff(formula58, axiom, % 1.41/1.61 compose($i!val!2, $i!val!2) = $i!val!2). % 1.41/1.61 tff(formula59, axiom, % 1.41/1.61 compose($i!val!5, $i!val!5) = $i!val!5). % 1.41/1.61 tff(formula60, axiom, % 1.41/1.61 compose($i!val!1, $i!val!11) = $i!val!1). % 1.41/1.61 tff(formula61, axiom, % 1.41/1.61 compose($i!val!4, $i!val!11) = $i!val!4). % 1.41/1.61 tff(formula62, axiom, % 1.41/1.61 compose($i!val!7, $i!val!11) = $i!val!7). % 1.41/1.61 tff(formula63, axiom, % 1.41/1.61 compose($i!val!12, $i!val!3) = $i!val!3). % 1.41/1.61 tff(formula64, axiom, % 1.41/1.61 compose($i!val!12, $i!val!7) = $i!val!7). % 1.41/1.61 tff(formula65, axiom, % 1.41/1.61 compose($i!val!12, $i!val!6) = $i!val!6). % 1.41/1.61 tff(formula66, axiom, % 1.41/1.61 compose($i!val!11, $i!val!11) = $i!val!11). % 1.41/1.61 tff(formula67, axiom, % 1.41/1.61 compose($i!val!12, $i!val!12) = $i!val!12). % 1.41/1.61 tff(formula68, axiom, % 1.41/1.61 compose($i!val!12, $i!val!21) = $i!val!21). % 1.41/1.61 tff(formula69, axiom, % 1.41/1.61 compose($i!val!12, $i!val!22) = $i!val!22). % 1.41/1.61 tff(formula70, axiom, % 1.41/1.61 compose($i!val!22, $i!val!1) = $i!val!7). % 1.41/1.61 tff(formula71, axiom, % 1.41/1.61 compose($i!val!22, $i!val!2) = $i!val!22). % 1.41/1.61 tff(formula72, axiom, % 1.41/1.61 compose($i!val!21, $i!val!2) = $i!val!21). % 1.41/1.61 tff(formula73, axiom, % 1.41/1.61 compose($i!val!21, $i!val!1) = $i!val!7). % 1.41/1.61 tff(formula74, axiom, % 1.41/1.61 compose($i!val!12, $i!val!1) = $i!val!23). % 1.41/1.61 tff(formula75, axiom, % 1.41/1.61 compose($i!val!12, $i!val!0) = $i!val!24). % 1.41/1.61 tff(formula76, axiom, % 1.41/1.61 compose($i!val!11, $i!val!1) = $i!val!25). % 1.41/1.61 tff(formula77, axiom, % 1.41/1.61 compose($i!val!11, $i!val!0) = $i!val!26). % 1.41/1.61 tff(formula78, axiom, % 1.41/1.61 compose($i!val!21, $i!val!0) = $i!val!27). % 1.41/1.61 tff(formula79, axiom, % 1.41/1.61 compose($i!val!22, $i!val!0) = $i!val!28). % 1.41/1.61 tff(formula80, axiom, % 1.41/1.61 compose($i!val!10, $i!val!1) = $i!val!31). % 1.41/1.61 tff(formula81, axiom, % 1.41/1.61 compose($i!val!9, $i!val!0) = $i!val!34). % 1.41/1.61 tff(formula82, axiom, % 1.41/1.61 compose($i!val!29, $i!val!0) = $i!val!35). % 1.41/1.61 tff(formula83, axiom, % 1.41/1.61 compose($i!val!15, $i!val!1) = $i!val!38). % 1.41/1.61 tff(formula84, axiom, % 1.41/1.61 compose($i!val!20, $i!val!0) = $i!val!41). % 1.41/1.61 tff(formula85, axiom, % 1.41/1.61 compose($i!val!30, $i!val!10) = $i!val!10). % 1.41/1.61 tff(formula86, axiom, % 1.41/1.61 compose($i!val!30, $i!val!1) = $i!val!45). % 1.41/1.61 tff(formula87, axiom, % 1.41/1.61 compose($i!val!30, $i!val!0) = $i!val!46). % 1.41/1.61 tff(formula88, axiom, % 1.41/1.61 compose($i!val!30, $i!val!30) = $i!val!30). % 1.41/1.61 tff(formula89, axiom, % 1.41/1.61 compose($i!val!10, $i!val!0) = $i!val!47). % 1.41/1.61 tff(formula90, axiom, % 