TSTP Solution File: SYN227-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN227-1 : 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 03:33:41 EDT 2023
% Result : Unsatisfiable 16.99s 2.63s
% Output : Proof 16.99s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SYN227-1 : TPTP v8.1.2. Released v1.1.0.
% 0.11/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35 % Computer : n031.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Aug 26 19:13:23 EDT 2023
% 0.14/0.35 % CPUTime :
% 16.99/2.63 Command-line arguments: --no-flatten-goal
% 16.99/2.63
% 16.99/2.63 % SZS status Unsatisfiable
% 16.99/2.63
% 16.99/2.63 % SZS output start Proof
% 16.99/2.63 Take the following subset of the input axioms:
% 16.99/2.63 fof(axiom_24, axiom, l0(c)).
% 16.99/2.63 fof(axiom_32, axiom, k0(b)).
% 16.99/2.63 fof(axiom_9, axiom, r0(b)).
% 16.99/2.63 fof(prove_this, negated_conjecture, ~l3(b, c)).
% 16.99/2.63 fof(rule_021, axiom, ![I, J]: (m1(I, J, I) | (~l0(I) | ~k0(J)))).
% 16.99/2.63 fof(rule_176, axiom, ![D, E]: (p2(D, E, D) | ~m1(E, D, E))).
% 16.99/2.63 fof(rule_215, axiom, ![G, H]: (l3(G, H) | (~r0(G) | ~p2(G, H, G)))).
% 16.99/2.63
% 16.99/2.63 Now clausify the problem and encode Horn clauses using encoding 3 of
% 16.99/2.63 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 16.99/2.63 We repeatedly replace C & s=t => u=v by the two clauses:
% 16.99/2.63 fresh(y, y, x1...xn) = u
% 16.99/2.63 C => fresh(s, t, x1...xn) = v
% 16.99/2.63 where fresh is a fresh function symbol and x1..xn are the free
% 16.99/2.63 variables of u and v.
% 16.99/2.63 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 16.99/2.63 input problem has no model of domain size 1).
% 16.99/2.63
% 16.99/2.63 The encoding turns the above axioms into the following unit equations and goals:
% 16.99/2.63
% 16.99/2.63 Axiom 1 (axiom_32): k0(b) = true.
% 16.99/2.63 Axiom 2 (axiom_24): l0(c) = true.
% 16.99/2.63 Axiom 3 (axiom_9): r0(b) = true.
% 16.99/2.63 Axiom 4 (rule_021): fresh415(X, X, Y, Z) = m1(Y, Z, Y).
% 16.99/2.63 Axiom 5 (rule_021): fresh414(X, X, Y, Z) = true.
% 16.99/2.63 Axiom 6 (rule_176): fresh208(X, X, Y, Z) = true.
% 16.99/2.64 Axiom 7 (rule_215): fresh160(X, X, Y, Z) = l3(Y, Z).
% 16.99/2.64 Axiom 8 (rule_215): fresh159(X, X, Y, Z) = true.
% 16.99/2.64 Axiom 9 (rule_021): fresh415(k0(X), true, Y, X) = fresh414(l0(Y), true, Y, X).
% 16.99/2.64 Axiom 10 (rule_176): fresh208(m1(X, Y, X), true, Y, X) = p2(Y, X, Y).
% 16.99/2.64 Axiom 11 (rule_215): fresh160(p2(X, Y, X), true, X, Y) = fresh159(r0(X), true, X, Y).
% 16.99/2.64
% 16.99/2.64 Goal 1 (prove_this): l3(b, c) = true.
% 16.99/2.64 Proof:
% 16.99/2.64 l3(b, c)
% 16.99/2.64 = { by axiom 7 (rule_215) R->L }
% 16.99/2.64 fresh160(true, true, b, c)
% 16.99/2.64 = { by axiom 6 (rule_176) R->L }
% 16.99/2.64 fresh160(fresh208(true, true, b, c), true, b, c)
% 16.99/2.64 = { by axiom 5 (rule_021) R->L }
% 16.99/2.64 fresh160(fresh208(fresh414(true, true, c, b), true, b, c), true, b, c)
% 16.99/2.64 = { by axiom 2 (axiom_24) R->L }
% 16.99/2.64 fresh160(fresh208(fresh414(l0(c), true, c, b), true, b, c), true, b, c)
% 16.99/2.64 = { by axiom 9 (rule_021) R->L }
% 16.99/2.64 fresh160(fresh208(fresh415(k0(b), true, c, b), true, b, c), true, b, c)
% 16.99/2.64 = { by axiom 1 (axiom_32) }
% 16.99/2.64 fresh160(fresh208(fresh415(true, true, c, b), true, b, c), true, b, c)
% 16.99/2.64 = { by axiom 4 (rule_021) }
% 16.99/2.64 fresh160(fresh208(m1(c, b, c), true, b, c), true, b, c)
% 16.99/2.64 = { by axiom 10 (rule_176) }
% 16.99/2.64 fresh160(p2(b, c, b), true, b, c)
% 16.99/2.64 = { by axiom 11 (rule_215) }
% 16.99/2.64 fresh159(r0(b), true, b, c)
% 16.99/2.64 = { by axiom 3 (axiom_9) }
% 16.99/2.64 fresh159(true, true, b, c)
% 16.99/2.64 = { by axiom 8 (rule_215) }
% 16.99/2.64 true
% 16.99/2.64 % SZS output end Proof
% 16.99/2.64
% 16.99/2.64 RESULT: Unsatisfiable (the axioms are contradictory).
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