%------------------------------------------------------------------------------ % File : Z3---4.15.1 % Problem : KLE181+1 : TPTP v9.0.0. Released v6.4.0. % Transfm : none % Format : tptp % Command : run_E %s %d THM % Computer : n013.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 05:13:09 AM UTC 2025 % Result : Satisfiable 76.32s 76.48s % Output : Model 76.47s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.14 % Problem : KLE181+1 : TPTP v9.0.0. Released v6.4.0. % 0.04/0.14 % Command : run_E %s %d THM % 0.14/0.35 % Computer : n013.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Thu Jun 19 19:09:08 EDT 2025 % 0.14/0.36 % CPUTime : % 76.32/76.48 % SZS status Satisfiable % 76.32/76.48 % SZS output start Model % 76.32/76.48 tff(tptp_fun__i_val_1_type, type, ( % 76.32/76.48 tptp_fun__i_val_1: $i)). % 76.32/76.48 tff(one_type, type, ( % 76.32/76.48 one: $i)). % 76.32/76.48 tff(tptp_fun__i_val_0_type, type, ( % 76.32/76.48 tptp_fun__i_val_0: $i)). % 76.32/76.48 tff(zero_type, type, ( % 76.32/76.48 zero: $i)). % 76.32/76.48 tff(addition_type, type, ( % 76.32/76.48 addition: ( $i * $i ) > $i)). % 76.32/76.48 tff(tptp_fun__i_val_2_type, type, ( % 76.32/76.48 tptp_fun__i_val_2: $i)). % 76.32/76.48 tff(multiplication_type, type, ( % 76.32/76.48 multiplication: ( $i * $i ) > $i)). % 76.32/76.48 tff(domain_type, type, ( % 76.32/76.48 domain: $i > $i)). % 76.32/76.48 tff(star_type, type, ( % 76.32/76.48 star: $i > $i)). % 76.32/76.48 tff(omega_type, type, ( % 76.32/76.48 omega: $i > $i)). % 76.32/76.48 tff(leq_type, type, ( % 76.32/76.48 leq: ( $i * $i ) > $o)). % 76.32/76.48 tff(formula1, axiom, % 76.32/76.48 one = $i!val!1). % 76.32/76.48 tff(formula2, axiom, % 76.32/76.48 zero = $i!val!0). % 76.32/76.48 tff(formula3, axiom, % 76.32/76.48 addition($i!val!0, $i!val!0) = $i!val!0). % 76.32/76.48 tff(formula4, axiom, % 76.32/76.48 addition($i!val!0, $i!val!1) = $i!val!1). % 76.32/76.48 tff(formula5, axiom, % 76.32/76.48 addition($i!val!1, $i!val!0) = $i!val!1). % 76.32/76.48 tff(formula6, axiom, % 76.32/76.48 addition($i!val!1, $i!val!1) = $i!val!1). % 76.32/76.48 tff(formula7, axiom, % 76.32/76.48 addition($i!val!0, $i!val!2) = $i!val!2). % 76.32/76.48 tff(formula8, axiom, % 76.32/76.48 addition($i!val!1, $i!val!2) = $i!val!2). % 76.32/76.48 tff(formula9, axiom, % 76.32/76.48 addition($i!val!2, $i!val!0) = $i!val!2). % 76.32/76.48 tff(formula10, axiom, % 76.32/76.48 addition($i!val!2, $i!val!1) = $i!val!2). % 76.32/76.48 tff(formula11, axiom, % 76.32/76.48 addition($i!val!2, $i!val!2) = $i!val!2). % 76.32/76.48 tff(formula12, axiom, % 76.32/76.48 ![X0: $i, X1: $i] : ((~((($i!val!0 = X0) & ($i!val!0 = X1)) | (($i!val!0 = X0) & ($i!val!1 = X1)) | (($i!val!1 = X0) & ($i!val!0 = X1)) | (($i!val!1 = X0) & ($i!val!1 = X1)) | (($i!val!0 = X0) & ($i!val!2 = X1)) | (($i!val!1 = X0) & ($i!val!2 = X1)) | (($i!val!2 = X0) & ($i!val!0 = X1)) | (($i!val!2 = X0) & ($i!val!1 = X1)) | (($i!val!2 = X0) & ($i!val!2 = X1)))) => (addition(X0, X1) = ite_t((X0 = multiplication(domain(X1), X1)), multiplication(domain(X1), X1), X1)))). % 76.32/76.48 tff(formula13, axiom, % 76.32/76.48 ![X0: $i] : (star(X0) = ite_t(((~(X0 = $i!val!1)) & (~(X0 = $i!val!0))), $i!val!2, $i!val!1))). % 