TSTP Solution File: SYN125-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN125-1 : 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 03:33:16 EDT 2023
% Result : Unsatisfiable 13.46s 2.15s
% Output : Proof 13.46s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SYN125-1 : TPTP v8.1.2. Released v1.1.0.
% 0.00/0.15 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.16/0.36 % Computer : n031.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Sat Aug 26 20:44:38 EDT 2023
% 0.16/0.37 % CPUTime :
% 13.46/2.15 Command-line arguments: --ground-connectedness --complete-subsets
% 13.46/2.15
% 13.46/2.15 % SZS status Unsatisfiable
% 13.46/2.15
% 13.46/2.16 % SZS output start Proof
% 13.46/2.16 Take the following subset of the input axioms:
% 13.46/2.16 fof(axiom_13, axiom, r0(e)).
% 13.46/2.16 fof(axiom_24, axiom, l0(c)).
% 13.46/2.16 fof(axiom_28, axiom, k0(e)).
% 13.46/2.16 fof(prove_this, negated_conjecture, ~l3(e, c)).
% 13.46/2.16 fof(rule_021, axiom, ![I, J]: (m1(I, J, I) | (~l0(I) | ~k0(J)))).
% 13.46/2.16 fof(rule_176, axiom, ![D, E]: (p2(D, E, D) | ~m1(E, D, E))).
% 13.46/2.16 fof(rule_215, axiom, ![G, H]: (l3(G, H) | (~r0(G) | ~p2(G, H, G)))).
% 13.46/2.16
% 13.46/2.16 Now clausify the problem and encode Horn clauses using encoding 3 of
% 13.46/2.16 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 13.46/2.16 We repeatedly replace C & s=t => u=v by the two clauses:
% 13.46/2.16 fresh(y, y, x1...xn) = u
% 13.46/2.16 C => fresh(s, t, x1...xn) = v
% 13.46/2.16 where fresh is a fresh function symbol and x1..xn are the free
% 13.46/2.16 variables of u and v.
% 13.46/2.16 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 13.46/2.16 input problem has no model of domain size 1).
% 13.46/2.16
% 13.46/2.16 The encoding turns the above axioms into the following unit equations and goals:
% 13.46/2.16
% 13.46/2.16 Axiom 1 (axiom_28): k0(e) = true.
% 13.46/2.16 Axiom 2 (axiom_24): l0(c) = true.
% 13.46/2.16 Axiom 3 (axiom_13): r0(e) = true.
% 13.46/2.16 Axiom 4 (rule_021): fresh415(X, X, Y, Z) = m1(Y, Z, Y).
% 13.46/2.16 Axiom 5 (rule_021): fresh414(X, X, Y, Z) = true.
% 13.46/2.16 Axiom 6 (rule_176): fresh208(X, X, Y, Z) = true.
% 13.46/2.16 Axiom 7 (rule_215): fresh160(X, X, Y, Z) = l3(Y, Z).
% 13.46/2.16 Axiom 8 (rule_215): fresh159(X, X, Y, Z) = true.
% 13.46/2.16 Axiom 9 (rule_021): fresh415(k0(X), true, Y, X) = fresh414(l0(Y), true, Y, X).
% 13.46/2.16 Axiom 10 (rule_176): fresh208(m1(X, Y, X), true, Y, X) = p2(Y, X, Y).
% 13.46/2.16 Axiom 11 (rule_215): fresh160(p2(X, Y, X), true, X, Y) = fresh159(r0(X), true, X, Y).
% 13.46/2.16
% 13.46/2.16 Goal 1 (prove_this): l3(e, c) = true.
% 13.46/2.16 Proof:
% 13.46/2.16 l3(e, c)
% 13.46/2.16 = { by axiom 7 (rule_215) R->L }
% 13.46/2.16 fresh160(true, true, e, c)
% 13.46/2.16 = { by axiom 6 (rule_176) R->L }
% 13.46/2.16 fresh160(fresh208(true, true, e, c), true, e, c)
% 13.46/2.16 = { by axiom 5 (rule_021) R->L }
% 13.46/2.16 fresh160(fresh208(fresh414(true, true, c, e), true, e, c), true, e, c)
% 13.46/2.16 = { by axiom 2 (axiom_24) R->L }
% 13.46/2.16 fresh160(fresh208(fresh414(l0(c), true, c, e), true, e, c), true, e, c)
% 13.46/2.16 = { by axiom 9 (rule_021) R->L }
% 13.46/2.16 fresh160(fresh208(fresh415(k0(e), true, c, e), true, e, c), true, e, c)
% 13.46/2.16 = { by axiom 1 (axiom_28) }
% 13.46/2.16 fresh160(fresh208(fresh415(true, true, c, e), true, e, c), true, e, c)
% 13.46/2.16 = { by axiom 4 (rule_021) }
% 13.46/2.16 fresh160(fresh208(m1(c, e, c), true, e, c), true, e, c)
% 13.46/2.16 = { by axiom 10 (rule_176) }
% 13.46/2.16 fresh160(p2(e, c, e), true, e, c)
% 13.46/2.16 = { by axiom 11 (rule_215) }
% 13.46/2.16 fresh159(r0(e), true, e, c)
% 13.46/2.16 = { by axiom 3 (axiom_13) }
% 13.46/2.16 fresh159(true, true, e, c)
% 13.46/2.16 = { by axiom 8 (rule_215) }
% 13.46/2.16 true
% 13.46/2.16 % SZS output end Proof
% 13.46/2.16
% 13.46/2.16 RESULT: Unsatisfiable (the axioms are contradictory).
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