%------------------------------------------------------------------------------ % File : Z3---4.15.1 % Problem : SYN522-1 : TPTP v9.0.0. Released v2.1.0. % 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 05:39:27 AM UTC 2025 % Result : Satisfiable 0.39s 0.55s % Output : Model 0.39s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SYN522-1 : TPTP v9.0.0. Released v2.1.0. % 0.07/0.12 % Command : run_E %s %d THM % 0.12/0.33 % Computer : n003.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 : Fri Jun 20 12:37:54 EDT 2025 % 0.12/0.34 % CPUTime : % 0.39/0.55 % SZS status Satisfiable % 0.39/0.55 % SZS output start Model % 0.39/0.55 tff(tptp_fun__i_val_1_type, type, ( % 0.39/0.55 tptp_fun__i_val_1: $i)). % 0.39/0.55 tff(a117_type, type, ( % 0.39/0.55 a117: $i)). % 0.39/0.55 tff(tptp_fun__i_val_6_type, type, ( % 0.39/0.55 tptp_fun__i_val_6: $i)). % 0.39/0.55 tff(a114_type, type, ( % 0.39/0.55 a114: $i)). % 0.39/0.55 tff(ssSkC4_type, type, ( % 0.39/0.55 ssSkC4: $o)). % 0.39/0.55 tff(tptp_fun__i_val_20_type, type, ( % 0.39/0.55 tptp_fun__i_val_20: $i)). % 0.39/0.55 tff(a140_type, type, ( % 0.39/0.55 a140: $i)). % 0.39/0.55 tff(tptp_fun__i_val_21_type, type, ( % 0.39/0.55 tptp_fun__i_val_21: $i)). % 0.39/0.55 tff(a111_type, type, ( % 0.39/0.55 a111: $i)). % 0.39/0.55 tff(c2_0_type, type, ( % 0.39/0.55 c2_0: $o)). % 0.39/0.55 tff(tptp_fun__i_val_4_type, type, ( % 0.39/0.55 tptp_fun__i_val_4: $i)). % 0.39/0.55 tff(a106_type, type, ( % 0.39/0.55 a106: $i)). % 0.39/0.55 tff(ssSkC3_type, type, ( % 0.39/0.55 ssSkC3: $o)). % 0.39/0.55 tff(tptp_fun__i_val_15_type, type, ( % 0.39/0.55 tptp_fun__i_val_15: $i)). % 0.39/0.55 tff(a131_type, type, ( % 0.39/0.55 a131: $i)). % 0.39/0.55 tff(tptp_fun__i_val_14_type, type, ( % 0.39/0.55 tptp_fun__i_val_14: $i)). % 0.39/0.55 tff(a104_type, type, ( % 0.39/0.55 a104: $i)). % 0.39/0.55 tff(ssSkC1_type, type, ( % 0.39/0.55 ssSkC1: $o)). % 0.39/0.55 tff(ssSkC5_type, type, ( % 0.39/0.55 ssSkC5: $o)). % 0.39/0.55 tff(ssSkC0_type, type, ( % 0.39/0.55 ssSkC0: $o)). % 0.39/0.55 tff(ndr1_0_type, type, ( % 0.39/0.55 ndr1_0: $o)). % 0.39/0.55 tff(c3_0_type, type, ( % 0.39/0.55 c3_0: $o)). % 0.39/0.55 tff(tptp_fun__i_val_3_type, type, ( % 0.39/0.55 tptp_fun__i_val_3: $i)). % 0.39/0.55 tff(a109_type, type, ( % 0.39/0.55 a109: $i)). % 0.39/0.55 tff(ssSkC7_type, type, ( % 0.39/0.55 ssSkC7: $o)). % 0.39/0.55 tff(tptp_fun__i_val_17_type, type, ( % 