TSTP Solution File: SYN255-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SYN255-1 : 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 03:33:47 EDT 2023
% Result : Unsatisfiable 21.71s 3.26s
% Output : Proof 21.71s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN255-1 : TPTP v8.1.2. Released v1.1.0.
% 0.12/0.13 % 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 : n031.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 18:36:53 EDT 2023
% 0.13/0.34 % CPUTime :
% 21.71/3.26 Command-line arguments: --no-flatten-goal
% 21.71/3.26
% 21.71/3.26 % SZS status Unsatisfiable
% 21.71/3.26
% 21.71/3.26 % SZS output start Proof
% 21.71/3.26 Take the following subset of the input axioms:
% 21.71/3.26 fof(axiom_20, axiom, l0(a)).
% 21.71/3.26 fof(axiom_9, axiom, r0(b)).
% 21.71/3.26 fof(prove_this, negated_conjecture, ~n2(a)).
% 21.71/3.26 fof(rule_087, axiom, p1(a, b, a) | (~r0(b) | ~p1(a, a, a))).
% 21.71/3.26 fof(rule_088, axiom, p1(a, a, a) | ~l0(a)).
% 21.71/3.26 fof(rule_137, axiom, ![C, B, A2]: (n2(A2) | ~p1(B, C, A2))).
% 21.71/3.26
% 21.71/3.26 Now clausify the problem and encode Horn clauses using encoding 3 of
% 21.71/3.26 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 21.71/3.26 We repeatedly replace C & s=t => u=v by the two clauses:
% 21.71/3.26 fresh(y, y, x1...xn) = u
% 21.71/3.26 C => fresh(s, t, x1...xn) = v
% 21.71/3.26 where fresh is a fresh function symbol and x1..xn are the free
% 21.71/3.26 variables of u and v.
% 21.71/3.26 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 21.71/3.26 input problem has no model of domain size 1).
% 21.71/3.26
% 21.71/3.26 The encoding turns the above axioms into the following unit equations and goals:
% 21.71/3.26
% 21.71/3.26 Axiom 1 (axiom_20): l0(a) = true.
% 21.71/3.26 Axiom 2 (axiom_9): r0(b) = true.
% 21.71/3.26 Axiom 3 (rule_087): fresh324(X, X) = true.
% 21.71/3.26 Axiom 4 (rule_088): fresh323(X, X) = true.
% 21.71/3.26 Axiom 5 (rule_137): fresh262(X, X, Y) = true.
% 21.71/3.26 Axiom 6 (rule_088): fresh323(l0(a), true) = p1(a, a, a).
% 21.71/3.26 Axiom 7 (rule_087): fresh325(X, X) = p1(a, b, a).
% 21.71/3.26 Axiom 8 (rule_087): fresh325(p1(a, a, a), true) = fresh324(r0(b), true).
% 21.71/3.26 Axiom 9 (rule_137): fresh262(p1(X, Y, Z), true, Z) = n2(Z).
% 21.71/3.26
% 21.71/3.26 Goal 1 (prove_this): n2(a) = true.
% 21.71/3.26 Proof:
% 21.71/3.26 n2(a)
% 21.71/3.26 = { by axiom 9 (rule_137) R->L }
% 21.71/3.26 fresh262(p1(a, b, a), true, a)
% 21.71/3.26 = { by axiom 7 (rule_087) R->L }
% 21.71/3.26 fresh262(fresh325(true, true), true, a)
% 21.71/3.26 = { by axiom 4 (rule_088) R->L }
% 21.71/3.26 fresh262(fresh325(fresh323(true, true), true), true, a)
% 21.71/3.26 = { by axiom 1 (axiom_20) R->L }
% 21.71/3.26 fresh262(fresh325(fresh323(l0(a), true), true), true, a)
% 21.71/3.26 = { by axiom 6 (rule_088) }
% 21.71/3.26 fresh262(fresh325(p1(a, a, a), true), true, a)
% 21.71/3.26 = { by axiom 8 (rule_087) }
% 21.71/3.26 fresh262(fresh324(r0(b), true), true, a)
% 21.71/3.26 = { by axiom 2 (axiom_9) }
% 21.71/3.26 fresh262(fresh324(true, true), true, a)
% 21.71/3.26 = { by axiom 3 (rule_087) }
% 21.71/3.26 fresh262(true, true, a)
% 21.71/3.26 = { by axiom 5 (rule_137) }
% 21.71/3.26 true
% 21.71/3.26 % SZS output end Proof
% 21.71/3.26
% 21.71/3.26 RESULT: Unsatisfiable (the axioms are contradictory).
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