%------------------------------------------------------------------------------ % File : Z3---4.15.1 % Problem : KRS008-1 : TPTP v9.0.0. Released v2.0.0. % Transfm : none % Format : tptp % Command : run_E %s %d THM % Computer : n003.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 05:13:11 AM UTC 2025 % Result : Satisfiable 0.63s 0.82s % Output : Model 0.63s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.09/0.14 % Problem : KRS008-1 : TPTP v9.0.0. Released v2.0.0. % 0.09/0.14 % Command : run_E %s %d THM % 0.13/0.36 % Computer : n003.cluster.edu % 0.13/0.36 % Model : x86_64 x86_64 % 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.36 % Memory : 8042.1875MB % 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.36 % CPULimit : 300 % 0.13/0.36 % WCLimit : 300 % 0.13/0.36 % DateTime : Thu Jun 19 19:09:39 EDT 2025 % 0.13/0.36 % CPUTime : % 0.63/0.82 % SZS status Satisfiable % 0.63/0.82 % SZS output start Model % 0.63/0.82 tff(tptp_fun__i_val_0_type, type, ( % 0.63/0.82 tptp_fun__i_val_0: $i)). % 0.63/0.82 tff(exist_type, type, ( % 0.63/0.82 exist: $i)). % 0.63/0.82 tff(f_type, type, ( % 0.63/0.82 f: $i > $o)). % 0.63/0.82 tff(e_type, type, ( % 0.63/0.82 e: $i > $o)). % 0.63/0.82 tff(tptp_fun__i_val_5_type, type, ( % 0.63/0.82 tptp_fun__i_val_5: $i)). % 0.63/0.82 tff(k!753_type, type, ( % 0.63/0.82 k!753: $i > $i)). % 0.63/0.82 tff(tptp_fun__i_val_3_type, type, ( % 0.63/0.82 tptp_fun__i_val_3: $i)). % 0.63/0.82 tff(tptp_fun__i_val_8_type, type, ( % 0.63/0.82 tptp_fun__i_val_8: $i)). % 0.63/0.82 tff(tptp_fun__i_val_7_type, type, ( % 0.63/0.82 tptp_fun__i_val_7: $i)). % 0.63/0.82 tff(tptp_fun__i_val_10_type, type, ( % 0.63/0.82 tptp_fun__i_val_10: $i)). % 0.63/0.82 tff(tptp_fun__i_val_9_type, type, ( % 0.63/0.82 tptp_fun__i_val_9: $i)). % 0.63/0.82 tff(tptp_fun__i_val_11_type, type, ( % 0.63/0.82 tptp_fun__i_val_11: $i)). % 0.63/0.82 tff(tptp_fun__i_val_14_type, type, ( % 0.63/0.82 tptp_fun__i_val_14: $i)). % 0.63/0.82 tff(tptp_fun__i_val_13_type, type, ( % 0.63/0.82 tptp_fun__i_val_13: $i)). % 0.63/0.82 tff(tptp_fun__i_val_12_type, type, ( % 0.63/0.82 tptp_fun__i_val_12: $i)). % 0.63/0.82 tff(tptp_fun__i_val_26_type, type, ( % 0.63/0.82 tptp_fun__i_val_26: $i)). % 0.63/0.82 tff(tptp_fun__i_val_32_type, type, ( % 0.63/0.82 tptp_fun__i_val_32: $i)). % 0.63/0.82 tff(tptp_fun__i_val_17_type, type, ( % 0.63/0.82 tptp_fun__i_val_17: $i)). % 