TSTP Solution File: SYN294-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SYN294-1 : 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 03:33:57 EDT 2023
% Result : Unsatisfiable 23.14s 3.42s
% Output : Proof 23.14s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SYN294-1 : TPTP v8.1.2. Released v1.1.0.
% 0.12/0.14 % 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 : n031.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 21:43:38 EDT 2023
% 0.13/0.35 % CPUTime :
% 23.14/3.42 Command-line arguments: --no-flatten-goal
% 23.14/3.42
% 23.14/3.42 % SZS status Unsatisfiable
% 23.14/3.42
% 23.14/3.42 % SZS output start Proof
% 23.14/3.42 Take the following subset of the input axioms:
% 23.14/3.42 fof(axiom_14, axiom, ![X]: p0(b, X)).
% 23.14/3.42 fof(axiom_17, axiom, ![X2]: q0(X2, d)).
% 23.14/3.42 fof(axiom_34, axiom, n0(c, d)).
% 23.14/3.42 fof(prove_this, negated_conjecture, ~q1(d, d, c)).
% 23.14/3.42 fof(rule_001, axiom, ![I, J]: (k1(I) | ~n0(J, I))).
% 23.14/3.42 fof(rule_109, axiom, ![G, E, F]: (q1(E, E, F) | (~p0(G, G) | (~q0(F, E) | ~k1(E))))).
% 23.14/3.42
% 23.14/3.42 Now clausify the problem and encode Horn clauses using encoding 3 of
% 23.14/3.42 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 23.14/3.42 We repeatedly replace C & s=t => u=v by the two clauses:
% 23.14/3.42 fresh(y, y, x1...xn) = u
% 23.14/3.42 C => fresh(s, t, x1...xn) = v
% 23.14/3.42 where fresh is a fresh function symbol and x1..xn are the free
% 23.14/3.42 variables of u and v.
% 23.14/3.42 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 23.14/3.42 input problem has no model of domain size 1).
% 23.14/3.42
% 23.14/3.42 The encoding turns the above axioms into the following unit equations and goals:
% 23.14/3.42
% 23.14/3.42 Axiom 1 (axiom_34): n0(c, d) = true.
% 23.14/3.42 Axiom 2 (axiom_17): q0(X, d) = true.
% 23.14/3.42 Axiom 3 (axiom_14): p0(b, X) = true.
% 23.14/3.42 Axiom 4 (rule_001): fresh440(X, X, Y) = true.
% 23.14/3.42 Axiom 5 (rule_109): fresh597(X, X, Y, Z) = true.
% 23.14/3.42 Axiom 6 (rule_109): fresh298(X, X, Y, Z) = q1(Y, Y, Z).
% 23.14/3.42 Axiom 7 (rule_001): fresh440(n0(X, Y), true, Y) = k1(Y).
% 23.14/3.42 Axiom 8 (rule_109): fresh596(X, X, Y, Z, W) = fresh597(q0(Z, Y), true, Y, Z).
% 23.14/3.42 Axiom 9 (rule_109): fresh596(k1(X), true, X, Y, Z) = fresh298(p0(Z, Z), true, X, Y).
% 23.14/3.42
% 23.14/3.42 Goal 1 (prove_this): q1(d, d, c) = true.
% 23.14/3.42 Proof:
% 23.14/3.42 q1(d, d, c)
% 23.14/3.42 = { by axiom 6 (rule_109) R->L }
% 23.14/3.42 fresh298(true, true, d, c)
% 23.14/3.42 = { by axiom 3 (axiom_14) R->L }
% 23.14/3.42 fresh298(p0(b, b), true, d, c)
% 23.14/3.42 = { by axiom 9 (rule_109) R->L }
% 23.14/3.42 fresh596(k1(d), true, d, c, b)
% 23.14/3.42 = { by axiom 7 (rule_001) R->L }
% 23.14/3.42 fresh596(fresh440(n0(c, d), true, d), true, d, c, b)
% 23.14/3.42 = { by axiom 1 (axiom_34) }
% 23.14/3.42 fresh596(fresh440(true, true, d), true, d, c, b)
% 23.14/3.42 = { by axiom 4 (rule_001) }
% 23.14/3.42 fresh596(true, true, d, c, b)
% 23.14/3.42 = { by axiom 8 (rule_109) }
% 23.14/3.42 fresh597(q0(c, d), true, d, c)
% 23.14/3.42 = { by axiom 2 (axiom_17) }
% 23.14/3.42 fresh597(true, true, d, c)
% 23.14/3.42 = { by axiom 5 (rule_109) }
% 23.14/3.42 true
% 23.14/3.42 % SZS output end Proof
% 23.14/3.42
% 23.14/3.42 RESULT: Unsatisfiable (the axioms are contradictory).
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