TSTP Solution File: SYN285-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN285-1 : 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 03:33:55 EDT 2023
% Result : Unsatisfiable 24.67s 3.53s
% Output : Proof 24.67s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.12 % Problem : SYN285-1 : TPTP v8.1.2. Released v1.1.0.
% 0.13/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34 % Computer : n031.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sat Aug 26 18:30:23 EDT 2023
% 0.14/0.34 % CPUTime :
% 24.67/3.53 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 24.67/3.53
% 24.67/3.53 % SZS status Unsatisfiable
% 24.67/3.53
% 24.67/3.53 % SZS output start Proof
% 24.67/3.53 Take the following subset of the input axioms:
% 24.67/3.53 fof(axiom_1, axiom, s0(d)).
% 24.67/3.53 fof(axiom_14, axiom, ![X]: p0(b, X)).
% 24.67/3.53 fof(axiom_20, axiom, l0(a)).
% 24.67/3.53 fof(axiom_32, axiom, k0(b)).
% 24.67/3.53 fof(prove_this, negated_conjecture, ~q1(a, d, d)).
% 24.67/3.53 fof(rule_099, axiom, ![G, E, F]: (q1(E, F, F) | (~k0(G) | (~l0(E) | ~q1(F, F, G))))).
% 24.67/3.53 fof(rule_105, axiom, ![C, D]: (q1(C, C, D) | (~s0(C) | ~p0(D, d)))).
% 24.67/3.53
% 24.67/3.53 Now clausify the problem and encode Horn clauses using encoding 3 of
% 24.67/3.53 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 24.67/3.53 We repeatedly replace C & s=t => u=v by the two clauses:
% 24.67/3.53 fresh(y, y, x1...xn) = u
% 24.67/3.53 C => fresh(s, t, x1...xn) = v
% 24.67/3.53 where fresh is a fresh function symbol and x1..xn are the free
% 24.67/3.53 variables of u and v.
% 24.67/3.53 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 24.67/3.53 input problem has no model of domain size 1).
% 24.67/3.53
% 24.67/3.53 The encoding turns the above axioms into the following unit equations and goals:
% 24.67/3.53
% 24.67/3.54 Axiom 1 (axiom_14): p0(b, X) = true.
% 24.67/3.54 Axiom 2 (axiom_1): s0(d) = true.
% 24.67/3.54 Axiom 3 (axiom_20): l0(a) = true.
% 24.67/3.54 Axiom 4 (axiom_32): k0(b) = true.
% 24.67/3.54 Axiom 5 (rule_099): fresh607(X, X, Y, Z) = true.
% 24.67/3.54 Axiom 6 (rule_099): fresh310(X, X, Y, Z) = q1(Y, Z, Z).
% 24.67/3.54 Axiom 7 (rule_105): fresh304(X, X, Y, Z) = q1(Y, Y, Z).
% 24.67/3.54 Axiom 8 (rule_105): fresh303(X, X, Y, Z) = true.
% 24.67/3.54 Axiom 9 (rule_099): fresh606(X, X, Y, Z, W) = fresh607(l0(Y), true, Y, Z).
% 24.67/3.54 Axiom 10 (rule_105): fresh304(p0(X, d), true, Y, X) = fresh303(s0(Y), true, Y, X).
% 24.67/3.54 Axiom 11 (rule_099): fresh606(q1(X, X, Y), true, Z, X, Y) = fresh310(k0(Y), true, Z, X).
% 24.67/3.54
% 24.67/3.54 Goal 1 (prove_this): q1(a, d, d) = true.
% 24.67/3.54 Proof:
% 24.67/3.54 q1(a, d, d)
% 24.67/3.54 = { by axiom 6 (rule_099) R->L }
% 24.67/3.54 fresh310(true, true, a, d)
% 24.67/3.54 = { by axiom 4 (axiom_32) R->L }
% 24.67/3.54 fresh310(k0(b), true, a, d)
% 24.67/3.54 = { by axiom 11 (rule_099) R->L }
% 24.67/3.54 fresh606(q1(d, d, b), true, a, d, b)
% 24.67/3.54 = { by axiom 7 (rule_105) R->L }
% 24.67/3.54 fresh606(fresh304(true, true, d, b), true, a, d, b)
% 24.67/3.54 = { by axiom 1 (axiom_14) R->L }
% 24.67/3.54 fresh606(fresh304(p0(b, d), true, d, b), true, a, d, b)
% 24.67/3.54 = { by axiom 10 (rule_105) }
% 24.67/3.54 fresh606(fresh303(s0(d), true, d, b), true, a, d, b)
% 24.67/3.54 = { by axiom 2 (axiom_1) }
% 24.67/3.54 fresh606(fresh303(true, true, d, b), true, a, d, b)
% 24.67/3.54 = { by axiom 8 (rule_105) }
% 24.67/3.54 fresh606(true, true, a, d, b)
% 24.67/3.54 = { by axiom 9 (rule_099) }
% 24.67/3.54 fresh607(l0(a), true, a, d)
% 24.67/3.54 = { by axiom 3 (axiom_20) }
% 24.67/3.54 fresh607(true, true, a, d)
% 24.67/3.54 = { by axiom 5 (rule_099) }
% 24.67/3.54 true
% 24.67/3.54 % SZS output end Proof
% 24.67/3.54
% 24.67/3.54 RESULT: Unsatisfiable (the axioms are contradictory).
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