0.63/0.82 tff(tptp_fun__i_val_23_type, type, ( % 0.63/0.82 tptp_fun__i_val_23: $i)). % 0.63/0.82 tff(tptp_fun__i_val_18_type, type, ( % 0.63/0.82 tptp_fun__i_val_18: $i)). % 0.63/0.82 tff(tptp_fun__i_val_16_type, type, ( % 0.63/0.82 tptp_fun__i_val_16: $i)). % 0.63/0.82 tff(tptp_fun__i_val_20_type, type, ( % 0.63/0.82 tptp_fun__i_val_20: $i)). % 0.63/0.82 tff(tptp_fun__i_val_19_type, type, ( % 0.63/0.82 tptp_fun__i_val_19: $i)). % 0.63/0.82 tff(tptp_fun__i_val_15_type, type, ( % 0.63/0.82 tptp_fun__i_val_15: $i)). % 0.63/0.82 tff(tptp_fun__i_val_27_type, type, ( % 0.63/0.82 tptp_fun__i_val_27: $i)). % 0.63/0.82 tff(equalish_type, type, ( % 0.63/0.82 equalish: ( $i * $i ) > $o)). % 0.63/0.82 tff(tptp_fun__i_val_1_type, type, ( % 0.63/0.82 tptp_fun__i_val_1: $i)). % 0.63/0.82 tff(s1most_type, type, ( % 0.63/0.82 s1most: $i > $o)). % 0.63/0.82 tff(r2most_type, type, ( % 0.63/0.82 r2most: $i > $o)). % 0.63/0.82 tff(tptp_fun__i_val_25_type, type, ( % 0.63/0.82 tptp_fun__i_val_25: $i)). % 0.63/0.82 tff(tptp_fun__i_val_4_type, type, ( % 0.63/0.82 tptp_fun__i_val_4: $i)). % 0.63/0.82 tff(tptp_fun__i_val_33_type, type, ( % 0.63/0.82 tptp_fun__i_val_33: $i)). % 0.63/0.82 tff(tptp_fun__i_val_35_type, type, ( % 0.63/0.82 tptp_fun__i_val_35: $i)). % 0.63/0.82 tff(tptp_fun__i_val_36_type, type, ( % 0.63/0.82 tptp_fun__i_val_36: $i)). % 0.63/0.82 tff(tptp_fun__i_val_6_type, type, ( % 0.63/0.82 tptp_fun__i_val_6: $i)). % 0.63/0.82 tff(u1r1_type, type, ( % 0.63/0.82 u1r1: $i > $i)). % 0.63/0.82 tff(tptp_fun__i_val_22_type, type, ( % 0.63/0.82 tptp_fun__i_val_22: $i)). % 0.63/0.82 tff(tptp_fun__i_val_30_type, type, ( % 0.63/0.82 tptp_fun__i_val_30: $i)). % 0.63/0.82 tff(tptp_fun__i_val_31_type, type, ( % 0.63/0.82 tptp_fun__i_val_31: $i)). % 0.63/0.82 tff(tptp_fun__i_val_21_type, type, ( % 0.63/0.82 tptp_fun__i_val_21: $i)). % 0.63/0.82 tff(tptp_fun__i_val_29_type, type, ( % 0.63/0.82 tptp_fun__i_val_29: $i)). % 0.63/0.82 tff(tptp_fun__i_val_28_type, type, ( % 0.63/0.82 tptp_fun__i_val_28: $i)). % 0.63/0.82 tff(tptp_fun__i_val_24_type, type, ( % 0.63/0.82 tptp_fun__i_val_24: $i)). % 0.63/0.82 tff(tptp_fun__i_val_34_type, type, ( % 0.63/0.82 tptp_fun__i_val_34: $i)). % 0.63/0.82 tff(tptp_fun__i_val_2_type, type, ( % 0.63/0.82 tptp_fun__i_val_2: $i)). % 0.63/0.82 tff(d_type, type, ( % 0.63/0.82 d: $i > $o)). % 0.63/0.82 tff(u6r3_type, type, ( % 0.63/0.82 u6r3: $i > $i)). % 