0.39/0.55 tptp_fun__i_val_17: $i)). % 0.39/0.55 tff(a110_type, type, ( % 0.39/0.55 a110: $i)). % 0.39/0.55 tff(a138_type, type, ( % 0.39/0.55 a138: $i)). % 0.39/0.55 tff(tptp_fun__i_val_2_type, type, ( % 0.39/0.55 tptp_fun__i_val_2: $i)). % 0.39/0.55 tff(a125_type, type, ( % 0.39/0.55 a125: $i)). % 0.39/0.55 tff(tptp_fun__i_val_18_type, type, ( % 0.39/0.55 tptp_fun__i_val_18: $i)). % 0.39/0.55 tff(a105_type, type, ( % 0.39/0.55 a105: $i)). % 0.39/0.55 tff(tptp_fun__i_val_16_type, type, ( % 0.39/0.55 tptp_fun__i_val_16: $i)). % 0.39/0.55 tff(a120_type, type, ( % 0.39/0.55 a120: $i)). % 0.39/0.55 tff(a115_type, type, ( % 0.39/0.55 a115: $i)). % 0.39/0.55 tff(tptp_fun__i_val_11_type, type, ( % 0.39/0.55 tptp_fun__i_val_11: $i)). % 0.39/0.55 tff(a133_type, type, ( % 0.39/0.55 a133: $i)). % 0.39/0.55 tff(ssSkC6_type, type, ( % 0.39/0.55 ssSkC6: $o)). % 0.39/0.55 tff(c1_0_type, type, ( % 0.39/0.55 c1_0: $o)). % 0.39/0.55 tff(tptp_fun__i_val_19_type, type, ( % 0.39/0.55 tptp_fun__i_val_19: $i)). % 0.39/0.55 tff(a132_type, type, ( % 0.39/0.55 a132: $i)). % 0.39/0.55 tff(tptp_fun__i_val_13_type, type, ( % 0.39/0.55 tptp_fun__i_val_13: $i)). % 0.39/0.55 tff(a119_type, type, ( % 0.39/0.55 a119: $i)). % 0.39/0.55 tff(tptp_fun__i_val_7_type, type, ( % 0.39/0.55 tptp_fun__i_val_7: $i)). % 0.39/0.55 tff(a108_type, type, ( % 0.39/0.55 a108: $i)). % 0.39/0.55 tff(tptp_fun__i_val_0_type, type, ( % 0.39/0.55 tptp_fun__i_val_0: $i)). % 0.39/0.55 tff(a118_type, type, ( % 0.39/0.55 a118: $i)). % 0.39/0.55 tff(a128_type, type, ( % 0.39/0.55 a128: $i)). % 0.39/0.55 tff(tptp_fun__i_val_12_type, type, ( % 0.39/0.55 tptp_fun__i_val_12: $i)). % 0.39/0.55 tff(a127_type, type, ( % 0.39/0.55 a127: $i)). % 0.39/0.55 tff(tptp_fun__i_val_5_type, type, ( % 0.39/0.55 tptp_fun__i_val_5: $i)). % 0.39/0.55 tff(a121_type, type, ( % 0.39/0.55 a121: $i)). % 0.39/0.55 tff(tptp_fun__i_val_8_type, type, ( % 0.39/0.55 tptp_fun__i_val_8: $i)). % 0.39/0.55 tff(a134_type, type, ( % 0.39/0.55 a134: $i)). % 0.39/0.55 tff(c5_0_type, type, ( % 0.39/0.55 c5_0: $o)). % 0.39/0.55 tff(a139_type, type, ( % 0.39/0.55 a139: $i)). % 0.39/0.55 tff(tptp_fun__i_val_10_type, type, ( % 0.39/0.55 tptp_fun__i_val_10: $i)). % 0.39/0.55 tff(a126_type, type, ( % 0.39/0.55 a126: $i)). % 0.39/0.55 tff(a116_type, type, ( % 0.39/0.55 a116: $i)). % 0.39/0.55 tff(ssSkC2_type, type, ( % 0.39/0.55 ssSkC2: $o)). % 0.39/0.55 