TSTP Solution File: SYN144-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN144-1 : 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 : n020.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 03:33:21 EDT 2023
% Result : Unsatisfiable 37.56s 5.21s
% Output : Proof 37.93s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SYN144-1 : TPTP v8.1.2. Released v1.1.0.
% 0.00/0.14 % 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 : n020.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 17:38:59 EDT 2023
% 0.13/0.35 % CPUTime :
% 37.56/5.21 Command-line arguments: --no-flatten-goal
% 37.56/5.21
% 37.56/5.21 % SZS status Unsatisfiable
% 37.56/5.21
% 37.93/5.21 % SZS output start Proof
% 37.93/5.21 Take the following subset of the input axioms:
% 37.93/5.21 fof(axiom_13, axiom, r0(e)).
% 37.93/5.21 fof(axiom_15, axiom, n0(a, b)).
% 37.93/5.21 fof(axiom_20, axiom, l0(a)).
% 37.93/5.21 fof(axiom_28, axiom, k0(e)).
% 37.93/5.21 fof(prove_this, negated_conjecture, ~m5(e, a)).
% 37.93/5.21 fof(rule_001, axiom, ![I, J]: (k1(I) | ~n0(J, I))).
% 37.93/5.21 fof(rule_021, axiom, ![I2, J2]: (m1(I2, J2, I2) | (~l0(I2) | ~k0(J2)))).
% 37.93/5.21 fof(rule_155, axiom, ![H, I2, J2]: (p2(H, I2, I2) | (~k1(J2) | ~p2(e, H, I2)))).
% 37.93/5.21 fof(rule_176, axiom, ![D, E]: (p2(D, E, D) | ~m1(E, D, E))).
% 37.93/5.21 fof(rule_267, axiom, ![C, B, D2]: (r3(B, C, B) | ~p2(B, D2, C))).
% 37.93/5.21 fof(rule_285, axiom, ![G, H2]: (p4(G, G, H2) | (~r0(G) | ~r3(H2, G, H2)))).
% 37.93/5.21 fof(rule_303, axiom, ![F, D2, E2]: (m5(D2, E2) | (~r0(D2) | ~p4(D2, F, E2)))).
% 37.93/5.21
% 37.93/5.21 Now clausify the problem and encode Horn clauses using encoding 3 of
% 37.93/5.21 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 37.93/5.21 We repeatedly replace C & s=t => u=v by the two clauses:
% 37.93/5.21 fresh(y, y, x1...xn) = u
% 37.93/5.21 C => fresh(s, t, x1...xn) = v
% 37.93/5.21 where fresh is a fresh function symbol and x1..xn are the free
% 37.93/5.21 variables of u and v.
% 37.93/5.22 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 37.93/5.22 input problem has no model of domain size 1).
% 37.93/5.22
% 37.93/5.22 The encoding turns the above axioms into the following unit equations and goals:
% 37.93/5.22
% 37.93/5.22 Axiom 1 (axiom_28): k0(e) = true.
% 37.93/5.22 Axiom 2 (axiom_20): l0(a) = true.
% 37.93/5.22 Axiom 3 (axiom_13): r0(e) = true.
% 37.93/5.22 Axiom 4 (axiom_15): n0(a, b) = true.
% 37.93/5.22 Axiom 5 (rule_001): fresh440(X, X, Y) = true.
% 37.93/5.22 Axiom 6 (rule_021): fresh415(X, X, Y, Z) = m1(Y, Z, Y).
% 37.93/5.22 Axiom 7 (rule_021): fresh414(X, X, Y, Z) = true.
% 37.93/5.22 Axiom 8 (rule_155): fresh239(X, X, Y, Z) = true.
% 37.93/5.22 Axiom 9 (rule_176): fresh208(X, X, Y, Z) = true.
% 37.93/5.22 Axiom 10 (rule_267): fresh88(X, X, Y, Z) = true.
% 37.93/5.22 Axiom 11 (rule_285): fresh66(X, X, Y, Z) = p4(Y, Y, Z).
% 37.93/5.22 Axiom 12 (rule_285): fresh65(X, X, Y, Z) = true.
% 37.93/5.22 Axiom 13 (rule_303): fresh38(X, X, Y, Z) = m5(Y, Z).
% 37.93/5.22 Axiom 14 (rule_303): fresh37(X, X, Y, Z) = true.
% 37.93/5.22 Axiom 15 (rule_001): fresh440(n0(X, Y), true, Y) = k1(Y).
% 37.93/5.22 Axiom 16 (rule_021): fresh415(k0(X), true, Y, X) = fresh414(l0(Y), true, Y, X).
% 37.93/5.22 Axiom 17 (rule_155): fresh240(X, X, Y, Z, W) = p2(Y, Z, Z).
% 37.93/5.22 Axiom 18 (rule_176): fresh208(m1(X, Y, X), true, Y, X) = p2(Y, X, Y).
% 37.93/5.22 Axiom 19 (rule_267): fresh88(p2(X, Y, Z), true, X, Z) = r3(X, Z, X).
% 37.93/5.22 Axiom 20 (rule_285): fresh66(r3(X, Y, X), true, Y, X) = fresh65(r0(Y), true, Y, X).
% 37.93/5.22 Axiom 21 (rule_303): fresh38(p4(X, Y, Z), true, X, Z) = fresh37(r0(X), true, X, Z).
