%------------------------------------------------------------------------------ % File : Z3---4.15.1 % Problem : GRP124-3.005 : TPTP v9.0.0. Released v1.2.0. % Transfm : none % Format : tptp % Command : run_E %s %d THM % Computer : n008.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 05:07:04 AM UTC 2025 % Result : Satisfiable 0.77s 0.97s % Output : Model 0.77s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : GRP124-3.005 : TPTP v9.0.0. Released v1.2.0. % 0.07/0.12 % Command : run_E %s %d THM % 0.12/0.33 % Computer : n008.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 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Thu Jun 19 15:41:48 EDT 2025 % 0.12/0.34 % CPUTime : % 0.77/0.97 % SZS status Satisfiable % 0.77/0.97 % SZS output start Model % 0.77/0.97 tff(tptp_fun__i_val_2_type, type, ( % 0.77/0.97 tptp_fun__i_val_2: $i)). % 0.77/0.97 tff(e_2_type, type, ( % 0.77/0.97 e_2: $i)). % 0.77/0.97 tff(tptp_fun__i_val_4_type, type, ( % 0.77/0.97 tptp_fun__i_val_4: $i)). % 0.77/0.97 tff(e_4_type, type, ( % 0.77/0.97 e_4: $i)). % 0.77/0.97 tff(tptp_fun__i_val_3_type, type, ( % 0.77/0.97 tptp_fun__i_val_3: $i)). % 0.77/0.97 tff(e_3_type, type, ( % 0.77/0.97 e_3: $i)). % 0.77/0.97 tff(tptp_fun__i_val_0_type, type, ( % 0.77/0.97 tptp_fun__i_val_0: $i)). % 0.77/0.97 tff(e_0_type, type, ( % 0.77/0.97 e_0: $i)). % 0.77/0.97 tff(tptp_fun__i_val_1_type, type, ( % 0.77/0.97 tptp_fun__i_val_1: $i)). % 0.77/0.97 tff(e_1_type, type, ( % 0.77/0.97 e_1: $i)). % 0.77/0.97 tff(tptp_fun__i_val_5_type, type, ( % 0.77/0.97 tptp_fun__i_val_5: $i)). % 0.77/0.97 tff(e_5_type, type, ( % 0.77/0.97 e_5: $i)). % 0.77/0.97 tff(equalish_type, type, ( % 0.77/0.97 equalish: ( $i * $i ) > $o)). % 0.77/0.97 tff(next_type, type, ( % 0.77/0.97 next: ( $i * $i ) > $o)). % 0.77/0.97 tff(greater_type, type, ( % 0.77/0.97 greater: ( $i * $i ) > $o)). % 0.77/0.97 tff(group_element_type, type, ( % 0.77/0.97 group_element: $i > $o)). % 0.77/0.97 tff(product_type, type, ( % 0.77/0.97 product: ( $i * $i * $i ) > $o)). % 0.77/0.97 tff(cycle_type, type, ( % 0.77/0.97 cycle: ( $i * $i ) > $o)). % 0.77/0.97 tff(formula1, axiom, % 0.77/0.97 e_2 = $i!val!2). % 0.77/0.97 tff(formula2, axiom, % 0.77/0.97 e_4 = $i!val!4). % 0.77/0.97 tff(formula3, axiom, % 0.77/0.97 e_3 = $i!val!3). % 0.77/0.97 tff(formula4, axiom, % 0.77/0.97 e_0 = $i!val!0). % 0.77/0.97 tff(formula5, axiom, % 0.77/0.97 e_1 = $i!val!1). % 0.77/0.97 tff(formula6, axiom, % 0.77/0.97 e_5 = $i!val!5). % 0.77/0.97 tff(formula7, axiom, % 0.77/0.97 ![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!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!5) & (~(X1 = $i!val!0)) & (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))))). % 0.77/0.97 tff(formula8, axiom, % 0.77/0.97 ![X0: $i, X1: $i] : (next(X0, X1) <=> (((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))) | ((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!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)))))). % 0.77/0.97 tff(formula9, axiom, % 0.77/0.97 ![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!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!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)))))). % 0.77/0.97 tff(formula10, axiom, % 0.77/0.97 ![X0: $i] : (group_element(X0) <=> (~(X0 = $i!val!0)))). % 0.77/0.97 tff(formula11, axiom, % 0.77/0.97 ![X0: $i, X1: $i, X2: $i] : (product(X0, X1, X2) <=> (((~(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!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!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!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!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!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!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!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!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!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!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!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!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!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!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!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!5) & (~(X1 = $i!val!0)) & (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!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!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!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))))). % 0.77/0.97 tff(formula12, axiom, % 0.77/0.97 ![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!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)) | ((X1 = $i!val!5) & (~(X1 = $i!val!0)) & (X0 = $i!val!0))))). % 0.77/0.97 % SZS output end Model % 0.77/0.97 % E exiting %------------------------------------------------------------------------------