TSTP Solution File: SYN062+1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN062+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n006.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 : Fri Sep 1 03:32:57 EDT 2023
% Result : Theorem 0.19s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN062+1 : TPTP v8.1.2. Released v2.0.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n006.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 18:37:22 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.38 Command-line arguments: --no-flatten-goal
% 0.19/0.38
% 0.19/0.38 % SZS status Theorem
% 0.19/0.38
% 0.19/0.39 % SZS output start Proof
% 0.19/0.39 Take the following subset of the input axioms:
% 0.19/0.39 fof(pel32, conjecture, ![X]: ((big_f(X) & big_k(X)) => big_j(X))).
% 0.19/0.39 fof(pel32_1, axiom, ![X2]: ((big_f(X2) & (big_g(X2) | big_h(X2))) => big_i(X2))).
% 0.19/0.39 fof(pel32_2, axiom, ![X2]: ((big_i(X2) & big_h(X2)) => big_j(X2))).
% 0.19/0.39 fof(pel32_3, axiom, ![X2]: (big_k(X2) => big_h(X2))).
% 0.19/0.39
% 0.19/0.39 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.39 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.39 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.39 fresh(y, y, x1...xn) = u
% 0.19/0.39 C => fresh(s, t, x1...xn) = v
% 0.19/0.39 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.39 variables of u and v.
% 0.19/0.39 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.39 input problem has no model of domain size 1).
% 0.19/0.39
% 0.19/0.39 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.39
% 0.19/0.39 Axiom 1 (pel32_1): big_k(x) = true.
% 0.19/0.39 Axiom 2 (pel32): big_f(x) = true.
% 0.19/0.39 Axiom 3 (pel32_3): fresh(X, X, Y) = true.
% 0.19/0.39 Axiom 4 (pel32_1_1): fresh5(X, X, Y) = big_i(Y).
% 0.19/0.39 Axiom 5 (pel32_1_1): fresh4(X, X, Y) = true.
% 0.19/0.39 Axiom 6 (pel32_2): fresh3(X, X, Y) = big_j(Y).
% 0.19/0.39 Axiom 7 (pel32_2): fresh2(X, X, Y) = true.
% 0.19/0.39 Axiom 8 (pel32_3): fresh(big_k(X), true, X) = big_h(X).
% 0.19/0.39 Axiom 9 (pel32_1_1): fresh5(big_h(X), true, X) = fresh4(big_f(X), true, X).
% 0.19/0.39 Axiom 10 (pel32_2): fresh3(big_i(X), true, X) = fresh2(big_h(X), true, X).
% 0.19/0.39
% 0.19/0.39 Lemma 11: big_h(x) = true.
% 0.19/0.39 Proof:
% 0.19/0.39 big_h(x)
% 0.19/0.39 = { by axiom 8 (pel32_3) R->L }
% 0.19/0.39 fresh(big_k(x), true, x)
% 0.19/0.39 = { by axiom 1 (pel32_1) }
% 0.19/0.39 fresh(true, true, x)
% 0.19/0.39 = { by axiom 3 (pel32_3) }
% 0.19/0.39 true
% 0.19/0.39
% 0.19/0.39 Goal 1 (pel32_2): big_j(x) = true.
% 0.19/0.39 Proof:
% 0.19/0.39 big_j(x)
% 0.19/0.39 = { by axiom 6 (pel32_2) R->L }
% 0.19/0.39 fresh3(true, true, x)
% 0.19/0.39 = { by axiom 5 (pel32_1_1) R->L }
% 0.19/0.39 fresh3(fresh4(true, true, x), true, x)
% 0.19/0.39 = { by axiom 2 (pel32) R->L }
% 0.19/0.39 fresh3(fresh4(big_f(x), true, x), true, x)
% 0.19/0.39 = { by axiom 9 (pel32_1_1) R->L }
% 0.19/0.39 fresh3(fresh5(big_h(x), true, x), true, x)
% 0.19/0.39 = { by lemma 11 }
% 0.19/0.39 fresh3(fresh5(true, true, x), true, x)
% 0.19/0.39 = { by axiom 4 (pel32_1_1) }
% 0.19/0.39 fresh3(big_i(x), true, x)
% 0.19/0.39 = { by axiom 10 (pel32_2) }
% 0.19/0.39 fresh2(big_h(x), true, x)
% 0.19/0.39 = { by lemma 11 }
% 0.19/0.39 fresh2(true, true, x)
% 0.19/0.39 = { by axiom 7 (pel32_2) }
% 0.19/0.39 true
% 0.19/0.39 % SZS output end Proof
% 0.19/0.39
% 0.19/0.39 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------