%------------------------------------------------------------------------------ % File : Z3---4.15.1 % Problem : BOO037-1 : TPTP v9.0.0. Released v2.5.0. % 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 05:00:13 AM UTC 2025 % Result : Satisfiable 37.39s 37.66s % Output : Model 37.50s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.13 % Problem : BOO037-1 : TPTP v9.0.0. Released v2.5.0. % 0.03/0.13 % Command : run_E %s %d THM % 0.12/0.34 % Computer : n008.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % 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 11:38:18 EDT 2025 % 0.12/0.34 % CPUTime : % 37.39/37.66 % SZS status Satisfiable % 37.39/37.66 % SZS output start Model % 37.39/37.66 tff(tptp_fun__i_val_0_type, type, ( % 37.39/37.66 tptp_fun__i_val_0: $i)). % 37.39/37.66 tff(additive_identity_type, type, ( % 37.39/37.66 additive_identity: $i)). % 37.39/37.66 tff(tptp_fun__i_val_1_type, type, ( % 37.39/37.66 tptp_fun__i_val_1: $i)). % 37.39/37.66 tff(multiplicative_identity_type, type, ( % 37.39/37.66 multiplicative_identity: $i)). % 37.39/37.66 tff(tptp_fun__i_val_3_type, type, ( % 37.39/37.66 tptp_fun__i_val_3: $i)). % 37.39/37.66 tff(tptp_fun__i_val_2_type, type, ( % 37.39/37.66 tptp_fun__i_val_2: $i)). % 37.39/37.66 tff(multiply_type, type, ( % 37.39/37.66 multiply: ( $i * $i ) > $i)). % 37.39/37.66 tff(add_type, type, ( % 37.39/37.66 add: ( $i * $i ) > $i)). % 37.39/37.66 tff(sum_type, type, ( % 37.39/37.66 sum: ( $i * $i * $i ) > $o)). % 37.39/37.66 tff(product_type, type, ( % 37.39/37.66 product: ( $i * $i * $i ) > $o)). % 37.39/37.66 tff(inverse_type, type, ( % 37.39/37.66 inverse: $i > $i)). % 37.39/37.66 tff(formula1, axiom, % 37.39/37.66 additive_identity = $i!val!0). % 37.39/37.66 tff(formula2, axiom, % 37.39/37.66 multiplicative_identity = $i!val!1). % 37.39/37.66 tff(formula3, axiom, % 37.39/37.66 ![X0: $i, X1: $i] : (multiply(X0, X1) = ite_t((((X1 = $i!val!2) & (~(X1 = $i!val!1)) & (~(X1 = $i!val!3)) & (X0 = $i!val!2) & (~(X0 = $i!val!1)) & (~(X0 = $i!val!3))) | ((X1 = $i!val!1) & (~(X1 = $i!val!3)) & (X0 = $i!val!2) & (~(X0 = $i!val!1)) & (~(X0 = $i!val!3)))), $i!val!2, ite_t(((X1 = $i!val!1) & (~(X1 = $i!val!3)) & (X0 = $i!val!3)), $i!val!3, ite_t(((X1 = $i!val!1) & (~(X1 = $i!val!3)) & (X0 = $i!val!1) & (~(X0 = $i!val!3))), $i!val!1, ite_t(((X1 = $i!val!2) & (~(X1 = $i!val!1)) & (~(X1 = $i!val!3)) & (X0 = $i!val!1) & (~(X0 = $i!val!3))), $i!val!2, ite_t((((X1 = $i!val!3) & (X0 = $i!val!1) & (~(X0 = $i!val!3))) | ((X1 = $i!val!3) & (X0 = $i!val!3))), $i!val!3, $i!val!0))))))). % 37.39/37.66 tff(formula4, axiom, % 37.39/37.66 add($i!val!3, $i!val!3) = $i!val!3). % 37.39/37.66 tff(formula5, axiom, % 37.39/37.66 ![X0: $i, X1: $i] : ((~(($i!val!3 = X0) & ($i!val!3 = X1))) => (add(X0, X1) = ite_t((((~(X1 = $i!val!2)) & (~(X1 = $i!val!1)) & (~(X1 = $i!val!3)) & (X0 = $i!val!2) & (~(X0 = $i!val!1)) & (~(X0 = $i!val!3))) | ((X1 = $i!val!2) & (~(X1 = $i!val!1)) & (~(X1 = $i!val!3)) & (~(X0 = $i!val!2)) & (~(X0 = $i!val!1)) & (~(X0 = $i!val!3)))), $i!val!2, ite_t(((X1 = $i!val!3) & (~(X0 = $i!val!2)) & (~(X0 = $i!val!1)) & (~(X0 = $i!val!3))), $i!val!3, ite_t(((~(X1 = $i!val!2)) & (~(X1 = $i!val!1)) & (~(X1 = $i!val!3)) & (~(X0 = $i!val!2)) & (~(X0 = $i!val!1)) & (~(X0 = $i!val!3))), $i!val!0, ite_t(((~(X1 = $i!val!2)) & (~(X1 = $i!val!1)) & (~(X1 = $i!val!3)) & (X0 = $i!val!3)), $i!val!3, ite_t(((X1 = $i!val!2) & (~(X1 = $i!val!1)) & (~(X1 = $i!val!3)) & (X0 = $i!val!2) & (~(X0 = $i!val!1)) & (~(X0 = $i!val!3))), $i!val!2, $i!val!1)))))))). % 37.39/37.66 tff(formula6, axiom, % 37.39/37.66 ![X0: $i, X1: $i, X2: $i] : (sum(X0, X1, X2) <=> (((X2 = $i!val!1) & (~(X2 = $i!val!3)) & (~(X1 = $i!val!2)) & (~(X1 = $i!val!1)) & (~(X1 = $i!val!3)) & (X0 = $i!val!1) & (~(X0 = $i!val!3))) | ((X2 = $i!val!1) & (~(X2 = $i!val!3)) & (X1 = $i!val!1) & (~(X1 = $i!val!3)) & (X0 = $i!val!1) & (~(X0 = $i!val!3))) | ((X2 = $i!val!1) & (~(X2 = $i!val!3)) & (X1 = $i!val!2) & (~(X1 = $i!val!1)) & (~(X1 = $i!val!3)) & (X0 = $i!val!1) & (~(X0 = $i!val!3))) | ((X2 = $i!val!2) & (~(X2 = $i!val!1)) & (~(X2 = $i!val!3)) & (X1 = $i!val!2) & (~(X1 = $i!val!1)) & (~(X1 = $i!val!3)) & (X0 = $i!val!2) & (~(X0 = $i!val!1)) & (~(X0 = $i!val!3))) | ((~(X2 = $i!val!2)) & (~(X2 = $i!val!1)) & (~(X2 = $i!val!3)) & (X1 = $i!val!2) & (~(X1 = $i!val!1)) & (~(X1 = $i!val!3)) & (X0 = $i!val!2) & (~(X0 = $i!val!1)) & (~(X0 = $i!val!3))) | ((X2 = $i!val!2) & (~(X2 = $i!val!1)) & (~(X2 = $i!val!3)) & (~(X1 = $i!val!2)) & (~(X1 = $i!val!1)) & (~(X1 = $i!val!3)) & (X0 = $i!val!2) & (~(X0 = $i!val!1)) & (~(X0 = $i!val!3))) | ((X2 = $i!val!3) & (X1 = $i!val!2) & (~(X1 = $i!val!1)) & (~(X1 = $i!val!3)) & (X0 = $i!val!1) & (~(X0 = $i!val!3))) | ((X2 = $i!val!1) & (~(X2 = $i!val!3)) & (X1 = $i!val!3) & (X0 = $i!val!1) & (~(X0 = $i!val!3))) | ((~(X2 = $i!val!2)) & (~(X2 = $i!val!1)) & (~(X2 = $i!val!3)) & (~(X1 = $i!val!2)) & (~(X1 = $i!val!1)) & (~(X1 = $i!val!3)) & (~(X0 = $i!val!2)) & (~(X0 = $i!val!1)) & (~(X0 = $i!val!3))) | ((X2 = $i!val!3) & (~(X1 = $i!val!2)) & (~(X1 = $i!val!1)) & (~(X1 = $i!val!3)) & (X0 = $i!val!3)) | ((~(X2 = $i!val!2)) & (~(X2 = $i!val!1)) & (~(X2 = $i!val!3)) & (X1 = $i!val!3) & (X0 = $i!val!3)) | ((X2 = $i!val!2) & (~(X2 = $i!val!1)) & (~(X2 = $i!val!3)) & (X1 = $i!val!3) & (X0 = $i!val!1) & (~(X0 = $i!val!3))) | ((~(X2 = $i!val!2)) & (~(X2 = $i!val!1)) & (~(X2 = $i!val!3)) & (X1 = $i!val!1) & (~(X1 = $i!val!3)) & (X0 = $i!val!1) & (~(X0 = $i!val!3))) | ((X2 = $i!val!3) & (X1 = $i!val!1) & (~(X1 = $i!val!3)) & (X0 = $i!val!1) & (~(X0 = $i!val!3))) | ((X2 = $i!val!2) & (~(X2 = $i!val!1)) & (~(X2 = $i!val!3)) & (X1 = $i!val!1) & (~(X1 = $i!val!3)) & (X0 = $i!val!1) & (~(X0 = $i!val!3))) | ((X2 = $i!val!3) & (X1 = $i!val!3) & (X0 = $i!val!3))))). % 37.50/37.69 tff(formula7, axiom, % 37.50/37.69 ![X0: $i, X1: $i, X2: $i] : (product(X0, X1, X2) <=> (((X2 = $i!val!1) & (~(X2 = $i!val!3)) & (X1 = $i!val!1) & (~(X1 = $i!val!3)) & (X0 = $i!val!1) & (~(X0 = $i!val!3))) | ((X2 = $i!val!2) & (~(X2 = $i!val!1)) & (~(X2 = $i!val!3)) & (X1 = $i!val!2) & (~(X1 = $i!val!1)) & (~(X1 = $i!val!3)) & (X0 = $i!val!2) & (~(X0 = $i!val!1)) & (~(X0 = $i!val!3))) | ((X2 = $i!val!3) & (X1 = $i!val!2) & (~(X1 = $i!val!1)) & (~(X1 = $i!val!3)) & (~(X0 = $i!val!2)) & (~(X0 = $i!val!1)) & (~(X0 = $i!val!3))) | ((X2 = $i!val!2) & (~(X2 = $i!val!1)) & (~(X2 = $i!val!3)) & (X1 = $i!val!3) & (~(X0 = $i!val!2)) & (~(X0 = $i!val!1)) & (~(X0 = $i!val!3))) | ((X2 = $i!val!1) & (~(X2 = $i!val!3)) & (X1 = $i!val!2) & (~(X1 = $i!val!1)) & (~(X1 = $i!val!3)) & (X0 = $i!val!2) & (~(X0 = $i!val!1)) & (~(X0 = $i!val!3))) | ((X2 = $i!val!1) & (~(X2 = $i!val!3)) & (~(X1 = $i!val!2)) & (~(X1 = $i!val!1)) & (~(X1 = $i!val!3)) & (~(X0 = $i!val!2)) & (~(X0 = $i!val!1)) & (~(X0 = $i!val!3))) | ((X2 = $i!val!2) & (~(X2 = $i!val!1)) & (~(X2 = $i!val!3)) & (X1 = $i!val!1) & (~(X1 = $i!val!3)) & (X0 = $i!val!2) & (~(X0 = $i!val!1)) & (~(X0 = $i!val!3))) | ((X2 = $i!val!3) & (X1 = $i!val!1) & (~(X1 = $i!val!3)) & (X0 = $i!val!3)) | ((~(X2 = $i!val!2)) & (~(X2 = $i!val!1)) & (~(X2 = $i!val!3)) & (~(X1 = $i!val!2)) & (~(X1 = $i!val!1)) & (~(X1 = $i!val!3)) & (~(X0 = $i!val!2)) & (~(X0 = $i!val!1)) & (~(X0 = $i!val!3))) | ((X2 = $i!val!1) & (~(X2 = $i!val!3)) & (X1 = $i!val!3) & (X0 = $i!val!3)) | ((X2 = $i!val!2) & (~(X2 = $i!val!1)) & (~(X2 = $i!val!3)) & (~(X1 = $i!val!2)) & (~(X1 = $i!val!1)) & (~(X1 = $i!val!3)) & (~(X0 = $i!val!2)) & (~(X0 = $i!val!1)) & (~(X0 = $i!val!3))) | ((~(X2 = $i!val!2)) & (~(X2 = $i!val!1)) & (~(X2 = $i!val!3)) & (X1 = $i!val!1) & (~(X1 = $i!val!3)) & (~(X0 = $i!val!2)) & (~(X0 = $i!val!1)) & (~(X0 = $i!val!3))) | ((~(X2 = $i!val!2)) & (~(X2 = $i!val!1)) & (~(X2 = $i!val!3)) & (X1 = $i!val!2) & (~(X1 = $i!val!1)) & (~(X1 = $i!val!3)) & (~(X0 = $i!val!2)) & (~(X0 = $i!val!1)) & (~(X0 = $i!val!3))) | ((X2 = $i!val!3) & (~(X1 = $i!val!2)) & (~(X1 = $i!val!1)) & (~(X1 = $i!val!3)) & (~(X0 = $i!val!2)) & (~(X0 = $i!val!1)) & (~(X0 = $i!val!3))) | ((~(X2 = $i!val!2)) & (~(X2 = $i!val!1)) & (~(X2 = $i!val!3)) & (X1 = $i!val!3) & (~(X0 = $i!val!2)) & (~(X0 = $i!val!1)) & (~(X0 = $i!val!3))) | ((X2 = $i!val!3) & (X1 = $i!val!3) & (X0 = $i!val!3))))). % 37.50/37.69 tff(formula8, axiom, % 37.50/37.69 ![X0: $i] : (inverse(X0) = ite_t(((~(X0 = $i!val!2)) & (~(X0 = $i!val!1)) & (~(X0 = $i!val!3))), $i!val!1, ite_t(((X0 = $i!val!1) & (~(X0 = $i!val!3))), $i!val!0, ite_t((X0 = $i!val!3), $i!val!2, $i!val!3))))). % 37.50/37.69 % SZS output end Model % 37.50/37.69 % E exiting %------------------------------------------------------------------------------