%------------------------------------------------------------------------------ % File : Z3---4.15.1 % Problem : KRS006-1 : TPTP v9.0.0. Released v2.0.0. % Transfm : none % Format : tptp % Command : run_E %s %d THM % Computer : n011.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 05:13:10 AM UTC 2025 % Result : Satisfiable 0.43s 0.62s % Output : Model 0.43s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : KRS006-1 : TPTP v9.0.0. Released v2.0.0. % 0.07/0.12 % Command : run_E %s %d THM % 0.12/0.33 % Computer : n011.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 19:09:57 EDT 2025 % 0.12/0.34 % CPUTime : % 0.43/0.62 % SZS status Satisfiable % 0.43/0.62 % SZS output start Model % 0.43/0.62 tff(tptp_fun__i_val_0_type, type, ( % 0.43/0.62 tptp_fun__i_val_0: $i)). % 0.43/0.62 tff(exist_type, type, ( % 0.43/0.62 exist: $i)). % 0.43/0.62 tff(e_type, type, ( % 0.43/0.62 e: $i > $o)). % 0.43/0.62 tff(tptp_fun__i_val_1_type, type, ( % 0.43/0.62 tptp_fun__i_val_1: $i)). % 0.43/0.62 tff(k!359_type, type, ( % 0.43/0.62 k!359: $i > $i)). % 0.43/0.62 tff(tptp_fun__i_val_3_type, type, ( % 0.43/0.62 tptp_fun__i_val_3: $i)). % 0.43/0.62 tff(tptp_fun__i_val_4_type, type, ( % 0.43/0.62 tptp_fun__i_val_4: $i)). % 0.43/0.62 tff(tptp_fun__i_val_5_type, type, ( % 0.43/0.62 tptp_fun__i_val_5: $i)). % 0.43/0.62 tff(tptp_fun__i_val_14_type, type, ( % 0.43/0.62 tptp_fun__i_val_14: $i)). % 0.43/0.62 tff(tptp_fun__i_val_9_type, type, ( % 0.43/0.62 tptp_fun__i_val_9: $i)). % 0.43/0.62 tff(s1most_type, type, ( % 0.43/0.62 s1most: $i > $o)). % 0.43/0.62 tff(tptp_fun__i_val_11_type, type, ( % 0.43/0.62 tptp_fun__i_val_11: $i)). % 0.43/0.62 tff(tptp_fun__i_val_12_type, type, ( % 0.43/0.62 tptp_fun__i_val_12: $i)). % 0.43/0.62 tff(tptp_fun__i_val_17_type, type, ( % 0.43/0.62 tptp_fun__i_val_17: $i)). % 0.43/0.62 tff(tptp_fun__i_val_19_type, type, ( % 0.43/0.62 tptp_fun__i_val_19: $i)). % 0.43/0.62 tff(tptp_fun__i_val_28_type, type, ( % 0.43/0.62 tptp_fun__i_val_28: $i)). % 0.43/0.62 tff(u1r1_type, type, ( % 0.43/0.62 u1r1: $i > $i)). % 0.43/0.62 tff(d_type, type, ( % 0.43/0.62 d: $i > $o)). % 0.43/0.62 tff(tptp_fun__i_val_29_type, type, ( % 0.43/0.62 tptp_fun__i_val_29: $i)). % 0.43/0.62 tff(u5r2_type, type, ( % 0.43/0.62 u5r2: $i > $i)). % 0.43/0.62 tff(u4r1_type, type, ( % 0.43/0.62 u4r1: $i > $i)). % 0.43/0.62 tff(tptp_fun__i_val_2_type, type, ( % 0.43/0.62 tptp_fun__i_val_2: $i)). % 