76.32/76.48 tff(formula14, axiom, % 76.32/76.48 multiplication($i!val!0, $i!val!0) = $i!val!0). % 76.32/76.48 tff(formula15, axiom, % 76.32/76.48 multiplication($i!val!1, $i!val!1) = $i!val!1). % 76.32/76.48 tff(formula16, axiom, % 76.32/76.48 multiplication($i!val!1, $i!val!0) = $i!val!0). % 76.32/76.48 tff(formula17, axiom, % 76.32/76.48 multiplication($i!val!0, $i!val!1) = $i!val!0). % 76.32/76.48 tff(formula18, axiom, % 76.32/76.48 multiplication($i!val!0, $i!val!2) = $i!val!0). % 76.32/76.48 tff(formula19, axiom, % 76.32/76.48 multiplication($i!val!1, $i!val!2) = $i!val!2). % 76.32/76.48 tff(formula20, axiom, % 76.32/76.48 multiplication($i!val!2, $i!val!1) = $i!val!2). % 76.32/76.48 tff(formula21, axiom, % 76.32/76.48 multiplication($i!val!2, $i!val!0) = $i!val!0). % 76.32/76.48 tff(formula22, axiom, % 76.32/76.48 multiplication($i!val!2, $i!val!2) = $i!val!2). % 76.32/76.48 tff(formula23, axiom, % 76.32/76.48 ![X0: $i, X1: $i] : ((~((($i!val!0 = X0) & ($i!val!0 = X1)) | (($i!val!1 = X0) & ($i!val!1 = X1)) | (($i!val!1 = X0) & ($i!val!0 = X1)) | (($i!val!0 = X0) & ($i!val!1 = X1)) | (($i!val!0 = X0) & ($i!val!2 = X1)) | (($i!val!1 = X0) & ($i!val!2 = X1)) | (($i!val!2 = X0) & ($i!val!1 = X1)) | (($i!val!2 = X0) & ($i!val!0 = X1)) | (($i!val!2 = X0) & ($i!val!2 = X1)))) => (multiplication(X0, X1) = ite_t((X0 = omega(X1)), omega(X1), ite_t(((X1 = $i!val!0) | (X0 = $i!val!0)), $i!val!0, ite_t((X1 = $i!val!1), X0, X1)))))). % 76.32/76.48 tff(formula24, axiom, % 76.32/76.48 domain($i!val!0) = $i!val!0). % 76.32/76.48 tff(formula25, axiom, % 76.32/76.48 ![X0: $i] : ((~(($i!val!0 = X0))) => (domain(X0) = $i!val!1))). % 76.32/76.48 tff(formula26, axiom, % 76.32/76.48 omega($i!val!0) = $i!val!0). % 76.32/76.48 tff(formula27, axiom, % 76.32/76.48 ![X0: $i] : ((~(($i!val!0 = X0))) => (omega(X0) = $i!val!2))). % 76.32/76.48 tff(formula28, axiom, % 76.32/76.48 leq($i!val!0, $i!val!0) <=> $true). % 76.32/76.48 tff(formula29, axiom, % 76.32/76.48 leq($i!val!0, $i!val!1) <=> $true). % 76.32/76.48 tff(formula30, axiom, % 76.32/76.48 leq($i!val!1, $i!val!0) <=> $false). % 76.32/76.48 tff(formula31, axiom, % 76.32/76.48 leq($i!val!1, $i!val!1) <=> $true). % 76.32/76.48 tff(formula32, axiom, % 76.32/76.48 leq($i!val!0, $i!val!2) <=> $true). % 76.32/76.48 tff(formula33, axiom, % 76.32/76.48 leq($i!val!1, $i!val!2) <=> $true). % 76.32/76.48 tff(formula34, axiom, % 76.32/76.48 leq($i!val!2, $i!val!1) <=> $false). % 76.32/76.48 tff(formula35, axiom, % 76.32/76.48 leq($i!val!2, $i!val!0) <=> $false). % 76.32/76.48 tff(formula36, axiom, % 76.32/76.48 leq($i!val!2, $i!val!2) <=> $true). % 76.32/76.48 tff(formula37, axiom, % 76.32/76.48 ![X0: $i, X1: $i] : ((~((($i!val!0 = X0) & ($i!val!0 = X1)) | (($i!val!0 = X0) & ($i!val!1 = X1)) | (($i!val!1 = X0) & ($i!val!0 = X1)) | (($i!val!1 = X0) & ($i!val!1 = X1)) | (($i!val!0 = X0) & ($i!val!2 = X1)) | (($i!val!1 = X0) & ($i!val!2 = X1)) | (($i!val!2 = X0) & ($i!val!1 = X1)) | (($i!val!2 = X0) & ($i!val!0 = X1)) | (($i!val!2 = X0) & ($i!val!2 = X1)))) => (leq(X0, X1) <=> (addition(X1, X0) = X0)))). % 76.47/76.67 % SZS output end Model % 76.47/76.68 % E exiting %------------------------------------------------------------------------------