TSTP Solution File: SYN136-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SYN136-1 : 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 : n001.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 03:33:18 EDT 2023
% Result : Unsatisfiable 15.74s 2.42s
% Output : Proof 15.74s
% 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 : SYN136-1 : TPTP v8.1.2. Released v1.1.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.33 % Computer : n001.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.34 % DateTime : Sat Aug 26 22:19:01 EDT 2023
% 0.14/0.34 % CPUTime :
% 15.74/2.42 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 15.74/2.42
% 15.74/2.42 % SZS status Unsatisfiable
% 15.74/2.42
% 15.74/2.43 % SZS output start Proof
% 15.74/2.43 Take the following subset of the input axioms:
% 15.74/2.43 fof(axiom_19, axiom, ![X, Y]: m0(X, d, Y)).
% 15.74/2.43 fof(prove_this, negated_conjecture, ![X2]: ~m3(X2, a, a)).
% 15.74/2.43 fof(rule_122, axiom, ![G, H]: (q1(G, G, G) | ~m0(G, H, G))).
% 15.74/2.43 fof(rule_154, axiom, ![A2]: (p2(A2, A2, A2) | ~q1(A2, A2, A2))).
% 15.74/2.43 fof(rule_238, axiom, ![I]: (m3(I, I, I) | ~p2(I, I, I))).
% 15.74/2.43
% 15.74/2.43 Now clausify the problem and encode Horn clauses using encoding 3 of
% 15.74/2.43 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 15.74/2.43 We repeatedly replace C & s=t => u=v by the two clauses:
% 15.74/2.43 fresh(y, y, x1...xn) = u
% 15.74/2.43 C => fresh(s, t, x1...xn) = v
% 15.74/2.43 where fresh is a fresh function symbol and x1..xn are the free
% 15.74/2.43 variables of u and v.
% 15.74/2.43 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 15.74/2.43 input problem has no model of domain size 1).
% 15.74/2.43
% 15.74/2.43 The encoding turns the above axioms into the following unit equations and goals:
% 15.74/2.43
% 15.74/2.43 Axiom 1 (axiom_19): m0(X, d, Y) = true2.
% 15.74/2.43 Axiom 2 (rule_122): fresh279(X, X, Y) = true2.
% 15.74/2.43 Axiom 3 (rule_154): fresh241(X, X, Y) = true2.
% 15.74/2.43 Axiom 4 (rule_238): fresh129(X, X, Y) = true2.
% 15.74/2.43 Axiom 5 (rule_122): fresh279(m0(X, Y, X), true2, X) = q1(X, X, X).
% 15.74/2.43 Axiom 6 (rule_154): fresh241(q1(X, X, X), true2, X) = p2(X, X, X).
% 15.74/2.43 Axiom 7 (rule_238): fresh129(p2(X, X, X), true2, X) = m3(X, X, X).
% 15.74/2.43
% 15.74/2.43 Goal 1 (prove_this): m3(X, a, a) = true2.
% 15.74/2.43 The goal is true when:
% 15.74/2.43 X = a
% 15.74/2.43
% 15.74/2.43 Proof:
% 15.74/2.43 m3(a, a, a)
% 15.74/2.43 = { by axiom 7 (rule_238) R->L }
% 15.74/2.43 fresh129(p2(a, a, a), true2, a)
% 15.74/2.43 = { by axiom 6 (rule_154) R->L }
% 15.74/2.43 fresh129(fresh241(q1(a, a, a), true2, a), true2, a)
% 15.74/2.43 = { by axiom 5 (rule_122) R->L }
% 15.74/2.43 fresh129(fresh241(fresh279(m0(a, d, a), true2, a), true2, a), true2, a)
% 15.74/2.43 = { by axiom 1 (axiom_19) }
% 15.74/2.43 fresh129(fresh241(fresh279(true2, true2, a), true2, a), true2, a)
% 15.74/2.43 = { by axiom 2 (rule_122) }
% 15.74/2.43 fresh129(fresh241(true2, true2, a), true2, a)
% 15.74/2.43 = { by axiom 3 (rule_154) }
% 15.74/2.43 fresh129(true2, true2, a)
% 15.74/2.43 = { by axiom 4 (rule_238) }
% 15.74/2.43 true2
% 15.74/2.43 % SZS output end Proof
% 15.74/2.43
% 15.74/2.43 RESULT: Unsatisfiable (the axioms are contradictory).
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