tff(a130_type, type, ( % 0.39/0.55 a130: $i)). % 0.39/0.55 tff(c4_0_type, type, ( % 0.39/0.55 c4_0: $o)). % 0.39/0.55 tff(a112_type, type, ( % 0.39/0.55 a112: $i)). % 0.39/0.55 tff(tptp_fun__i_val_9_type, type, ( % 0.39/0.55 tptp_fun__i_val_9: $i)). % 0.39/0.55 tff(a129_type, type, ( % 0.39/0.55 a129: $i)). % 0.39/0.55 tff(k!456_type, type, ( % 0.39/0.55 k!456: $i > $i)). % 0.39/0.55 tff(ndr1_1_type, type, ( % 0.39/0.55 ndr1_1: $i > $o)). % 0.39/0.55 tff(k!457_type, type, ( % 0.39/0.55 k!457: $i > $i)). % 0.39/0.55 tff(c5_1_type, type, ( % 0.39/0.55 c5_1: $i > $o)). % 0.39/0.55 tff(ssSkP0_type, type, ( % 0.39/0.55 ssSkP0: $i > $o)). % 0.39/0.55 tff(c3_1_type, type, ( % 0.39/0.55 c3_1: $i > $o)). % 0.39/0.55 tff(c2_1_type, type, ( % 0.39/0.55 c2_1: $i > $o)). % 0.39/0.55 tff(c1_2_type, type, ( % 0.39/0.55 c1_2: ( $i * $i ) > $o)). % 0.39/0.55 tff(c4_1_type, type, ( % 0.39/0.55 c4_1: $i > $o)). % 0.39/0.55 tff(ssSkP1_type, type, ( % 0.39/0.55 ssSkP1: $i > $o)). % 0.39/0.55 tff(c1_1_type, type, ( % 0.39/0.55 c1_1: $i > $o)). % 0.39/0.55 tff(c3_2_type, type, ( % 0.39/0.55 c3_2: ( $i * $i ) > $o)). % 0.39/0.55 tff(ssSkP4_type, type, ( % 0.39/0.55 ssSkP4: $i > $o)). % 0.39/0.55 tff(c4_2_type, type, ( % 0.39/0.55 c4_2: ( $i * $i ) > $o)). % 0.39/0.55 tff(ssSkP2_type, type, ( % 0.39/0.55 ssSkP2: $i > $o)). % 0.39/0.55 tff(c5_2_type, type, ( % 0.39/0.55 c5_2: ( $i * $i ) > $o)). % 0.39/0.55 tff(c2_2_type, type, ( % 0.39/0.55 c2_2: ( $i * $i ) > $o)). % 0.39/0.55 tff(ssSkP3_type, type, ( % 0.39/0.55 ssSkP3: $i > $o)). % 0.39/0.55 tff(formula1, axiom, % 0.39/0.55 a117 = $i!val!1). % 0.39/0.55 tff(formula2, axiom, % 0.39/0.55 a114 = $i!val!6). % 0.39/0.55 tff(formula3, axiom, % 0.39/0.55 ssSkC4 <=> $false). % 0.39/0.55 tff(formula4, axiom, % 0.39/0.55 a140 = $i!val!20). % 0.39/0.55 tff(formula5, axiom, % 0.39/0.55 a111 = $i!val!21). % 0.39/0.55 tff(formula6, axiom, % 0.39/0.55 c2_0 <=> $false). % 0.39/0.55 tff(formula7, axiom, % 0.39/0.55 a106 = $i!val!4). % 0.39/0.55 tff(formula8, axiom, % 0.39/0.55 ssSkC3 <=> $false). % 0.39/0.55 tff(formula9, axiom, % 0.39/0.55 a131 = $i!val!15). % 0.39/0.55 tff(formula10, axiom, % 0.39/0.55 a104 = $i!val!14). % 0.39/0.55 tff(formula11, axiom, % 0.39/0.55 ssSkC1 <=> $true). % 0.39/0.55 tff(formula12, axiom, % 0.39/0.55 ssSkC5 <=> $false). % 0.39/0.55 tff(formula13, axiom, % 0.39/0.55 ssSkC0 <=> $false). % 0.39/0.55 tff(formula14, axiom, % 