TSTP Solution File: SYN112-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN112-1 : TPTP v8.1.2. Released v1.1.0.
% 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 : n031.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 03:33:12 EDT 2023
% Result : Unsatisfiable 22.72s 3.31s
% Output : Proof 22.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SYN112-1 : TPTP v8.1.2. Released v1.1.0.
% 0.10/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.33 % Computer : n031.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Aug 26 21:26:08 EDT 2023
% 0.12/0.33 % CPUTime :
% 22.72/3.31 Command-line arguments: --no-flatten-goal
% 22.72/3.31
% 22.72/3.31 % SZS status Unsatisfiable
% 22.72/3.31
% 22.72/3.32 % SZS output start Proof
% 22.72/3.32 Take the following subset of the input axioms:
% 22.72/3.32 fof(axiom_19, axiom, ![X, Y]: m0(X, d, Y)).
% 22.72/3.32 fof(prove_this, negated_conjecture, ![X2]: ~k2(e, X2)).
% 22.72/3.32 fof(rule_107, axiom, ![A2]: (q1(e, A2, A2) | (~m0(A2, d, A2) | ~m0(e, d, A2)))).
% 22.72/3.32 fof(rule_129, axiom, ![J, A]: (k2(J, J) | ~q1(A, J, J))).
% 22.72/3.32
% 22.72/3.32 Now clausify the problem and encode Horn clauses using encoding 3 of
% 22.72/3.32 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 22.72/3.32 We repeatedly replace C & s=t => u=v by the two clauses:
% 22.72/3.32 fresh(y, y, x1...xn) = u
% 22.72/3.32 C => fresh(s, t, x1...xn) = v
% 22.72/3.32 where fresh is a fresh function symbol and x1..xn are the free
% 22.72/3.32 variables of u and v.
% 22.72/3.32 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 22.72/3.32 input problem has no model of domain size 1).
% 22.72/3.32
% 22.72/3.32 The encoding turns the above axioms into the following unit equations and goals:
% 22.72/3.32
% 22.72/3.32 Axiom 1 (rule_107): fresh300(X, X, Y) = true2.
% 22.72/3.32 Axiom 2 (rule_129): fresh270(X, X, Y) = true2.
% 22.72/3.32 Axiom 3 (rule_107): fresh301(X, X, Y) = q1(e, Y, Y).
% 22.72/3.32 Axiom 4 (axiom_19): m0(X, d, Y) = true2.
% 22.72/3.32 Axiom 5 (rule_107): fresh301(m0(e, d, X), true2, X) = fresh300(m0(X, d, X), true2, X).
% 22.72/3.32 Axiom 6 (rule_129): fresh270(q1(X, Y, Y), true2, Y) = k2(Y, Y).
% 22.72/3.32
% 22.72/3.32 Goal 1 (prove_this): k2(e, X) = true2.
% 22.72/3.32 The goal is true when:
% 22.72/3.32 X = e
% 22.72/3.32
% 22.72/3.32 Proof:
% 22.72/3.32 k2(e, e)
% 22.72/3.32 = { by axiom 6 (rule_129) R->L }
% 22.72/3.32 fresh270(q1(e, e, e), true2, e)
% 22.72/3.32 = { by axiom 3 (rule_107) R->L }
% 22.72/3.32 fresh270(fresh301(true2, true2, e), true2, e)
% 22.72/3.32 = { by axiom 4 (axiom_19) R->L }
% 22.72/3.32 fresh270(fresh301(m0(e, d, e), true2, e), true2, e)
% 22.72/3.32 = { by axiom 5 (rule_107) }
% 22.72/3.32 fresh270(fresh300(m0(e, d, e), true2, e), true2, e)
% 22.72/3.32 = { by axiom 4 (axiom_19) }
% 22.72/3.32 fresh270(fresh300(true2, true2, e), true2, e)
% 22.72/3.32 = { by axiom 1 (rule_107) }
% 22.72/3.32 fresh270(true2, true2, e)
% 22.72/3.32 = { by axiom 2 (rule_129) }
% 22.72/3.32 true2
% 22.72/3.32 % SZS output end Proof
% 22.72/3.32
% 22.72/3.32 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------