TSTP Solution File: SYN213-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN213-1 : 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 : n029.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 03:33:37 EDT 2023
% Result : Unsatisfiable 22.20s 3.20s
% Output : Proof 22.32s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SYN213-1 : 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
% 0.17/0.35 % Computer : n029.cluster.edu
% 0.17/0.35 % Model : x86_64 x86_64
% 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35 % Memory : 8042.1875MB
% 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35 % CPULimit : 300
% 0.17/0.35 % WCLimit : 300
% 0.17/0.35 % DateTime : Sat Aug 26 20:05:40 EDT 2023
% 0.17/0.35 % CPUTime :
% 22.20/3.20 Command-line arguments: --no-flatten-goal
% 22.20/3.20
% 22.20/3.20 % SZS status Unsatisfiable
% 22.20/3.20
% 22.32/3.22 % SZS output start Proof
% 22.32/3.22 Take the following subset of the input axioms:
% 22.32/3.22 fof(axiom_14, axiom, ![X]: p0(b, X)).
% 22.32/3.22 fof(axiom_19, axiom, ![Y, X2]: m0(X2, d, Y)).
% 22.32/3.22 fof(axiom_30, axiom, n0(e, e)).
% 22.32/3.22 fof(axiom_34, axiom, n0(c, d)).
% 22.32/3.22 fof(axiom_5, axiom, s0(b)).
% 22.32/3.22 fof(prove_this, negated_conjecture, ~s5(b)).
% 22.32/3.22 fof(rule_001, axiom, ![I, J]: (k1(I) | ~n0(J, I))).
% 22.32/3.22 fof(rule_029, axiom, ![H, I2]: (m1(H, I2, H) | (~p0(H, I2) | ~s0(H)))).
% 22.32/3.22 fof(rule_036, axiom, ![B, A2]: (n1(A2, A2, B) | ~m0(b, B, A2))).
% 22.32/3.22 fof(rule_110, axiom, ![C, D, B2]: (q1(B2, B2, B2) | ~m0(C, D, B2))).
% 22.32/3.22 fof(rule_154, axiom, ![A2_2]: (p2(A2_2, A2_2, A2_2) | ~q1(A2_2, A2_2, A2_2))).
% 22.32/3.22 fof(rule_176, axiom, ![E, D2]: (p2(D2, E, D2) | ~m1(E, D2, E))).
% 22.32/3.22 fof(rule_179, axiom, ![J2, A2_2]: (q2(J2, J2, J2) | (~k1(A2_2) | ~n1(J2, J2, A2_2)))).
% 22.32/3.22 fof(rule_240, axiom, ![F, D2, E2]: (n3(D2) | ~p2(E2, F, D2))).
% 22.32/3.22 fof(rule_248, axiom, ![I2, J2]: (p3(I2, I2, I2) | (~p2(J2, I2, I2) | ~n3(I2)))).
% 22.32/3.22 fof(rule_255, axiom, ![G, I2, H2]: (q3(G, H2) | (~q2(I2, G, H2) | ~n0(I2, G)))).
% 22.32/3.22 fof(rule_277, axiom, ![A, J2, B2]: (l4(J2) | ~p3(A, B2, J2))).
% 22.32/3.22 fof(rule_298, axiom, ![I2, H2, J2, G2]: (r4(G2) | (~n3(G2) | (~q3(H2, I2) | ~p0(J2, G2))))).
% 22.32/3.22 fof(rule_329, axiom, ![I2, H2]: (s5(H2) | (~l4(H2) | ~r4(I2)))).
% 22.32/3.22
% 22.32/3.22 Now clausify the problem and encode Horn clauses using encoding 3 of
% 22.32/3.22 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 22.32/3.22 We repeatedly replace C & s=t => u=v by the two clauses:
% 22.32/3.22 fresh(y, y, x1...xn) = u
% 22.32/3.22 C => fresh(s, t, x1...xn) = v
% 22.32/3.22 where fresh is a fresh function symbol and x1..xn are the free
% 22.32/3.22 variables of u and v.