0.39/0.55 ndr1_0 <=> $true). % 0.39/0.55 tff(formula15, axiom, % 0.39/0.55 c3_0 <=> $false). % 0.39/0.55 tff(formula16, axiom, % 0.39/0.55 a109 = $i!val!3). % 0.39/0.55 tff(formula17, axiom, % 0.39/0.55 ssSkC7 <=> $true). % 0.39/0.55 tff(formula18, axiom, % 0.39/0.55 a110 = $i!val!17). % 0.39/0.55 tff(formula19, axiom, % 0.39/0.55 a138 = $i!val!1). % 0.39/0.55 tff(formula20, axiom, % 0.39/0.55 a125 = $i!val!2). % 0.39/0.55 tff(formula21, axiom, % 0.39/0.55 a105 = $i!val!18). % 0.39/0.55 tff(formula22, axiom, % 0.39/0.55 a120 = $i!val!16). % 0.39/0.55 tff(formula23, axiom, % 0.39/0.55 a115 = $i!val!1). % 0.39/0.55 tff(formula24, axiom, % 0.39/0.55 a133 = $i!val!11). % 0.39/0.55 tff(formula25, axiom, % 0.39/0.55 ssSkC6 <=> $false). % 0.39/0.55 tff(formula26, axiom, % 0.39/0.55 c1_0 <=> $false). % 0.39/0.55 tff(formula27, axiom, % 0.39/0.55 a132 = $i!val!19). % 0.39/0.55 tff(formula28, axiom, % 0.39/0.55 a119 = $i!val!13). % 0.39/0.55 tff(formula29, axiom, % 0.39/0.55 a108 = $i!val!7). % 0.39/0.55 tff(formula30, axiom, % 0.39/0.55 a118 = $i!val!0). % 0.39/0.55 tff(formula31, axiom, % 0.39/0.55 a128 = $i!val!1). % 0.39/0.55 tff(formula32, axiom, % 0.39/0.55 a127 = $i!val!12). % 0.39/0.55 tff(formula33, axiom, % 0.39/0.55 a121 = $i!val!5). % 0.39/0.55 tff(formula34, axiom, % 0.39/0.55 a134 = $i!val!8). % 0.39/0.55 tff(formula35, axiom, % 0.39/0.55 c5_0 <=> $true). % 0.39/0.55 tff(formula36, axiom, % 0.39/0.55 a139 = $i!val!19). % 0.39/0.55 tff(formula37, axiom, % 0.39/0.55 a126 = $i!val!10). % 0.39/0.55 tff(formula38, axiom, % 0.39/0.55 a116 = $i!val!1). % 0.39/0.55 tff(formula39, axiom, % 0.39/0.55 ssSkC2 <=> $true). % 0.39/0.55 tff(formula40, axiom, % 0.39/0.55 a130 = $i!val!10). % 0.39/0.55 tff(formula41, axiom, % 0.39/0.55 c4_0 <=> $true). % 0.39/0.55 tff(formula42, axiom, % 0.39/0.55 a112 = $i!val!15). % 0.39/0.55 tff(formula43, axiom, % 0.39/0.55 a129 = $i!val!9). % 0.39/0.55 tff(formula44, axiom, % 0.39/0.55 ![X0: $i] : (ndr1_1(X0) <=> ((~(k!456(X0) = $i!val!6)) & (~(k!456(X0) = $i!val!19))))). % 0.39/0.55 tff(formula45, axiom, % 0.39/0.55 k!457($i!val!18) = $i!val!18). % 0.39/0.55 tff(formula46, axiom, % 0.39/0.55 k!457($i!val!16) = $i!val!16). % 0.39/0.55 tff(formula47, axiom, % 0.39/0.55 k!457($i!val!20) = $i!val!20). % 0.39/0.55 tff(formula48, axiom, % 0.39/0.55 k!457($i!val!21) = $i!val!21). % 0.39/0.55 tff(formula49, axiom, % 0.39/0.55 