TSTP Solution File: SYN167-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SYN167-1 : 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 : n010.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 03:33:26 EDT 2023
% Result : Unsatisfiable 13.19s 2.13s
% Output : Proof 13.19s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SYN167-1 : TPTP v8.1.2. Released v1.1.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35 % Computer : n010.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 : Sat Aug 26 19:23:05 EDT 2023
% 0.13/0.35 % CPUTime :
% 13.19/2.13 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 13.19/2.13
% 13.19/2.13 % SZS status Unsatisfiable
% 13.19/2.13
% 13.19/2.14 % SZS output start Proof
% 13.19/2.14 Take the following subset of the input axioms:
% 13.19/2.14 fof(axiom_17, axiom, ![X]: q0(X, d)).
% 13.19/2.14 fof(prove_this, negated_conjecture, ![X2]: ~p1(d, X2, d)).
% 13.19/2.14 fof(rule_067, axiom, ![E, F]: (p1(E, E, E) | ~q0(F, E))).
% 13.19/2.14
% 13.19/2.14 Now clausify the problem and encode Horn clauses using encoding 3 of
% 13.19/2.14 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 13.19/2.14 We repeatedly replace C & s=t => u=v by the two clauses:
% 13.19/2.14 fresh(y, y, x1...xn) = u
% 13.19/2.14 C => fresh(s, t, x1...xn) = v
% 13.19/2.14 where fresh is a fresh function symbol and x1..xn are the free
% 13.19/2.14 variables of u and v.
% 13.19/2.14 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 13.19/2.14 input problem has no model of domain size 1).
% 13.19/2.14
% 13.19/2.14 The encoding turns the above axioms into the following unit equations and goals:
% 13.19/2.14
% 13.19/2.14 Axiom 1 (axiom_17): q0(X, d) = true2.
% 13.19/2.14 Axiom 2 (rule_067): fresh351(X, X, Y) = true2.
% 13.19/2.14 Axiom 3 (rule_067): fresh351(q0(X, Y), true2, Y) = p1(Y, Y, Y).
% 13.19/2.14
% 13.19/2.14 Goal 1 (prove_this): p1(d, X, d) = true2.
% 13.19/2.14 The goal is true when:
% 13.19/2.14 X = d
% 13.19/2.14
% 13.19/2.14 Proof:
% 13.19/2.14 p1(d, d, d)
% 13.19/2.14 = { by axiom 3 (rule_067) R->L }
% 13.19/2.14 fresh351(q0(X, d), true2, d)
% 13.19/2.14 = { by axiom 1 (axiom_17) }
% 13.19/2.14 fresh351(true2, true2, d)
% 13.19/2.14 = { by axiom 2 (rule_067) }
% 13.19/2.14 true2
% 13.19/2.14 % SZS output end Proof
% 13.19/2.14
% 13.19/2.14 RESULT: Unsatisfiable (the axioms are contradictory).
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