%------------------------------------------------------------------------------ % File : Z3---4.15.1 % Problem : KLE178+1 : TPTP v9.0.0. Released v6.4.0. % Transfm : none % Format : tptp % Command : run_E %s %d THM % Computer : n007.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 0.21s 0.45s % Output : Model 0.21s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : KLE178+1 : TPTP v9.0.0. Released v6.4.0. % 0.03/0.12 % Command : run_E %s %d THM % 0.12/0.34 % Computer : n007.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 19:09:49 EDT 2025 % 0.12/0.34 % CPUTime : % 0.21/0.45 % SZS status Satisfiable % 0.21/0.45 % SZS output start Model % 0.21/0.45 tff(tptp_fun__i_val_1_type, type, ( % 0.21/0.45 tptp_fun__i_val_1: $i)). % 0.21/0.45 tff(one_type, type, ( % 0.21/0.45 one: $i)). % 0.21/0.45 tff(tptp_fun__i_val_0_type, type, ( % 0.21/0.45 tptp_fun__i_val_0: $i)). % 0.21/0.45 tff(zero_type, type, ( % 0.21/0.45 zero: $i)). % 0.21/0.45 tff(addition_type, type, ( % 0.21/0.45 addition: ( $i * $i ) > $i)). % 0.21/0.45 tff(multiplication_type, type, ( % 0.21/0.45 multiplication: ( $i * $i ) > $i)). % 0.21/0.45 tff(domain_type, type, ( % 0.21/0.45 domain: $i > $i)). % 0.21/0.45 tff(star_type, type, ( % 0.21/0.45 star: $i > $i)). % 0.21/0.45 tff(leq_type, type, ( % 0.21/0.45 leq: ( $i * $i ) > $o)). % 0.21/0.45 tff(formula1, axiom, % 0.21/0.45 one = $i!val!1). % 0.21/0.45 tff(formula2, axiom, % 0.21/0.45 zero = $i!val!0). % 0.21/0.45 tff(formula3, axiom, % 0.21/0.45 addition($i!val!0, $i!val!0) = $i!val!0). % 0.21/0.45 tff(formula4, axiom, % 0.21/0.45 addition($i!val!0, $i!val!1) = $i!val!1). % 0.21/0.45 tff(formula5, axiom, % 0.21/0.45 addition($i!val!1, $i!val!0) = $i!val!1). % 0.21/0.45 tff(formula6, axiom, % 0.21/0.45 addition($i!val!1, $i!val!1) = $i!val!1). % 0.21/0.45 tff(formula7, axiom, % 0.21/0.45 ![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)))) => (addition(X0, X1) = ite_t((X0 = multiplication(domain(X1), X1)), multiplication(domain(X1), X1), X1)))). % 0.21/0.45 tff(formula8, axiom, % 0.21/0.45 ![X0: $i] : (star(X0) = $i!val!1)). % 0.21/0.45 tff(formula9, axiom, % 0.21/0.45 multiplication($i!val!0, $i!val!0) = $i!val!0). % 0.21/0.45 tff(formula10, axiom, % 0.21/0.45 multiplication($i!val!1, $i!val!1) = $i!val!1). % 0.21/0.45 tff(formula11, axiom, % 0.21/0.45 multiplication($i!val!1, $i!val!0) = $i!val!0). % 0.21/0.45 tff(formula12, axiom, % 0.21/0.45 multiplication($i!val!0, $i!val!1) = $i!val!0). % 0.21/0.45 tff(formula13, axiom, % 0.21/0.45 ![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)))) => (multiplication(X0, X1) = ite_t(((X1 = $i!val!0) | (X0 = $i!val!0)), $i!val!0, ite_t((X1 = $i!val!1), X0, X1))))). % 0.21/0.45 tff(formula14, axiom, % 0.21/0.45 domain($i!val!0) = $i!val!0). % 0.21/0.45 tff(formula15, axiom, % 0.21/0.45 ![X0: $i] : ((~(($i!val!0 = X0))) => (domain(X0) = $i!val!1))). % 0.21/0.45 tff(formula16, axiom, % 0.21/0.45 leq($i!val!0, $i!val!0) <=> $true). % 0.21/0.45 tff(formula17, axiom, % 0.21/0.45 leq($i!val!0, $i!val!1) <=> $true). % 0.21/0.45 tff(formula18, axiom, % 0.21/0.45 leq($i!val!1, $i!val!0) <=> $false). % 0.21/0.45 tff(formula19, axiom, % 0.21/0.45 leq($i!val!1, $i!val!1) <=> $true). % 0.21/0.45 tff(formula20, axiom, % 0.21/0.45 ![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)))) => (leq(X0, X1) <=> (addition(X1, X0) = X0)))). % 0.21/0.45 % SZS output end Model % 0.21/0.45 % E exiting %------------------------------------------------------------------------------