0.43/0.62 tff(r_type, type, ( % 0.43/0.62 r: ( $i * $i ) > $o)). % 0.43/0.62 tff(c_type, type, ( % 0.43/0.62 c: $i > $o)). % 0.43/0.62 tff(u4r2_type, type, ( % 0.43/0.62 u4r2: $i > $i)). % 0.43/0.62 tff(tptp_fun__i_val_7_type, type, ( % 0.43/0.62 tptp_fun__i_val_7: $i)). % 0.43/0.62 tff(tptp_fun__i_val_10_type, type, ( % 0.43/0.62 tptp_fun__i_val_10: $i)). % 0.43/0.62 tff(tptp_fun__i_val_16_type, type, ( % 0.43/0.62 tptp_fun__i_val_16: $i)). % 0.43/0.62 tff(tptp_fun__i_val_23_type, type, ( % 0.43/0.62 tptp_fun__i_val_23: $i)). % 0.43/0.62 tff(tptp_fun__i_val_18_type, type, ( % 0.43/0.62 tptp_fun__i_val_18: $i)). % 0.43/0.62 tff(tptp_fun__i_val_24_type, type, ( % 0.43/0.62 tptp_fun__i_val_24: $i)). % 0.43/0.62 tff(tptp_fun__i_val_15_type, type, ( % 0.43/0.62 tptp_fun__i_val_15: $i)). % 0.43/0.62 tff(tptp_fun__i_val_25_type, type, ( % 0.43/0.62 tptp_fun__i_val_25: $i)). % 0.43/0.62 tff(tptp_fun__i_val_26_type, type, ( % 0.43/0.62 tptp_fun__i_val_26: $i)). % 0.43/0.62 tff(u3r2_type, type, ( % 0.43/0.62 u3r2: $i > $i)). % 0.43/0.62 tff(s2least_type, type, ( % 0.43/0.62 s2least: $i > $o)). % 0.43/0.62 tff(tptp_fun__i_val_27_type, type, ( % 0.43/0.62 tptp_fun__i_val_27: $i)). % 0.43/0.62 tff(tptp_fun__i_val_13_type, type, ( % 0.43/0.62 tptp_fun__i_val_13: $i)). % 0.43/0.62 tff(tptp_fun__i_val_8_type, type, ( % 0.43/0.62 tptp_fun__i_val_8: $i)). % 0.43/0.62 tff(tptp_fun__i_val_21_type, type, ( % 0.43/0.62 tptp_fun__i_val_21: $i)). % 0.43/0.62 tff(tptp_fun__i_val_22_type, type, ( % 0.43/0.62 tptp_fun__i_val_22: $i)). % 0.43/0.62 tff(tptp_fun__i_val_6_type, type, ( % 0.43/0.62 tptp_fun__i_val_6: $i)). % 0.43/0.62 tff(s_type, type, ( % 0.43/0.62 s: ( $i * $i ) > $o)). % 0.43/0.62 tff(tptp_fun__i_val_20_type, type, ( % 0.43/0.62 tptp_fun__i_val_20: $i)). % 0.43/0.62 tff(u3r1_type, type, ( % 0.43/0.62 u3r1: $i > $i)). % 0.43/0.62 tff(u5r1_type, type, ( % 0.43/0.62 u5r1: $i > $i)). % 0.43/0.62 tff(u1r2_type, type, ( % 0.43/0.62 u1r2: $i > $i)). % 0.43/0.62 tff(r1most_type, type, ( % 0.43/0.62 r1most: $i > $o)). % 0.43/0.62 tff(equalish_type, type, ( % 0.43/0.62 equalish: ( $i * $i ) > $o)). % 0.43/0.62 tff(formula1, axiom, % 0.43/0.62 exist = $i!val!0). % 0.43/0.62 tff(formula2, axiom, % 0.43/0.62 ![X0: $i] : (e(X0) <=> $true)). % 0.43/0.62 tff(formula3, axiom, % 0.43/0.62 ![X0: $i] : (s1most(X0) <=> ((~(k!359(X0) = $i!val!9)) & (~(k!359(X0) = $i!val!14)) & (~(k!359(X0) = $i!val!5)) & (~(k!359(X0) = $i!val!4)) & (~(k!359(X0) = $i!val!3)) & (~(k!359(X0) = $i!val!1))))). % 