0.63/0.82 tff(u5r2_type, type, ( % 0.63/0.82 u5r2: $i > $i)). % 0.63/0.82 tff(u4r1_type, type, ( % 0.63/0.82 u4r1: $i > $i)). % 0.63/0.82 tff(r_type, type, ( % 0.63/0.82 r: ( $i * $i ) > $o)). % 0.63/0.82 tff(c_type, type, ( % 0.63/0.82 c: $i > $o)). % 0.63/0.82 tff(u4r2_type, type, ( % 0.63/0.82 u4r2: $i > $i)). % 0.63/0.82 tff(u6r2_type, type, ( % 0.63/0.82 u6r2: $i > $i)). % 0.63/0.82 tff(s2least_type, type, ( % 0.63/0.82 s2least: $i > $o)). % 0.63/0.82 tff(s_type, type, ( % 0.63/0.82 s: ( $i * $i ) > $o)). % 0.63/0.82 tff(u6r1_type, type, ( % 0.63/0.82 u6r1: $i > $i)). % 0.63/0.82 tff(u3r2_type, type, ( % 0.63/0.82 u3r2: $i > $i)). % 0.63/0.82 tff(u3r1_type, type, ( % 0.63/0.82 u3r1: $i > $i)). % 0.63/0.82 tff(u5r1_type, type, ( % 0.63/0.82 u5r1: $i > $i)). % 0.63/0.82 tff(u5r3_type, type, ( % 0.63/0.82 u5r3: $i > $i)). % 0.63/0.82 tff(u6r4_type, type, ( % 0.63/0.82 u6r4: $i > $i)). % 0.63/0.82 tff(u1r2_type, type, ( % 0.63/0.82 u1r2: $i > $i)). % 0.63/0.82 tff(formula1, axiom, % 0.63/0.82 exist = $i!val!0). % 0.63/0.82 tff(formula2, axiom, % 0.63/0.82 ![X0: $i] : (f(X0) <=> $false)). % 0.63/0.82 tff(formula3, axiom, % 0.63/0.82 ![X0: $i] : (e(X0) <=> $true)). % 0.63/0.82 tff(formula4, axiom, % 0.63/0.82 ![X0: $i, X1: $i] : (equalish(X0, X1) <=> ((~((k!753(X1) = $i!val!27) & (k!753(X0) = $i!val!15))) & (~((k!753(X1) = $i!val!19) & (k!753(X0) = $i!val!20))) & (~((k!753(X1) = $i!val!16) & (k!753(X0) = $i!val!18))) & (~((k!753(X1) = $i!val!23) & (k!753(X0) = $i!val!17))) & (~((k!753(X1) = $i!val!32) & (k!753(X0) = $i!val!26))) & (~((k!753(X1) = $i!val!12) & (k!753(X0) = $i!val!13))) & (~((k!753(X1) = $i!val!14) & (k!753(X0) = $i!val!11))) & (~((k!753(X1) = $i!val!9) & (k!753(X0) = $i!val!10))) & (~((k!753(X1) = $i!val!7) & (k!753(X0) = $i!val!8))) & (~((k!753(X1) = $i!val!3) & (k!753(X0) = $i!val!5)))))). % 0.63/0.82 tff(formula5, axiom, % 0.63/0.82 ![X0: $i] : (s1most(X0) <=> ((~(k!753(X0) = $i!val!14)) & (~(k!753(X0) = $i!val!8)) & (~(k!753(X0) = $i!val!9)) & (~(k!753(X0) = $i!val!1))))). % 0.63/0.82 tff(formula6, axiom, % 0.63/0.82 ![X0: $i] : (r2most(X0) <=> $true)). % 0.63/0.82 tff(formula7, axiom, % 0.63/0.82 ![X0: $i] : (u1r1(X0) = ite_t((k!753(X0) = $i!val!6), $i!val!36, ite_t((k!753(X0) = $i!val!5), $i!val!35, ite_t((k!753(X0) = $i!val!13), $i!val!33, ite_t((k!753(X0) = $i!val!4), $i!val!25, ite_t((k!753(X0) = $i!val!8), $i!val!20, ite_t((k!753(X0) = $i!val!14), $i!val!15, ite_t((k!753(X0) = $i!val!9), $i!val!11, $i!val!8))))))))). % 