%------------------------------------------------------------------------------ % File : Z3---4.15.1 % Problem : GRP126-3.005 : TPTP v9.0.0. Released v1.2.0. % Transfm : none % Format : tptp % Command : run_E %s %d THM % Computer : n009.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 05:07:07 AM UTC 2025 % Result : Satisfiable 0.48s 0.66s % Output : Model 0.48s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : GRP126-3.005 : TPTP v9.0.0. Released v1.2.0. % 0.07/0.12 % Command : run_E %s %d THM % 0.12/0.33 % Computer : n009.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 15:42:48 EDT 2025 % 0.12/0.33 % CPUTime : % 0.48/0.66 % SZS status Satisfiable % 0.48/0.66 % SZS output start Model % 0.48/0.66 tff(tptp_fun__i_val_2_type, type, ( % 0.48/0.66 tptp_fun__i_val_2: $i)). % 0.48/0.66 tff(e_2_type, type, ( % 0.48/0.66 e_2: $i)). % 0.48/0.66 tff(tptp_fun__i_val_4_type, type, ( % 0.48/0.66 tptp_fun__i_val_4: $i)). % 0.48/0.66 tff(e_4_type, type, ( % 0.48/0.66 e_4: $i)). % 0.48/0.66 tff(tptp_fun__i_val_3_type, type, ( % 0.48/0.66 tptp_fun__i_val_3: $i)). % 0.48/0.66 tff(e_3_type, type, ( % 0.48/0.66 e_3: $i)). % 0.48/0.66 tff(tptp_fun__i_val_0_type, type, ( % 0.48/0.66 tptp_fun__i_val_0: $i)). % 0.48/0.66 tff(e_0_type, type, ( % 0.48/0.66 e_0: $i)). % 0.48/0.66 tff(tptp_fun__i_val_1_type, type, ( % 0.48/0.66 tptp_fun__i_val_1: $i)). % 0.48/0.66 tff(e_1_type, type, ( % 0.48/0.66 e_1: $i)). % 0.48/0.66 tff(tptp_fun__i_val_5_type, type, ( % 0.48/0.66 tptp_fun__i_val_5: $i)). % 0.48/0.66 tff(e_5_type, type, ( % 0.48/0.66 e_5: $i)). % 0.48/0.66 tff(product_type, type, ( % 0.48/0.66 product: ( $i * $i * $i ) > $o)). % 0.48/0.66 tff(next_type, type, ( % 0.48/0.66 next: ( $i * $i ) > $o)). % 0.48/0.66 tff(greater_type, type, ( % 0.48/0.66 greater: ( $i * $i ) > $o)). % 0.48/0.66 tff(equalish_type, type, ( % 0.48/0.66 equalish: ( $i * $i ) > $o)). % 0.48/0.66 tff(group_element_type, type, ( % 0.48/0.66 group_element: $i > $o)). % 0.48/0.66 tff(cycle_type, type, ( % 0.48/0.66 cycle: ( $i * $i ) > $o)). % 0.48/0.66 tff(formula1, axiom, % 0.48/0.66 e_2 = $i!val!2). % 0.48/0.66 tff(formula2, axiom, % 0.48/0.66 e_4 = $i!val!4). % 0.48/0.66 tff(formula3, axiom, % 0.48/0.66 e_3 = $i!val!3). % 0.48/0.66 tff(formula4, axiom, % 0.48/0.66 e_0 = $i!val!0). % 0.48/0.66 tff(formula5, axiom, % 0.48/0.66 e_1 = $i!val!1). % 