% 37.93/5.22 Axiom 22 (rule_155): fresh240(p2(e, X, Y), true, X, Y, Z) = fresh239(k1(Z), true, X, Y).
% 37.93/5.22
% 37.93/5.22 Goal 1 (prove_this): m5(e, a) = true.
% 37.93/5.22 Proof:
% 37.93/5.22 m5(e, a)
% 37.93/5.22 = { by axiom 13 (rule_303) R->L }
% 37.93/5.22 fresh38(true, true, e, a)
% 37.93/5.22 = { by axiom 12 (rule_285) R->L }
% 37.93/5.22 fresh38(fresh65(true, true, e, a), true, e, a)
% 37.93/5.22 = { by axiom 3 (axiom_13) R->L }
% 37.93/5.22 fresh38(fresh65(r0(e), true, e, a), true, e, a)
% 37.93/5.22 = { by axiom 20 (rule_285) R->L }
% 37.93/5.22 fresh38(fresh66(r3(a, e, a), true, e, a), true, e, a)
% 37.93/5.22 = { by axiom 19 (rule_267) R->L }
% 37.93/5.22 fresh38(fresh66(fresh88(p2(a, e, e), true, a, e), true, e, a), true, e, a)
% 37.93/5.22 = { by axiom 17 (rule_155) R->L }
% 37.93/5.22 fresh38(fresh66(fresh88(fresh240(true, true, a, e, b), true, a, e), true, e, a), true, e, a)
% 37.93/5.22 = { by axiom 9 (rule_176) R->L }
% 37.93/5.22 fresh38(fresh66(fresh88(fresh240(fresh208(true, true, e, a), true, a, e, b), true, a, e), true, e, a), true, e, a)
% 37.93/5.22 = { by axiom 7 (rule_021) R->L }
% 37.93/5.22 fresh38(fresh66(fresh88(fresh240(fresh208(fresh414(true, true, a, e), true, e, a), true, a, e, b), true, a, e), true, e, a), true, e, a)
% 37.93/5.22 = { by axiom 2 (axiom_20) R->L }
% 37.93/5.22 fresh38(fresh66(fresh88(fresh240(fresh208(fresh414(l0(a), true, a, e), true, e, a), true, a, e, b), true, a, e), true, e, a), true, e, a)
% 37.93/5.22 = { by axiom 16 (rule_021) R->L }
% 37.93/5.22 fresh38(fresh66(fresh88(fresh240(fresh208(fresh415(k0(e), true, a, e), true, e, a), true, a, e, b), true, a, e), true, e, a), true, e, a)
% 37.93/5.22 = { by axiom 1 (axiom_28) }
% 37.93/5.22 fresh38(fresh66(fresh88(fresh240(fresh208(fresh415(true, true, a, e), true, e, a), true, a, e, b), true, a, e), true, e, a), true, e, a)
% 37.93/5.22 = { by axiom 6 (rule_021) }
% 37.93/5.22 fresh38(fresh66(fresh88(fresh240(fresh208(m1(a, e, a), true, e, a), true, a, e, b), true, a, e), true, e, a), true, e, a)
% 37.93/5.22 = { by axiom 18 (rule_176) }
% 37.93/5.22 fresh38(fresh66(fresh88(fresh240(p2(e, a, e), true, a, e, b), true, a, e), true, e, a), true, e, a)
% 37.93/5.22 = { by axiom 22 (rule_155) }
% 37.93/5.22 fresh38(fresh66(fresh88(fresh239(k1(b), true, a, e), true, a, e), true, e, a), true, e, a)
% 37.93/5.22 = { by axiom 15 (rule_001) R->L }
% 37.93/5.22 fresh38(fresh66(fresh88(fresh239(fresh440(n0(a, b), true, b), true, a, e), true, a, e), true, e, a), true, e, a)
% 37.93/5.22 = { by axiom 4 (axiom_15) }
% 37.93/5.22 fresh38(fresh66(fresh88(fresh239(fresh440(true, true, b), true, a, e), true, a, e), true, e, a), true, e, a)
% 37.93/5.22 = { by axiom 5 (rule_001) }
% 37.93/5.22 fresh38(fresh66(fresh88(fresh239(true, true, a, e), true, a, e), true, e, a), true, e, a)
% 37.93/5.22 = { by axiom 8 (rule_155) }
% 37.93/5.22 fresh38(fresh66(fresh88(true, true, a, e), true, e, a), true, e, a)
% 37.93/5.22 = { by axiom 10 (rule_267) }
% 37.93/5.22 fresh38(fresh66(true, true, e, a), true, e, a)
% 37.93/5.22 = { by axiom 11 (rule_285) }
% 37.93/5.22 fresh38(p4(e, e, a), true, e, a)
% 37.93/5.22 = { by axiom 21 (rule_303) }
% 37.93/5.22 fresh37(r0(e), true, e, a)
% 37.93/5.22 = { by axiom 3 (axiom_13) }
% 37.93/5.22 fresh37(true, true, e, a)
% 37.93/5.22 = { by axiom 14 (rule_303) }
% 37.93/5.22 true
% 37.93/5.22 % SZS output end Proof
% 37.93/5.22
% 37.93/5.22 RESULT: Unsatisfiable (the axioms are contradictory).
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