1.41/1.61 compose($i!val!10, $i!val!32) = $i!val!10). % 1.41/1.61 tff(formula91, axiom, % 1.41/1.61 compose($i!val!32, $i!val!32) = $i!val!32). % 1.41/1.61 tff(formula92, axiom, % 1.41/1.61 compose($i!val!32, $i!val!1) = $i!val!48). % 1.41/1.61 tff(formula93, axiom, % 1.41/1.61 compose($i!val!32, $i!val!0) = $i!val!49). % 1.41/1.61 tff(formula94, axiom, % 1.41/1.61 compose($i!val!29, $i!val!23) = $i!val!23). % 1.41/1.61 tff(formula95, axiom, % 1.41/1.61 compose($i!val!29, $i!val!29) = $i!val!29). % 1.41/1.61 tff(formula96, axiom, % 1.41/1.61 compose($i!val!23, $i!val!1) = $i!val!50). % 1.41/1.61 tff(formula97, axiom, % 1.41/1.61 compose($i!val!23, $i!val!0) = $i!val!51). % 1.41/1.61 tff(formula98, axiom, % 1.41/1.61 compose($i!val!23, $i!val!44) = $i!val!23). % 1.41/1.61 tff(formula99, axiom, % 1.41/1.61 compose($i!val!44, $i!val!44) = $i!val!44). % 1.41/1.61 tff(formula100, axiom, % 1.41/1.61 compose($i!val!44, $i!val!1) = $i!val!52). % 1.41/1.61 tff(formula101, axiom, % 1.41/1.61 compose($i!val!44, $i!val!0) = $i!val!53). % 1.41/1.61 tff(formula102, axiom, % 1.41/1.61 compose($i!val!9, $i!val!33) = $i!val!9). % 1.41/1.61 tff(formula103, axiom, % 1.41/1.61 compose($i!val!33, $i!val!33) = $i!val!33). % 1.41/1.61 tff(formula104, axiom, % 1.41/1.61 compose($i!val!42, $i!val!9) = $i!val!9). % 1.41/1.61 tff(formula105, axiom, % 1.41/1.61 compose($i!val!42, $i!val!1) = $i!val!54). % 1.41/1.61 tff(formula106, axiom, % 1.41/1.61 compose($i!val!42, $i!val!42) = $i!val!42). % 1.41/1.61 tff(formula107, axiom, % 1.41/1.61 compose($i!val!37, $i!val!15) = $i!val!15). % 1.41/1.61 tff(formula108, axiom, % 1.41/1.61 compose($i!val!37, $i!val!1) = $i!val!55). % 1.41/1.61 tff(formula109, axiom, % 1.41/1.61 compose($i!val!37, $i!val!0) = $i!val!56). % 1.41/1.61 tff(formula110, axiom, % 1.41/1.61 compose($i!val!37, $i!val!37) = $i!val!37). % 1.41/1.61 tff(formula111, axiom, % 1.41/1.61 compose($i!val!15, $i!val!0) = $i!val!57). % 1.41/1.61 tff(formula112, axiom, % 1.41/1.61 compose($i!val!15, $i!val!39) = $i!val!15). % 1.41/1.61 tff(formula113, axiom, % 1.41/1.61 compose($i!val!39, $i!val!39) = $i!val!39). % 1.41/1.61 tff(formula114, axiom, % 1.41/1.61 compose($i!val!39, $i!val!1) = $i!val!58). % 1.41/1.61 tff(formula115, axiom, % 1.41/1.61 compose($i!val!39, $i!val!0) = $i!val!59). % 1.41/1.61 tff(formula116, axiom, % 1.41/1.61 compose($i!val!36, $i!val!35) = $i!val!35). % 1.41/1.61 tff(formula117, axiom, % 1.41/1.61 compose($i!val!36, $i!val!36) = $i!val!36). % 1.41/1.61 tff(formula118, axiom, % 1.41/1.61 compose($i!val!35, $i!val!1) = $i!val!61). % 1.41/1.61 tff(formula119, axiom, % 1.41/1.61 compose($i!val!35, $i!val!0) = $i!val!62). % 1.41/1.61 tff(formula120, axiom, % 1.41/1.61 compose($i!val!35, $i!val!60) = $i!val!35). % 1.41/1.61 tff(formula121, axiom, % 1.41/1.61 compose($i!val!60, $i!val!60) = $i!val!60). % 1.41/1.61 