0.43/0.62 tff(formula4, axiom, % 0.43/0.62 ![X0: $i] : (u1r1(X0) = ite_t((k!359(X0) = $i!val!9), $i!val!28, ite_t((k!359(X0) = $i!val!14), $i!val!19, ite_t((k!359(X0) = $i!val!4), $i!val!17, ite_t((k!359(X0) = $i!val!5), $i!val!12, ite_t((k!359(X0) = $i!val!3), $i!val!11, $i!val!4))))))). % 0.43/0.62 tff(formula5, axiom, % 0.43/0.62 ![X0: $i] : (d(X0) <=> ((~(k!359(X0) = $i!val!14)) & (~(k!359(X0) = $i!val!3)) & (~(k!359(X0) = $i!val!4)) & (~(k!359(X0) = $i!val!5)) & (~(k!359(X0) = $i!val!9)) & (~(k!359(X0) = $i!val!1))))). % 0.43/0.62 tff(formula6, axiom, % 0.43/0.62 ![X0: $i] : (u5r2(X0) = $i!val!29)). % 0.43/0.62 tff(formula7, axiom, % 0.43/0.62 ![X0: $i] : (u4r1(X0) = $i!val!1)). % 0.43/0.62 tff(formula8, axiom, % 0.43/0.62 ![X0: $i, X1: $i] : (r(X0, X1) <=> ((k!359(X0) = $i!val!1) | (k!359(X0) = $i!val!2)))). % 0.43/0.62 tff(formula9, axiom, % 0.43/0.62 ![X0: $i] : (c(X0) <=> ((k!359(X0) = $i!val!3) | (k!359(X0) = $i!val!1) | (k!359(X0) = $i!val!4) | (k!359(X0) = $i!val!5) | (k!359(X0) = $i!val!14) | (k!359(X0) = $i!val!9)))). % 0.43/0.62 tff(formula10, axiom, % 0.43/0.62 ![X0: $i] : (u4r2(X0) = $i!val!2)). % 0.43/0.62 tff(formula11, axiom, % 0.43/0.62 ![X0: $i] : (u3r2(X0) = ite_t((k!359(X0) = $i!val!9), $i!val!26, ite_t((k!359(X0) = $i!val!14), $i!val!25, ite_t((k!359(X0) = $i!val!15), $i!val!24, ite_t((k!359(X0) = $i!val!18), $i!val!23, ite_t((k!359(X0) = $i!val!5), $i!val!16, ite_t((k!359(X0) = $i!val!3), $i!val!10, ite_t((k!359(X0) = $i!val!4), $i!val!7, $i!val!5))))))))). % 0.43/0.62 tff(formula12, axiom, % 0.43/0.62 ![X0: $i] : (s2least(X0) <=> ((k!359(X0) = $i!val!3) | (k!359(X0) = $i!val!1) | (k!359(X0) = $i!val!4) | (k!359(X0) = $i!val!5) | (k!359(X0) = $i!val!14) | (k!359(X0) = $i!val!9)))). % 0.43/0.62 tff(formula13, axiom, % 0.43/0.62 ![X0: $i, X1: $i] : (s(X0, X1) <=> (((k!359(X1) = $i!val!5) & (k!359(X0) = $i!val!12)) | ((k!359(X1) = $i!val!1) & (k!359(X0) = $i!val!6)) | ((k!359(X1) = $i!val!1) & (k!359(X0) = $i!val!4)) | ((k!359(X1) = $i!val!14) & (k!359(X0) = $i!val!22)) | ((k!359(X1) = $i!val!9) & (k!359(X0) = $i!val!21)) | ((k!359(X1) = $i!val!3) & (k!359(X0) = $i!val!15)) | ((k!359(X1) = $i!val!5) & (k!359(X0) = $i!val!18)) | ((k!359(X1) = $i!val!5) & (k!359(X0) = $i!val!14)) | ((k!359(X1) = $i!val!4) & (k!359(X0) = $i!val!8)) | ((k!359(X1) = $i!val