TSTP Solution File: SYN123-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN123-1 : 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 : n011.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 03:33:15 EDT 2023
% Result : Unsatisfiable 25.08s 3.57s
% Output : Proof 25.08s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SYN123-1 : TPTP v8.1.2. Released v1.1.0.
% 0.08/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.36 % Computer : n011.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sat Aug 26 21:17:09 EDT 2023
% 0.14/0.36 % CPUTime :
% 25.08/3.57 Command-line arguments: --no-flatten-goal
% 25.08/3.57
% 25.08/3.57 % SZS status Unsatisfiable
% 25.08/3.57
% 25.08/3.57 % SZS output start Proof
% 25.08/3.57 Take the following subset of the input axioms:
% 25.08/3.57 fof(axiom_14, axiom, ![X]: p0(b, X)).
% 25.08/3.57 fof(axiom_19, axiom, ![Y, X2]: m0(X2, d, Y)).
% 25.08/3.57 fof(axiom_5, axiom, s0(b)).
% 25.08/3.57 fof(prove_this, negated_conjecture, ~l2(d, d)).
% 25.08/3.57 fof(rule_029, axiom, ![I, H]: (m1(H, I, H) | (~p0(H, I) | ~s0(H)))).
% 25.08/3.57 fof(rule_134, axiom, ![G, I2, H2]: (l2(G, G) | (~m0(H2, G, I2) | (~m1(I2, H2, H2) | ~p0(H2, G))))).
% 25.08/3.57
% 25.08/3.57 Now clausify the problem and encode Horn clauses using encoding 3 of
% 25.08/3.57 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 25.08/3.57 We repeatedly replace C & s=t => u=v by the two clauses:
% 25.08/3.57 fresh(y, y, x1...xn) = u
% 25.08/3.57 C => fresh(s, t, x1...xn) = v
% 25.08/3.57 where fresh is a fresh function symbol and x1..xn are the free
% 25.08/3.57 variables of u and v.
% 25.08/3.57 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 25.08/3.57 input problem has no model of domain size 1).
% 25.08/3.57
% 25.08/3.57 The encoding turns the above axioms into the following unit equations and goals:
% 25.08/3.57
% 25.08/3.57 Axiom 1 (axiom_5): s0(b) = true.
% 25.08/3.57 Axiom 2 (axiom_14): p0(b, X) = true.
% 25.08/3.57 Axiom 3 (rule_134): fresh583(X, X, Y) = true.
% 25.08/3.58 Axiom 4 (axiom_19): m0(X, d, Y) = true.
% 25.08/3.58 Axiom 5 (rule_029): fresh404(X, X, Y, Z) = m1(Y, Z, Y).
% 25.08/3.58 Axiom 6 (rule_029): fresh403(X, X, Y, Z) = true.
% 25.08/3.58 Axiom 7 (rule_134): fresh266(X, X, Y, Z, W) = l2(Y, Y).
% 25.08/3.58 Axiom 8 (rule_134): fresh582(X, X, Y, Z, W) = fresh583(m0(Z, Y, W), true, Y).
% 25.08/3.58 Axiom 9 (rule_029): fresh404(p0(X, Y), true, X, Y) = fresh403(s0(X), true, X, Y).
% 25.08/3.58 Axiom 10 (rule_134): fresh582(m1(X, Y, Y), true, Z, Y, X) = fresh266(p0(Y, Z), true, Z, Y, X).
% 25.08/3.58
% 25.08/3.58 Goal 1 (prove_this): l2(d, d) = true.
% 25.08/3.58 Proof:
% 25.08/3.58 l2(d, d)
% 25.08/3.58 = { by axiom 7 (rule_134) R->L }
% 25.08/3.58 fresh266(true, true, d, b, b)
% 25.08/3.58 = { by axiom 2 (axiom_14) R->L }
% 25.08/3.58 fresh266(p0(b, d), true, d, b, b)
% 25.08/3.58 = { by axiom 10 (rule_134) R->L }
% 25.08/3.58 fresh582(m1(b, b, b), true, d, b, b)
% 25.08/3.58 = { by axiom 5 (rule_029) R->L }
% 25.08/3.58 fresh582(fresh404(true, true, b, b), true, d, b, b)
% 25.08/3.58 = { by axiom 2 (axiom_14) R->L }
% 25.08/3.58 fresh582(fresh404(p0(b, b), true, b, b), true, d, b, b)
% 25.08/3.58 = { by axiom 9 (rule_029) }
% 25.08/3.58 fresh582(fresh403(s0(b), true, b, b), true, d, b, b)
% 25.08/3.58 = { by axiom 1 (axiom_5) }
% 25.08/3.58 fresh582(fresh403(true, true, b, b), true, d, b, b)
% 25.08/3.58 = { by axiom 6 (rule_029) }
% 25.08/3.58 fresh582(true, true, d, b, b)
% 25.08/3.58 = { by axiom 8 (rule_134) }
% 25.08/3.58 fresh583(m0(b, d, b), true, d)
% 25.08/3.58 = { by axiom 4 (axiom_19) }
% 25.08/3.58 fresh583(true, true, d)
% 25.08/3.58 = { by axiom 3 (rule_134) }
% 25.08/3.58 true
% 25.08/3.58 % SZS output end Proof
% 25.08/3.58
% 25.08/3.58 RESULT: Unsatisfiable (the axioms are contradictory).
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