TSTP Solution File: COM010-2 by Toma---0.4
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- Process Solution
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% File : Toma---0.4
% Problem : COM010-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n011.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 : Wed Aug 30 18:44:49 EDT 2023
% Result : Unsatisfiable 0.20s 0.52s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : COM010-2 : TPTP v8.1.2. Released v3.2.0.
% 0.12/0.14 % Command : toma --casc %s
% 0.13/0.35 % Computer : n011.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 29 12:43:41 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.52 % SZS status Unsatisfiable
% 0.20/0.52 % SZS output start Proof
% 0.20/0.52 original problem:
% 0.20/0.52 axioms:
% 0.20/0.52 c_UNITY_OInit(v_F(), t_a()) = c_UNITY_OInit(v_G(), t_a())
% 0.20/0.52 c_UNITY_OActs(v_F(), t_a()) = c_UNITY_OActs(v_G(), t_a())
% 0.20/0.52 c_UNITY_OAllowedActs(v_F(), t_a()) = c_UNITY_OAllowedActs(v_G(), t_a())
% 0.20/0.52 c_UNITY_Omk__program(c_Pair(c_UNITY_OInit(V_y, T_a), c_Pair(c_UNITY_OActs(V_y, T_a), c_UNITY_OAllowedActs(V_y, T_a), tc_set(tc_set(tc_prod(T_a, T_a))), tc_set(tc_set(tc_prod(T_a, T_a)))), tc_set(T_a), tc_prod(tc_set(tc_set(tc_prod(T_a, T_a))), tc_set(tc_set(tc_prod(T_a, T_a))))), T_a) = V_y
% 0.20/0.52 goal:
% 0.20/0.52 v_F() != v_G()
% 0.20/0.52 To show the unsatisfiability of the original goal,
% 0.20/0.52 it suffices to show that v_F() = v_G() (skolemized goal) is valid under the axioms.
% 0.20/0.52 Here is an equational proof:
% 0.20/0.52 0: c_UNITY_OInit(v_F(), t_a()) = c_UNITY_OInit(v_G(), t_a()).
% 0.20/0.52 Proof: Axiom.
% 0.20/0.52
% 0.20/0.52 1: c_UNITY_OActs(v_F(), t_a()) = c_UNITY_OActs(v_G(), t_a()).
% 0.20/0.52 Proof: Axiom.
% 0.20/0.52
% 0.20/0.52 2: c_UNITY_OAllowedActs(v_F(), t_a()) = c_UNITY_OAllowedActs(v_G(), t_a()).
% 0.20/0.52 Proof: Axiom.
% 0.20/0.52
% 0.20/0.52 3: c_UNITY_Omk__program(c_Pair(c_UNITY_OInit(X0, X1), c_Pair(c_UNITY_OActs(X0, X1), c_UNITY_OAllowedActs(X0, X1), tc_set(tc_set(tc_prod(X1, X1))), tc_set(tc_set(tc_prod(X1, X1)))), tc_set(X1), tc_prod(tc_set(tc_set(tc_prod(X1, X1))), tc_set(tc_set(tc_prod(X1, X1))))), X1) = X0.
% 0.20/0.52 Proof: Axiom.
% 0.20/0.52
% 0.20/0.52 6: v_G() = c_UNITY_Omk__program(c_Pair(c_UNITY_OInit(v_G(), t_a()), c_Pair(c_UNITY_OActs(v_G(), t_a()), c_UNITY_OAllowedActs(v_F(), t_a()), tc_set(tc_set(tc_prod(t_a(), t_a()))), tc_set(tc_set(tc_prod(t_a(), t_a())))), tc_set(t_a()), tc_prod(tc_set(tc_set(tc_prod(t_a(), t_a()))), tc_set(tc_set(tc_prod(t_a(), t_a()))))), t_a()).
% 0.20/0.52 Proof: A critical pair between equations 3 and 2.
% 0.20/0.52
% 0.20/0.52 7: v_G() = v_F().
% 0.20/0.52 Proof: Rewrite equation 6,
% 0.20/0.52 lhs with equations []
% 0.20/0.52 rhs with equations [0,1,3].
% 0.20/0.52
% 0.20/0.52 8: v_F() = v_G().
% 0.20/0.52 Proof: Rewrite lhs with equations []
% 0.20/0.52 rhs with equations [7].
% 0.20/0.52
% 0.20/0.52 % SZS output end Proof
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