!3) & (k!359(X0) = $i!val!11)) | ((k!359(X1) = $i!val!4) & (k!359(X0) = $i!val!13)) | ((k!359(X1) = $i!val!14) & (k!359(X0) = $i!val!25)) | ((k!359(X1) = $i!val!14) & (k!359(X0) = $i!val!19)) | ((k!359(X1) = $i!val!3) & (k!359(X0) = $i!val!10)) | ((k!359(X1) = $i!val!3) & (k!359(X0) = $i!val!9)) | ((k!359(X1) = $i!val!1) & (k!359(X0) = $i!val!5)) | ((k!359(X1) = $i!val!1) & (k!359(X0) = $i!val!3)) | ((k!359(X1) = $i!val!9) & (k!359(X0) = $i!val!26)) | ((k!359(X1) = $i!val!5) & (k!359(X0) = $i!val!16)) | ((k!359(X1) = $i!val!9) & (k!359(X0) = $i!val!28)) | ((k!359(X1) = $i!val!4) & (k!359(X0) = $i!val!7)) | ((k!359(X1) = $i!val!9) & (k!359(X0) = $i!val!27)) | ((k!359(X1) = $i!val!4) & (k!359(X0) = $i!val!17)) | ((k!359(X1) = $i!val!14) & (k!359(X0) = $i!val!29))))). % 0.43/0.62 tff(formula14, axiom, % 0.43/0.62 k!359($i!val!18) = $i!val!18). % 0.43/0.62 tff(formula15, axiom, % 0.43/0.62 k!359($i!val!25) = $i!val!25). % 0.43/0.62 tff(formula16, axiom, % 0.43/0.62 k!359($i!val!13) = $i!val!13). % 0.43/0.62 tff(formula17, axiom, % 0.43/0.62 k!359($i!val!6) = $i!val!6). % 0.43/0.62 tff(formula18, axiom, % 0.43/0.62 k!359($i!val!15) = $i!val!15). % 0.43/0.62 tff(formula19, axiom, % 0.43/0.62 k!359($i!val!4) = $i!val!4). % 0.43/0.62 tff(formula20, axiom, % 0.43/0.62 k!359($i!val!21) = $i!val!21). % 0.43/0.62 tff(formula21, axiom, % 0.43/0.62 k!359($i!val!22) = $i!val!22). % 0.43/0.62 tff(formula22, axiom, % 0.43/0.62 k!359($i!val!19) = $i!val!19). % 0.43/0.62 tff(formula23, axiom, % 0.43/0.62 k!359($i!val!16) = $i!val!16). % 0.43/0.62 tff(formula24, axiom, % 0.43/0.62 k!359($i!val!7) = $i!val!7). % 0.43/0.62 tff(formula25, axiom, % 0.43/0.62 k!359($i!val!3) = $i!val!3). % 0.43/0.62 tff(formula26, axiom, % 0.43/0.62 k!359($i!val!10) = $i!val!10). % 0.43/0.62 tff(formula27, axiom, % 0.43/0.62 k!359($i!val!24) = $i!val!24). % 0.43/0.62 tff(formula28, axiom, % 0.43/0.62 k!359($i!val!20) = $i!val!20). % 0.43/0.62 tff(formula29, axiom, % 0.43/0.62 k!359($i!val!14) = $i!val!14). % 0.43/0.62 tff(formula30, axiom, % 0.43/0.62 k!359($i!val!26) = $i!val!26). % 0.43/0.62 tff(formula31, axiom, % 0.43/0.62 k!359($i!val!29) = $i!val!29). % 0.43/0.62 tff(formula32, axiom, % 0.43/0.62 k!359($i!val!8) = $i!val!8). % 0.43/0.62 tff(formula33, axiom, % 0.43/0.62 k!359($i!val!1) = $i!val!1). % 0.43/0.62 tff(formula34, axiom, % 0.43/0.62 k!359($i!val!12) = $i!val!12). % 0.43/0.62 tff(formula35, axiom, % 