0.63/0.82 tff(formula8, axiom, % 0.63/0.82 k!753($i!val!22) = $i!val!22). % 0.63/0.82 tff(formula9, axiom, % 0.63/0.82 k!753($i!val!19) = $i!val!19). % 0.63/0.82 tff(formula10, axiom, % 0.63/0.82 k!753($i!val!10) = $i!val!10). % 0.63/0.82 tff(formula11, axiom, % 0.63/0.82 k!753($i!val!30) = $i!val!30). % 0.63/0.82 tff(formula12, axiom, % 0.63/0.82 k!753($i!val!8) = $i!val!8). % 0.63/0.82 tff(formula13, axiom, % 0.63/0.82 k!753($i!val!18) = $i!val!18). % 0.63/0.82 tff(formula14, axiom, % 0.63/0.82 k!753($i!val!31) = $i!val!31). % 0.63/0.82 tff(formula15, axiom, % 0.63/0.82 k!753($i!val!15) = $i!val!15). % 0.63/0.82 tff(formula16, axiom, % 0.63/0.82 k!753($i!val!21) = $i!val!21). % 0.63/0.82 tff(formula17, axiom, % 0.63/0.82 k!753($i!val!29) = $i!val!29). % 0.63/0.82 tff(formula18, axiom, % 0.63/0.82 k!753($i!val!33) = $i!val!33). % 0.63/0.82 tff(formula19, axiom, % 0.63/0.82 k!753($i!val!3) = $i!val!3). % 0.63/0.82 tff(formula20, axiom, % 0.63/0.82 k!753($i!val!12) = $i!val!12). % 0.63/0.82 tff(formula21, axiom, % 0.63/0.82 k!753($i!val!36) = $i!val!36). % 0.63/0.82 tff(formula22, axiom, % 0.63/0.82 k!753($i!val!5) = $i!val!5). % 0.63/0.82 tff(formula23, axiom, % 0.63/0.82 k!753($i!val!23) = $i!val!23). % 0.63/0.82 tff(formula24, axiom, % 0.63/0.82 k!753($i!val!7) = $i!val!7). % 0.63/0.82 tff(formula25, axiom, % 0.63/0.82 k!753($i!val!32) = $i!val!32). % 0.63/0.82 tff(formula26, axiom, % 0.63/0.82 k!753($i!val!27) = $i!val!27). % 0.63/0.82 tff(formula27, axiom, % 0.63/0.82 k!753($i!val!28) = $i!val!28). % 0.63/0.82 tff(formula28, axiom, % 0.63/0.82 k!753($i!val!13) = $i!val!13). % 0.63/0.82 tff(formula29, axiom, % 0.63/0.82 k!753($i!val!24) = $i!val!24). % 0.63/0.82 tff(formula30, axiom, % 0.63/0.82 k!753($i!val!11) = $i!val!11). % 0.63/0.82 tff(formula31, axiom, % 0.63/0.82 k!753($i!val!1) = $i!val!1). % 0.63/0.82 tff(formula32, axiom, % 0.63/0.82 k!753($i!val!26) = $i!val!26). % 0.63/0.82 tff(formula33, axiom, % 0.63/0.82 k!753($i!val!17) = $i!val!17). % 0.63/0.82 tff(formula34, axiom, % 0.63/0.82 k!753($i!val!34) = $i!val!34). % 0.63/0.82 tff(formula35, axiom, % 0.63/0.82 k!753($i!val!20) = $i!val!20). % 0.63/0.82 tff(formula36, axiom, % 0.63/0.82 k!753($i!val!25) = $i!val!25). % 0.63/0.82 tff(formula37, axiom, % 0.63/0.82 k!753($i!val!4) = $i!val!4). % 