tff(formula122, axiom, % 1.41/1.61 compose($i!val!60, $i!val!1) = $i!val!63). % 1.41/1.61 tff(formula123, axiom, % 1.41/1.61 compose($i!val!60, $i!val!0) = $i!val!64). % 1.41/1.61 tff(formula124, axiom, % 1.41/1.61 compose($i!val!20, $i!val!40) = $i!val!20). % 1.41/1.61 tff(formula125, axiom, % 1.41/1.61 compose($i!val!40, $i!val!40) = $i!val!40). % 1.41/1.61 tff(formula126, axiom, % 1.41/1.61 compose($i!val!43, $i!val!20) = $i!val!20). % 1.41/1.61 tff(formula127, axiom, % 1.41/1.61 compose($i!val!43, $i!val!1) = $i!val!65). % 1.41/1.61 tff(formula128, axiom, % 1.41/1.61 compose($i!val!43, $i!val!0) = $i!val!66). % 1.41/1.61 tff(formula129, axiom, % 1.41/1.61 compose($i!val!43, $i!val!43) = $i!val!43). % 1.41/1.61 tff(formula130, axiom, % 1.41/1.61 ![X0: $i, X1: $i] : ((~((($i!val!0 = X0) & ($i!val!1 = X1)) | (($i!val!3 = X0) & ($i!val!4 = X1)) | (($i!val!6 = X0) & ($i!val!4 = X1)) | (($i!val!2 = X0) & ($i!val!1 = X1)) | (($i!val!5 = X0) & ($i!val!4 = X1)) | (($i!val!3 = X0) & ($i!val!1 = X1)) | (($i!val!6 = X0) & ($i!val!1 = X1)) | (($i!val!0 = X0) & ($i!val!0 = X1)) | (($i!val!3 = X0) & ($i!val!0 = X1)) | (($i!val!6 = X0) & ($i!val!0 = X1)) | (($i!val!0 = X0) & ($i!val!2 = X1)) | (($i!val!3 = X0) & ($i!val!5 = X1)) | (($i!val!6 = X0) & ($i!val!5 = X1)) | (($i!val!5 = X0) & ($i!val!1 = X1)) | (($i!val!4 = X0) & ($i!val!1 = X1)) | (($i!val!1 = X0) & ($i!val!1 = X1)) | (($i!val!7 = X0) & ($i!val!1 = X1)) | (($i!val!2 = X0) & ($i!val!0 = X1)) | (($i!val!5 = X0) & ($i!val!0 = X1)) | (($i!val!4 = X0) & ($i!val!0 = X1)) | (($i!val!1 = X0) & ($i!val!0 = X1)) | (($i!val!7 = X0) & ($i!val!0 = X1)) | (($i!val!2 = X0) & ($i!val!2 = X1)) | (($i!val!5 = X0) & ($i!val!5 = X1)) | (($i!val!1 = X0) & ($i!val!11 = X1)) | (($i!val!4 = X0) & ($i!val!11 = X1)) | (($i!val!7 = X0) & ($i!val!11 = X1)) | (($i!val!12 = X0) & ($i!val!3 = X1)) | (($i!val!12 = X0) & ($i!val!7 = X1)) | (($i!val!12 = X0) & ($i!val!6 = X1)) | (($i!val!11 = X0) & ($i!val!11 = X1)) | (($i!val!12 = X0) & ($i!val!12 = X1)) | (($i!val!12 = X0) & ($i!val!21 = X1)) | (($i!val!12 = X0) & ($i!val!22 = X1)) | (($i!val!22 = X0) & ($i!val!1 = X1)) | (($i!val!22 = X0) & ($i!val!2 = X1)) | (($i!val!21 = X0) & ($i!val!2 = X1)) | (($i!val!21 = X0) & ($i!val!1 = X1)) | (($i!val!12 = X0) & ($i!val!1 = X1)) | (($i!val!12 = X0) & ($i!val!0 = X1)) | (($i!val!11 = X0) & ($i!val!1 = X1)) | (($i!val!11 = X0) & ($i!val!0 = X1)) | (($i!val!21 = X0) & ($i!val!0 = X1)) | (($i!val!22 = X0) & ($i!val!0 = X1)) | (($i!val!10 = X0) & ($i!val!1 = X1)) | (($i!val!9 = X0) & ($i!val!0 = X1)) | (($i!val!29 = X0) & ($i!val!0 = X1)) | (($i!val!15 = X0) & ($i!val!1 = X1)) | (($i!val!20 = X0) & ($i!val!0 = X1)) | (($i!val!30 = X0) & ($i!val!10 = X1)) | (($i!val!30 = X0) & ($i!val!1 = X1)) | (($i!val!30 = X0) & ($i!val!0 = X1)) | (($i!val!30 = X0) & ($i!val!30 = X1)) | (($i!val!10 = X0) & ($i!val!0 = X1)) | (($i!val!10 = X0) & ($i!val!32 = X1)) | (($i!val!32 = X0) & ($i!val!32 = X1)) | (($i!val!32 = X0) & ($i!val!1 = X1)) | (($i!val!32 = X0) & ($i!val!0 = X1)) | (($i!val!29 = X0) & ($i!val!23 = X1)) | (($i!val!29 = X0) & ($i!val!29 = X1)) | (($i!val!23 = X0) & ($i!val!1 = X1)) | (($i!val!23 = X0) & ($i!val!0 = X1)) | (($i!val!23 = X0) & ($i!val!44 = X1)) | (($i!val!44 = X0) & ($i!val!44 = X1)) | (($i!val!44 = X0) & ($i!val!1 = X1)) | (($i!val!44 = X0) & ($i!val!0 = X1)) | (($i!val!9 = X0) & ($i!val!33 = X1)) | (($i!val!33 = X0) & ($i!val!33 = X1)) | (($i!val!42 = X0) & ($i!val!9 = X1)) | (($i!val!42 = X0) & ($i!val!1 = X1)) | (($i!val!42 = X0) & ($i!val!42 = X1)) | (($i!val!37 = X0) & ($i!val!15 = X1)) | (($i!val!37 = X0) & ($i!val!1 = X1)) | (($i!val!37 = X0) & ($i!val!0 = X1)) | (($i!val!37 = X0) & ($i!val!37 = X1)) | (($i!val!15 = X0) & ($i!val!0 = X1)) | (($i!val!15 = X0) & ($i!val!39 = X1)) | (($i!val!39 = X0) & ($i!val!39 = X1)) | (($i!val!39 = X0) & ($i!val!1 = X1)) | (($i!val!39 = X0) & ($i!val!0 = X1)) | (($i!val!36 = X0) & ($i!val!35 = X1)) | (($i!val!36 = X0) & ($i!val!36 = X1)) | (($i!val!35 = X0) & ($i!val!1 = X1)) | (($i!val!35 = X0) & ($i!val!0 = X1)) | (($i!val!35 = X0) & ($i!val!60 = X1)) | (($i!val!60 = X0) & ($i!val!60 = X1)) | (($i!val!60 = X0) & ($i!val!1 = X1)) | (($i!val!60 = X0) & ($i!val!0 = X1)) | (($i!val!20 = X0) & ($i!val!40 = X1)) | (($i!val!40 = X0) & ($i!val!40 = X1)) | (($i!val!43 = X0) & ($i!val!20 = X1)) | (($i!val!43 = X0) & ($i!val!1 = X1)) | (($i!val!43 = X0) & ($i!val!0 = X1)) | (($i!val!43 = X0) & ($i!val!43 = X1)))) => (compose(X0, X1) = ite_t((X0 = codomain(X1)), X1, X0)))). % 1.41/1.61 tff(formula131, axiom, % 1.41/1.61 ![X0: $i] : (domain(X0) = ite_t((k!36(X0) = $i!val!43), $i!val!43, ite_t((k!36(X0) = $i!val!40), $i!val!40, ite_t((k!36(X0) = $i!val!60), $i!val!60, ite_t((k!36(X0) = $i!val!36), $i!val!36, ite_t((k!36(X0) = $i!val!39), $i!val!39, ite_t((k!36(X0) = $i!val!37), $i!val!37, ite_t((k!36(X0) = $i!val!42), $i!val!42, ite_t((k!36(X0) = $i!val!33), $i!val!33, ite_t((k!36(X0) = $i!val!44), $i!val!44, ite_t((k!36(X0) = $i!val!29), $i!val!29, ite_t((k!36(X0) = $i!val!32), $i!val!32, ite_t((k!36(X0) = $i!val!30), $i!val!30, ite_t((k!36(X0) = $i!val!20), $i!val!43, ite_t((k!36(X0) = $i!val!9), $i!val!42, ite_t((k!36(X0) = $i!val!15), $i!val!37, ite_t((k!36(X0) = $i!val!35), $i!val!36, ite_t((k!36(X0) = $i!val!10), $i!val!30, ite_t((k!36(X0) = $i!val!23), $i!val!29, ite_t((k!36(X0) = $i!val!11), $i!val!11, ite_t((k!36(X0) = $i!val!5), $i!val!5, ite_t((k!36(X0) = $i!val!2), $i!val!2, ite_t(((k!36(X0) = $i!val!0) | (k!36(X0) = $i!val!4)), $i!val!5, ite_t((k!36(X0) = $i!val!1), $i!val!2, $i!val!12))))))))))))))))))))))))). % 1.41/1.61 % SZS output end Model % 1.41/1.61 % E exiting %------------------------------------------------------------------------------