0.43/0.62 k!359($i!val!17) = $i!val!17). % 0.43/0.62 tff(formula36, axiom, % 0.43/0.62 k!359($i!val!9) = $i!val!9). % 0.43/0.62 tff(formula37, axiom, % 0.43/0.62 k!359($i!val!2) = $i!val!2). % 0.43/0.62 tff(formula38, axiom, % 0.43/0.62 k!359($i!val!11) = $i!val!11). % 0.43/0.62 tff(formula39, axiom, % 0.43/0.62 k!359($i!val!5) = $i!val!5). % 0.43/0.62 tff(formula40, axiom, % 0.43/0.62 k!359($i!val!27) = $i!val!27). % 0.43/0.62 tff(formula41, axiom, % 0.43/0.62 k!359($i!val!23) = $i!val!23). % 0.43/0.62 tff(formula42, axiom, % 0.43/0.62 ![X0: $i] : ((~((($i!val!18 = X0)) | (($i!val!25 = X0)) | (($i!val!13 = X0)) | (($i!val!6 = X0)) | (($i!val!15 = X0)) | (($i!val!4 = X0)) | (($i!val!21 = X0)) | (($i!val!22 = X0)) | (($i!val!19 = X0)) | (($i!val!16 = X0)) | (($i!val!7 = X0)) | (($i!val!3 = X0)) | (($i!val!10 = X0)) | (($i!val!24 = X0)) | (($i!val!20 = X0)) | (($i!val!14 = X0)) | (($i!val!26 = X0)) | (($i!val!29 = X0)) | (($i!val!8 = X0)) | (($i!val!1 = X0)) | (($i!val!12 = X0)) | (($i!val!17 = X0)) | (($i!val!9 = X0)) | (($i!val!2 = X0)) | (($i!val!11 = X0)) | (($i!val!5 = X0)) | (($i!val!27 = X0)) | (($i!val!23 = X0)))) => (k!359(X0) = $i!val!28))). % 0.43/0.62 tff(formula43, axiom, % 0.43/0.62 ![X0: $i] : (u3r1(X0) = ite_t((k!359(X0) = $i!val!9), $i!val!27, ite_t((k!359(X0) = $i!val!14), $i!val!22, ite_t((k!359(X0) = $i!val!5), $i!val!14, ite_t((k!359(X0) = $i!val!3), $i!val!9, ite_t((k!359(X0) = $i!val!4), $i!val!8, $i!val!6))))))). % 0.43/0.62 tff(formula44, axiom, % 0.43/0.62 ![X0: $i] : (u5r1(X0) = $i!val!27)). % 0.43/0.62 tff(formula45, axiom, % 0.43/0.62 ![X0: $i] : (u1r2(X0) = ite_t((k!359(X0) = $i!val!14), $i!val!29, ite_t((k!359(X0) = $i!val!9), $i!val!21, ite_t((k!359(X0) = $i!val!18), $i!val!20, ite_t((k!359(X0) = $i!val!5), $i!val!18, ite_t((k!359(X0) = $i!val!3), $i!val!15, ite_t((k!359(X0) = $i!val!4), $i!val!13, $i!val!3)))))))). % 0.43/0.62 tff(formula46, axiom, % 0.43/0.62 ![X0: $i] : (r1most(X0) <=> $true)). % 0.43/0.62 tff(formula47, axiom, % 0.43/0.62 ![X0: $i, X1: $i] : (equalish(X0, X1) <=> (((k!359(X1) = $i!val!1) & (k!359(X0) = $i!val!2)) | ((k!359(X1) = $i!val!2) & (k!359(X0) = $i!val!1)) | ((k!359(X1) = $i!val!2) & (k!359(X0) = $i!val!2)) | ((k!359(X1) = $i!val!1) & (k!359(X0) = $i!val!1))))). % 0.43/0.62 % SZS output end Model % 0.43/0.62 % E exiting %------------------------------------------------------------------------------