0.63/0.82 tff(formula38, axiom, % 0.63/0.82 k!753($i!val!2) = $i!val!2). % 0.63/0.82 tff(formula39, axiom, % 0.63/0.82 k!753($i!val!9) = $i!val!9). % 0.63/0.82 tff(formula40, axiom, % 0.63/0.82 k!753($i!val!35) = $i!val!35). % 0.63/0.82 tff(formula41, axiom, % 0.63/0.82 k!753($i!val!16) = $i!val!16). % 0.63/0.82 tff(formula42, axiom, % 0.63/0.82 k!753($i!val!6) = $i!val!6). % 0.63/0.82 tff(formula43, axiom, % 0.63/0.82 ![X0: $i] : ((~((($i!val!22 = X0)) | (($i!val!19 = X0)) | (($i!val!10 = X0)) | (($i!val!30 = X0)) | (($i!val!8 = X0)) | (($i!val!18 = X0)) | (($i!val!31 = X0)) | (($i!val!15 = X0)) | (($i!val!21 = X0)) | (($i!val!29 = X0)) | (($i!val!33 = X0)) | (($i!val!3 = X0)) | (($i!val!12 = X0)) | (($i!val!36 = X0)) | (($i!val!5 = X0)) | (($i!val!23 = X0)) | (($i!val!7 = X0)) | (($i!val!32 = X0)) | (($i!val!27 = X0)) | (($i!val!28 = X0)) | (($i!val!13 = X0)) | (($i!val!24 = X0)) | (($i!val!11 = X0)) | (($i!val!1 = X0)) | (($i!val!26 = X0)) | (($i!val!17 = X0)) | (($i!val!34 = X0)) | (($i!val!20 = X0)) | (($i!val!25 = X0)) | (($i!val!4 = X0)) | (($i!val!2 = X0)) | (($i!val!9 = X0)) | (($i!val!35 = X0)) | (($i!val!16 = X0)) | (($i!val!6 = X0)))) => (k!753(X0) = $i!val!14))). % 0.63/0.82 tff(formula44, axiom, % 0.63/0.82 ![X0: $i] : (d(X0) <=> ((~(k!753(X0) = $i!val!8)) & (~(k!753(X0) = $i!val!14)) & (~(k!753(X0) = $i!val!9)) & (~(k!753(X0) = $i!val!1))))). % 0.63/0.82 tff(formula45, axiom, % 0.63/0.82 ![X0: $i] : (u6r3(X0) = $i!val!5)). % 0.63/0.82 tff(formula46, axiom, % 0.63/0.82 ![X0: $i] : (u5r2(X0) = $i!val!13)). % 0.63/0.82 tff(formula47, axiom, % 0.63/0.82 ![X0: $i] : (u4r1(X0) = $i!val!1)). % 0.63/0.82 tff(formula48, axiom, % 0.63/0.82 ![X0: $i, X1: $i] : (r(X0, X1) <=> ((k!753(X0) = $i!val!1) | (k!753(X0) = $i!val!2) | (k!753(X0) = $i!val!3) | (k!753(X0) = $i!val!5)))). % 0.63/0.82 tff(formula49, axiom, % 0.63/0.82 ![X0: $i] : (c(X0) <=> ((k!753(X0) = $i!val!8) | (k!753(X0) = $i!val!14) | (k!753(X0) = $i!val!1) | (k!753(X0) = $i!val!9)))). % 0.63/0.82 tff(formula50, axiom, % 0.63/0.82 ![X0: $i] : (u4r2(X0) = $i!val!2)). % 0.63/0.82 tff(formula51, axiom, % 0.63/0.82 ![X0: $i] : (u6r2(X0) = $i!val!4)). % 0.63/0.82 tff(formula52, axiom, % 0.63/0.82 ![X0: $i] : (s2least(X0) <=> ((k!753(X0) = $i!val!8) | (k!753(X0) = $i!val!14) | (k!753(X0) = $i!val!1) | (k!753(X0) = $i!val!9)))). % 0.63/0.82 tff(formula53, axiom, % 0.63/0.82 ![X0: $i, X1: $i] : (s(X0, X1) <=> (((k!753(X1) = $i!val!1) & (k!753(X0) = $i!val!10)) | ((k!753(X1) = $i!val!1) & (k!753(X0) = $i!val!7)) | ((k!753(X1) = $i!val!1) & (k!753(X0) = $i!val!9)) | ((k!753(X1) = $i!val!9) & (k!753(X0) = $i!val!11)) | ((k!753(X1) = $i!val!9) & (k!753(X0) = $i!val!13)) | ((k!753(X1) = $i!val!14) & (k!753(X0) = $i!val!16)) | ((k!753(X1) = $i!val!9) & (k!753(X0) = $i!val!12)) | ((k!753(X1) = $i!val!14) & (k!753(X0) = $i!val!18)) | ((k!753(X1) = $i!val!8) & (k!753(X0) = $i!val!17)) | ((k!753(X1) = $i!val!9) & (k!753(X0) = $i!val!14)) | ((k!753(X1) = $i!val!8) & (k!753(X0) = $i!val!20)) | ((k!753(X1) = $i!val!14) & (k!753(X0) = $i!val!15)) | ((k!753(X1) = $i!val!8) & (k!753(X0) = $i!val!23)) | ((k!753(X1) = $i!val!8) & (k!753(X0) = $i!val!19)) | ((k!753(X1) = $i!val!14) & (k!753(X0) = $i!val!27)) | ((k!753(X1) = $i!val!1) & (k!753(X0) = $i!val!8))))). % 0.63/0.82 tff(formula54, axiom, % 0.63/0.82 ![X0: $i] : (u6r1(X0) = $i!val!6)). % 0.63/0.82 tff(formula55, axiom, % 0.63/0.82 ![X0: $i] : (u3r2(X0) = ite_t((k!753(X0) = $i!val!4), $i!val!32, ite_t((k!753(X0) = $i!val!5), $i!val!28, ite_t((k!753(X0) = $i!val!8), $i!val!23, ite_t((k!753(X0) = $i!val!13), $i!val!22, ite_t((k!753(X0) = $i!val!14), $i!val!16, ite_t((k!753(X0) = $i!val!9), $i!val!12, $i!val!9)))))))). % 0.63/0.82 tff(formula56, axiom, % 0.63/0.82 ![X0: $i] : (u3r1(X0) = ite_t((k!753(X0) = $i!val!6), $i!val!29, ite_t((k!753(X0) = $i!val!4), $i!val!26, ite_t((k!753(X0) = $i!val!13), $i!val!21, ite_t((k!753(X0) = $i!val!14), $i!val!18, ite_t((k!753(X0) = $i!val!8), $i!val!17, ite_t((k!753(X0) = $i!val!9), $i!val!13, $i!val!10)))))))). % 0.63/0.82 tff(formula57, axiom, % 0.63/0.82 ![X0: $i] : (u5r1(X0) = $i!val!29)). % 0.63/0.82 tff(formula58, axiom, % 0.63/0.82 ![X0: $i] : (u5r3(X0) = $i!val!30)). % 0.63/0.82 tff(formula59, axiom, % 0.63/0.82 ![X0: $i] : (u6r4(X0) = $i!val!3)). % 0.63/0.82 tff(formula60, axiom, % 0.63/0.82 ![X0: $i] : (u1r2(X0) = ite_t((k!753(X0) = $i!val!6), $i!val!34, ite_t((k!753(X0) = $i!val!5), $i!val!31, ite_t((k!753(X0) = $i!val!4), $i!val!30, ite_t((k!753(X0) = $i!val!14), $i!val!27, ite_t((k!753(X0) = $i!val!13), $i!val!24, ite_t((k!753(X0) = $i!val!8), $i!val!19, ite_t((k!753(X0) = $i!val!9), $i!val!14, $i!val!7))))))))). % 0.63/0.82 % SZS output end Model % 0.63/0.83 % E exiting %------------------------------------------------------------------------------