k!457($i!val!10) = $i!val!10). % 0.39/0.55 tff(formula50, axiom, % 0.39/0.55 k!457($i!val!13) = $i!val!13). % 0.39/0.55 tff(formula51, axiom, % 0.39/0.55 k!457($i!val!15) = $i!val!15). % 0.39/0.55 tff(formula52, axiom, % 0.39/0.55 k!457($i!val!12) = $i!val!12). % 0.39/0.55 tff(formula53, axiom, % 0.39/0.55 k!457($i!val!14) = $i!val!14). % 0.39/0.55 tff(formula54, axiom, % 0.39/0.55 ![X0: $i] : ((~((($i!val!18 = X0)) | (($i!val!16 = X0)) | (($i!val!20 = X0)) | (($i!val!21 = X0)) | (($i!val!10 = X0)) | (($i!val!13 = X0)) | (($i!val!15 = X0)) | (($i!val!12 = X0)) | (($i!val!14 = X0)))) => (k!457(X0) = $i!val!9))). % 0.39/0.55 tff(formula55, axiom, % 0.39/0.55 ![X0: $i] : (c5_1(X0) <=> ((~(k!456(X0) = $i!val!8)) & (~(k!456(X0) = $i!val!11)) & (~(k!456(X0) = $i!val!4))))). % 0.39/0.55 tff(formula56, axiom, % 0.39/0.55 ![X0: $i] : (ssSkP0(X0) <=> ((~(k!456(X0) = $i!val!17)) & (~(k!456(X0) = $i!val!2)) & (~(k!456(X0) = $i!val!1)) & (~(k!456(X0) = $i!val!11)) & (~(k!456(X0) = $i!val!8))))). % 0.39/0.55 tff(formula57, axiom, % 0.39/0.55 ![X0: $i] : (c3_1(X0) <=> $true)). % 0.39/0.55 tff(formula58, axiom, % 0.39/0.55 ![X0: $i] : (c2_1(X0) <=> $false)). % 0.39/0.55 tff(formula59, axiom, % 0.39/0.55 ![X0: $i, X1: $i] : (c1_2(X0, X1) <=> ((k!456(X1) = $i!val!2) & (k!457(X0) = $i!val!10)))). % 0.39/0.55 tff(formula60, axiom, % 0.39/0.55 ![X0: $i] : (c4_1(X0) <=> ((k!456(X0) = $i!val!6) | (k!456(X0) = $i!val!19) | (k!456(X0) = $i!val!11)))). % 0.39/0.55 tff(formula61, axiom, % 0.39/0.55 ![X0: $i] : (ssSkP1(X0) <=> $true)). % 0.39/0.55 tff(formula62, axiom, % 0.39/0.55 c1_1($i!val!0) <=> $true). % 0.39/0.55 tff(formula63, axiom, % 0.39/0.55 ![X0: $i] : ((~(($i!val!0 = X0))) => (c1_1(X0) <=> $false))). % 0.39/0.55 tff(formula64, axiom, % 0.39/0.55 ![X0: $i, X1: $i] : (c3_2(X0, X1) <=> (((k!456(X1) = $i!val!2) & (k!457(X0) = $i!val!14)) | ((k!456(X1) = $i!val!8) & (k!457(X0) = $i!val!14)) | ((k!456(X1) = $i!val!1) & (k!457(X0) = $i!val!14)) | ((k!456(X1) = $i!val!11) & (k!457(X0) = $i!val!14)) | ((k!456(X1) = $i!val!17) & (k!457(X0) = $i!val!14))))). % 0.39/0.55 tff(formula65, axiom, % 0.39/0.55 ![X0: $i] : (ssSkP4(X0) <=> ((k!456(X0) = $i!val!5) | (k!456(X0) = $i!val!6) | (k!456(X0) = $i!val!19)))). % 0.39/0.55 tff(formula66, axiom, % 0.39/0.56 ![X0: $i, X1: $i] : (c4_2(X0, X1) <=> ((~((k!456(X1) = $i!val!0) & (k!457(X0) = $i!val!18))) & (~((k!456(X1) = $i!val!11) & (k!457(X0) = $i!val!15))) & (~((k!456(X1) = $i!val!8) & (k!457(X0) = $i!val!15))) & (~((k!456(X1) = $i!val!4) & (k!457(X0) = $i!val!15))) & (~((k!456(X1) = $i!val!2) & (k!457(X0) = $i!val!18))) & (~((k!456(X1) = $i!val!3) & (k!457(X0) = $i!val!15))) & (~((k!456(X1) = $i!val!1) & (k!457(X0) = $i!val!15))) & (~((k!456(X1) = $i!val!2) & (k!457(X0) = $i!val!15))) & (~((k!456(X1) = $i!val!0) & (k!457(X0) = $i!val!15))) & (~((k!456(X1) = $i!val!17) & (k!457(X0) = $i!val!15))) & (~((k!456(X1) = $i!val!7) & (k!457(X0) = $i!val!15))) & (~((k!456(X1) = $i!val!19) & (k!457(X0) = $i!val!20))) & (~((k!456(X1) = $i!val!2) & (k!457(X0) = $i!val!12)))))). % 0.39/0.56 tff(formula67, axiom, % 0.39/0.56 ![X0: $i] : (ssSkP2(X0) <=> $true)). % 0.39/0.56 tff(formula68, axiom, % 0.39/0.56 ![X0: $i, X1: $i] : (c5_2(X0, X1) <=> $false)). % 0.39/0.56 tff(formula69, axiom, % 0.39/0.56 k!456($i!val!11) = $i!val!11). % 0.39/0.56 tff(formula70, axiom, % 0.39/0.56 k!456($i!val!8) = $i!val!8). % 0.39/0.56 tff(formula71, axiom, % 0.39/0.56 k!456($i!val!6) = $i!val!6). % 0.39/0.56 tff(formula72, axiom, % 0.39/0.56 k!456($i!val!19) = $i!val!19). % 0.39/0.56 tff(formula73, axiom, % 0.39/0.56 k!456($i!val!4) = $i!val!4). % 0.39/0.56 tff(formula74, axiom, % 0.39/0.56 k!456($i!val!3) = $i!val!3). % 0.39/0.56 tff(formula75, axiom, % 0.39/0.56 k!456($i!val!17) = $i!val!17). % 0.39/0.56 tff(formula76, axiom, % 0.39/0.56 k!456($i!val!7) = $i!val!7). % 0.39/0.56 tff(formula77, axiom, % 0.39/0.56 k!456($i!val!0) = $i!val!0). % 0.39/0.56 tff(formula78, axiom, % 0.39/0.56 k!456($i!val!2) = $i!val!2). % 0.39/0.56 tff(formula79, axiom, % 0.39/0.56 k!456($i!val!1) = $i!val!1). % 0.39/0.56 tff(formula80, axiom, % 0.39/0.56 ![X0: $i] : ((~((($i!val!11 = X0)) | (($i!val!8 = X0)) | (($i!val!6 = X0)) | (($i!val!19 = X0)) | (($i!val!4 = X0)) | (($i!val!3 = X0)) | (($i!val!17 = X0)) | (($i!val!7 = X0)) | (($i!val!0 = X0)) | (($i!val!2 = X0)) | (($i!val!1 = X0)))) => (k!456(X0) = $i!val!5))). % 0.39/0.56 tff(formula81, axiom, % 0.39/0.56 ![X0: $i, X1: $i] : (c2_2(X0, X1) <=> ((k!456(X1) = $i!val!1) & (k!457(X0) = $i!val!9)))). % 0.39/0.56 tff(formula82, axiom, % 0.39/0.56 ![X0: $i] : (ssSkP3(X0) <=> ((k!456(X0) = $i!val!6) | (k!456(X0) = $i!val!19) | (k!456(X0) = $i!val!11)))). % 0.39/0.56 % SZS output end Model % 0.39/0.56 % E exiting %------------------------------------------------------------------------------