0.48/0.66 tff(formula6, axiom, % 0.48/0.66 e_5 = $i!val!5). % 0.48/0.66 tff(formula7, axiom, % 0.48/0.66 ![X0: $i, X1: $i, X2: $i] : (product(X0, X1, X2) <=> (((X2 = $i!val!5) & (~(X2 = $i!val!0)) & (X1 = $i!val!4) & (~(X1 = $i!val!3)) & (~(X1 = $i!val!1)) & (~(X1 = $i!val!5)) & (~(X1 = $i!val!0)) & (~(X0 = $i!val!4)) & (~(X0 = $i!val!3)) & (~(X0 = $i!val!1)) & (~(X0 = $i!val!5)) & (~(X0 = $i!val!0))) | ((X2 = $i!val!1) & (~(X2 = $i!val!5)) & (~(X2 = $i!val!0)) & (~(X1 = $i!val!4)) & (~(X1 = $i!val!3)) & (~(X1 = $i!val!1)) & (~(X1 = $i!val!5)) & (~(X1 = $i!val!0)) & (X0 = $i!val!4) & (~(X0 = $i!val!3)) & (~(X0 = $i!val!1)) & (~(X0 = $i!val!5)) & (~(X0 = $i!val!0))) | ((X2 = $i!val!1) & (~(X2 = $i!val!5)) & (~(X2 = $i!val!0)) & (X1 = $i!val!5) & (~(X1 = $i!val!0)) & (~(X0 = $i!val!4)) & (~(X0 = $i!val!3)) & (~(X0 = $i!val!1)) & (~(X0 = $i!val!5)) & (~(X0 = $i!val!0))) | ((X2 = $i!val!4) & (~(X2 = $i!val!3)) & (~(X2 = $i!val!1)) & (~(X2 = $i!val!5)) & (~(X2 = $i!val!0)) & (X1 = $i!val!3) & (~(X1 = $i!val!1)) & (~(X1 = $i!val!5)) & (~(X1 = $i!val!0)) & (~(X0 = $i!val!4)) & (~(X0 = $i!val!3)) & (~(X0 = $i!val!1)) & (~(X0 = $i!val!5)) & (~(X0 = $i!val!0))) | ((X2 = $i!val!5) & (~(X2 = $i!val!0)) & (X1 = $i!val!3) & (~(X1 = $i!val!1)) & (~(X1 = $i!val!5)) & (~(X1 = $i!val!0)) & (X0 = $i!val!1) & (~(X0 = $i!val!5)) & (~(X0 = $i!val!0))) | ((~(X2 = $i!val!4)) & (~(X2 = $i!val!3)) & (~(X2 = $i!val!1)) & (~(X2 = $i!val!5)) & (~(X2 = $i!val!0)) & (X1 = $i!val!4) & (~(X1 = $i!val!3)) & (~(X1 = $i!val!1)) & (~(X1 = $i!val!5)) & (~(X1 = $i!val!0)) & (X0 = $i!val!5) & (~(X0 = $i!val!0))) | ((X2 = $i!val!1) & (~(X2 = $i!val!5)) & (~(X2 = $i!val!0)) & (X1 = $i!val!4) & (~(X1 = $i!val!3)) & (~(X1 = $i!val!1)) & (~(X1 = $i!val!5)) & (~(X1 = $i!val!0)) & (X0 = $i!val!3) & (~(X0 = $i!val!1)) & (~(X0 = $i!val!5)) & (~(X0 = $i!val!0))) | ((X2 = $i!val!4) & (~(X2 = $i!val!3)) & (~(X2 = $i!val!1)) & (~(X2 = $i!val!5)) & (~(X2 = $i!val!0)) & (X1 = $i!val!5) & (~(X1 = $i!val!0)) & (X0 = $i!val!3) & (~(X0 = $i!val!1)) & (~(X0 = $i!val!5)) & (~(X0 = $i!val!0))) | ((X2 = $i!val!3) & (~(X2 = $i!val!1)) & (~(X2 = $i!val!5)) & (~(X2 = $i!val!0)) & (X1 = $i!val!4) & (~(X1 = $i!val!3)) & (~(X1 = $i!val!1)) & (~(X1 = $i!val!5)) & (~(X1 = $i!val!0)) & (X0 = $i!val!1) & (~(X0 = $i!val!5)) & (~(X0 = $i!val!0))) | ((~(X2 = $i!val!4)) & (~(X2 = $i!val!3)) & (~(X2 = $i!val!1)) & (~(X2 = $i!val!5)) & (~(X2 = $i!val!0)) & (X1 = $i!val!3) & (~(X1 = $i!val!1)) & (~(X1 = $i!val!5)) & (~(X1 = $i!val!0)) & (X0 = $i!val!4) & (~(X0 = $i!val!3)) & (~(X0 = $i!val!1)) & (~(X0 = $i!val!5)) & (~(X0 = $i!val!0))) | ((X2 = $i!val!3) & (~(X2 = $i!val!1)) & (~(X2 = $i!val!5)) & (~(X2 = $i!val!0)) & (~(X1 = $i!val!4)) & (~(X1 = $i!val!3)) & (~(X1 = $i!val!1)) & (~(X1 = $i!val!5)) & (~(X1 = $i!val!0)) & (X0 = $i!val!5) & (~(X0 = $i!val!0))) | ((X2 = $i!val!3) & (~(X2 = $i!val!1)) & (~(X2 = $i!val!5)) & (~(X2 = $i!val!0)) & (X1 = $i!val!1) & (~(X1 = $i!val!5)) & (~(X1 = $i!val!0)) & (~(X0 = $i!val!4)) & (~(X0 = $i!val!3)) & (~(X0 = $i!val!1)) & (~(X0 = $i!val!5)) & (~(X0 = $i!val!0))) | ((X2 = $i!val!1) & (~(X2 = $i!val!5)) & (~(X2 = $i!val!0)) & (X1 = $i!val!3) & (~(X1 = $i!val!1)) & (~(X1 = $i!val!5)) & (~(X1 = $i!val!0)) & (X0 = $i!val!5) & (~(X0 = $i!val!0))) | ((X2 = $i!val!4) & (~(X2 = $i!val!3)) & (~(X2 = $i!val!1)) & (~(X2 = $i!val!5)) & (~(X2 = $i!val!0)) & (~(X1 = $i!val!4)) & (~(X1 = $i!val!3)) & (~(X1 = $i!val!1)) & (~(X1 = $i!val!5)) & (~(X1 = $i!val!0)) & (X0 = $i!val!1) & (~(X0 = $i!val!5)) & (~(X0 = $i!val!0))) | ((X2 = $i!val!1) & (~(X2 = $i!val!5)) & (~(X2 = $i!val!0)) & (X1 = $i!val!1) & (~(X1 = $i!val!5)) & (~(X1 = $i!val!0)) & (X0 = $i!val!1) & (~(X0 = $i!val!5)) & (~(X0 = $i!val!0))) | ((X2 = $i!val!4) & (~(X2 = $i!val!3)) & (~(X2 = $i!val!1)) & (~(X2 = $i!val!5)) & (~(X2 = $i!val!0)) & (X1 = $i!val!1) & (~(X1 = $i!val!5)) & (~(X1 = $i!val!0)) & (X0 = $i!val!5) & (~(X0 = $i!val!0))) | ((X2 = $i!val!5) & (~(X2 = $i!val!0)) & (X1 = $i!val!1) & (~(X1 = $i!val!5)) & (~(X1 = $i!val!0)) & (X0 = $i!val!4) & (~(X0 = $i!val!3)) & (~(X0 = $i!val!1)) & (~(X0 = $i!val!5)) & (~(X0 = $i!val!0))) | ((X2 = $i!val!5) & (~(X2 = $i!val!0)) & (X1 = $i!val!5) & (~(X1 = $i!val!0)) & (X0 = $i!val!5) & (~(X0 = $i!val!0))) | ((X2 = $i!val!3) & (~(X2 = $i!val!1)) & (~(X2 = $i!val!5)) & (~(X2 = $i!val!0)) & (X1 = $i!val!5) & (~(X1 = $i!val!0)) & (X0 = $i!val!4) & (~(X0 = $i!val!3)) & (~(X0 = $i!val!1)) & (~(X0 = $i!val!5)) & (~(X0 = $i!val!0))) | ((X2 = $i!val!5) & (~(X2 = $i!val!0)) & (~(X1 = $i!val!4)) & (~(X1 = $i!val!3)) & (~(X1 = $i!val!1)) & (~(X1 = $i!val!5)) & (~(X1 = $i!val!0)) & (X0 = $i!val!3) & (~(X0 = $i!val!1)) & (~(X0 = $i!val!5)) & (~(X0 = $i!val!0))) | ((X2 = $i!val!3) & (~(X2 = $i!val!1)) & (~(X2 = $i!val!5)) & (~(X2 = $i!val!0)) & (X1 = $i!val!3) & (~(X1 = $i!val!1)) & (~(X1 = $i!val!5)) & (~(X1 = $i!val!0)) & (X0 = $i!val!3) & (~(X0 = $i!val!1)) & (~(X0 = $i!val!5)) & (~(X0 = $i!val!0))) | ((~(X2 = $i!val!4)) & (~(X2 = $i!val!3)) & (~(X2 = $i!val!1)) & (~(X2 = $i!val!5)) & (~(X2 = $i!val!0)) & (X1 = $i!val!1) & (~(X1 = $i!val!5)) & (~(X1 = $i!val!0)) & (X0 = $i!val!3) & (~(X0 = $i!val!1)) & (~(X0 = $i!val!5)) & (~(X0 = $i!val!0))) | ((~(X2 = $i!val!4)) & (~(X2 = $i!val!3)) & (~(X2 = $i!val!1)) & (~(X2 = $i!val!5)) & (~(X2 = $i!val!0)) & (X1 = $i!val!5) & (~(X1 = $i!val!0)) & (X0 = $i!val!1) & (~(X0 = $i!val!5)) & (~(X0 = $i!val!0))) | ((X2 = $i!val!4) & (~(X2 = $i!val!3)) & (~(X2 = $i!val!1)) & (~(X2 = $i!val!5)) & (~(X2 = $i!val!0)) & (X1 = $i!val!4) & (~(X1 = $i!val!3)) & (~(X1 = $i!val!1)) & (~(X1 = $i!val!5)) & (~(X1 = $i!val!0)) & (X0 = $i!val!4) & (~(X0 = $i!val!3)) & (~(X0 = $i!val!1)) & (~(X0 = $i!val!5)) & (~(X0 = $i!val!0))) | ((~(X2 = $i!val!4)) & (~(X2 = $i!val!3)) & (~(X2 = $i!val!1)) & (~(X2 = $i!val!5)) & (~(X2 = $i!val!0)) & (~(X1 = $i!val!4)) & (~(X1 = $i!val!3)) & (~(X1 = $i!val!1)) & (~(X1 = $i!val!5)) & (~(X1 = $i!val!0)) & (~(X0 = $i!val!4)) & (~(X0 = $i!val!3)) & (~(X0 = $i!val!1)) & (~(X0 = $i!val!5)) & (~(X0 = $i!val!0))) | ((X2 = $i!val!0) & (X1 = $i!val!0) & (X0 = $i!val!0))))). % 0.48/0.67 tff(formula8, axiom, % 0.48/0.67 ![X0: $i, X1: $i] : (next(X0, X1) <=> (((X1 = $i!val!1) & (~(X1 = $i!val!5)) & (~(X1 = $i!val!0)) & (~(X0 = $i!val!4)) & (~(X0 = $i!val!3)) & (~(X0 = $i!val!1)) & (~(X0 = $i!val!5)) & (~(X0 = $i!val!0))) | ((X1 = $i!val!0) & (X0 = $i!val!1) & (~(X0 = $i!val!5)) & (~(X0 = $i!val!0))) | ((X1 = $i!val!4) & (~(X1 = $i!val!3)) & (~(X1 = $i!val!1)) & (~(X1 = $i!val!5)) & (~(X1 = $i!val!0)) & (X0 = $i!val!5) & (~(X0 = $i!val!0))) | ((X1 = $i!val!3) & (~(X1 = $i!val!1)) & (~(X1 = $i!val!5)) & (~(X1 = $i!val!0)) & (X0 = $i!val!4) & (~(X0 = $i!val!3)) & (~(X0 = $i!val!1)) & (~(X0 = $i!val!5)) & (~(X0 = $i!val!0))) | ((~(X1 = $i!val!4)) & (~(X1 = $i!val!3)) & (~(X1 = $i!val!1)) & (~(X1 = $i!val!5)) & (~(X1 = $i!val!0)) & (X0 = $i!val!3) & (~(X0 = $i!val!1)) & (~(X0 = $i!val!5)) & (~(X0 = $i!val!0)))))). % 0.48/0.67 tff(formula9, axiom, % 0.48/0.67 ![X0: $i, X1: $i] : (greater(X0, X1) <=> ((~((X1 = $i!val!4) & (~(X1 = $i!val!3)) & (~(X1 = $i!val!1)) & (~(X1 = $i!val!5)) & (~(X1 = $i!val!0)) & (X0 = $i!val!5) & (~(X0 = $i!val!0)))) & (~((~(X1 = $i!val!4)) & (~(X1 = $i!val!3)) & (~(X1 = $i!val!1)) & (~(X1 = $i!val!5)) & (~(X1 = $i!val!0)) & (X0 = $i!val!3) & (~(X0 = $i!val!1)) & (~(X0 = $i!val!5)) & (~(X0 = $i!val!0)))) & (~((X1 = $i!val!0) & (X0 = $i!val!1) & (~(X0 = $i!val!5)) & (~(X0 = $i!val!0)))) & (~((X1 = $i!val!1) & (~(X1 = $i!val!5)) & (~(X1 = $i!val!0)) & (X0 = $i!val!1) & (~(X0 = $i!val!5)) & (~(X0 = $i!val!0)))) & (~((X1 = $i!val!0) & (X0 = $i!val!0)))))). % 0.48/0.67 tff(formula10, axiom, % 0.48/0.67 ![X0: $i, X1: $i] : (equalish(X0, X1) <=> (((X1 = $i!val!4) & (~(X1 = $i!val!3)) & (~(X1 = $i!val!1)) & (~(X1 = $i!val!5)) & (~(X1 = $i!val!0)) & (X0 = $i!val!4) & (~(X0 = $i!val!3)) & (~(X0 = $i!val!1)) & (~(X0 = $i!val!5)) & (~(X0 = $i!val!0))) | ((X1 = $i!val!3) & (~(X1 = $i!val!1)) & (~(X1 = $i!val!5)) & (~(X1 = $i!val!0)) & (X0 = $i!val!3) & (~(X0 = $i!val!1)) & (~(X0 = $i!val!5)) & (~(X0 = $i!val!0))) | ((X1 = $i!val!5) & (~(X1 = $i!val!0)) & (X0 = $i!val!5) & (~(X0 = $i!val!0))) | ((~(X1 = $i!val!4)) & (~(X1 = $i!val!3)) & (~(X1 = $i!val!1)) & (~(X1 = $i!val!5)) & (~(X1 = $i!val!0)) & (~(X0 = $i!val!4)) & (~(X0 = $i!val!3)) & (~(X0 = $i!val!1)) & (~(X0 = $i!val!5)) & (~(X0 = $i!val!0))) | ((X1 = $i!val!1) & (~(X1 = $i!val!5)) & (~(X1 = $i!val!0)) & (X0 = $i!val!1) & (~(X0 = $i!val!5)) & (~(X0 = $i!val!0))) | ((X1 = $i!val!0) & (X0 = $i!val!0))))). % 0.48/0.67 tff(formula11, axiom, % 0.48/0.67 ![X0: $i] : (group_element(X0) <=> (~(X0 = $i!val!0)))). % 0.48/0.67 tff(formula12, axiom, % 0.48/0.67 ![X0: $i, X1: $i] : (cycle(X0, X1) <=> (((X1 = $i!val!4) & (~(X1 = $i!val!3)) & (~(X1 = $i!val!1)) & (~(X1 = $i!val!5)) & (~(X1 = $i!val!0)) & (X0 = $i!val!1) & (~(X0 = $i!val!5)) & (~(X0 = $i!val!0))) | ((X1 = $i!val!3) & (~(X1 = $i!val!1)) & (~(X1 = $i!val!5)) & (~(X1 = $i!val!0)) & (X0 = $i!val!0)) | ((X1 = $i!val!5) & (~(X1 = $i!val!0)) & (X0 = $i!val!0)) | ((~(X1 = $i!val!4)) & (~(X1 = $i!val!3)) & (~(X1 = $i!val!1)) & (~(X1 = $i!val!5)) & (~(X1 = $i!val!0)) & (X0 = $i!val!1) & (~(X0 = $i!val!5)) & (~(X0 = $i!val!0))) | ((X1 = $i!val!1) & (~(X1 = $i!val!5)) & (~(X1 = $i!val!0)) & (X0 = $i!val!0))))). % 0.48/0.67 % SZS output end Model % 0.48/0.67 % E exiting %------------------------------------------------------------------------------