% 22.32/3.22 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 22.32/3.22 input problem has no model of domain size 1).
% 22.32/3.22
% 22.32/3.22 The encoding turns the above axioms into the following unit equations and goals:
% 22.32/3.22
% 22.32/3.22 Axiom 1 (axiom_5): s0(b) = true.
% 22.32/3.22 Axiom 2 (axiom_34): n0(c, d) = true.
% 22.32/3.22 Axiom 3 (axiom_30): n0(e, e) = true.
% 22.32/3.22 Axiom 4 (axiom_14): p0(b, X) = true.
% 22.32/3.22 Axiom 5 (rule_329): fresh(X, X, Y) = true.
% 22.32/3.22 Axiom 6 (rule_298): fresh459(X, X, Y) = true.
% 22.32/3.22 Axiom 7 (rule_001): fresh440(X, X, Y) = true.
% 22.32/3.22 Axiom 8 (rule_110): fresh297(X, X, Y) = true.
% 22.32/3.22 Axiom 9 (rule_154): fresh241(X, X, Y) = true.
% 22.32/3.22 Axiom 10 (rule_179): fresh202(X, X, Y) = true.
% 22.32/3.22 Axiom 11 (rule_240): fresh127(X, X, Y) = true.
% 22.32/3.22 Axiom 12 (rule_248): fresh116(X, X, Y) = true.
% 22.32/3.22 Axiom 13 (rule_277): fresh79(X, X, Y) = true.
% 22.32/3.22 Axiom 14 (rule_329): fresh2(X, X, Y) = s5(Y).
% 22.32/3.22 Axiom 15 (axiom_19): m0(X, d, Y) = true.
% 22.32/3.22 Axiom 16 (rule_029): fresh404(X, X, Y, Z) = m1(Y, Z, Y).
% 22.32/3.22 Axiom 17 (rule_029): fresh403(X, X, Y, Z) = true.
% 22.32/3.22 Axiom 18 (rule_036): fresh394(X, X, Y, Z) = true.
% 22.32/3.22 Axiom 19 (rule_176): fresh208(X, X, Y, Z) = true.
% 22.32/3.22 Axiom 20 (rule_179): fresh203(X, X, Y, Z) = q2(Y, Y, Y).
% 22.32/3.22 Axiom 21 (rule_248): fresh117(X, X, Y, Z) = p3(Y, Y, Y).
% 22.32/3.22 Axiom 22 (rule_255): fresh103(X, X, Y, Z) = true.
% 22.32/3.22 Axiom 23 (rule_298): fresh47(X, X, Y, Z) = r4(Y).
% 22.32/3.22 Axiom 24 (rule_329): fresh2(r4(X), true, Y) = fresh(l4(Y), true, Y).
% 22.32/3.22 Axiom 25 (rule_298): fresh458(X, X, Y, Z) = fresh459(p0(Z, Y), true, Y).
% 22.32/3.22 Axiom 26 (rule_001): fresh440(n0(X, Y), true, Y) = k1(Y).
% 22.32/3.22 Axiom 27 (rule_255): fresh104(X, X, Y, Z, W) = q3(Y, Z).
% 22.32/3.22 Axiom 28 (rule_298): fresh458(q3(X, Y), true, Z, W) = fresh47(n3(Z), true, Z, W).
% 22.32/3.22 Axiom 29 (rule_029): fresh404(p0(X, Y), true, X, Y) = fresh403(s0(X), true, X, Y).
% 22.32/3.22 Axiom 30 (rule_110): fresh297(m0(X, Y, Z), true, Z) = q1(Z, Z, Z).
% 22.32/3.22 Axiom 31 (rule_154): fresh241(q1(X, X, X), true, X) = p2(X, X, X).
% 22.32/3.22 Axiom 32 (rule_240): fresh127(p2(X, Y, Z), true, Z) = n3(Z).
% 22.32/3.22 Axiom 33 (rule_248): fresh117(n3(X), true, X, Y) = fresh116(p2(Y, X, X), true, X).
% 22.32/3.22 Axiom 34 (rule_277): fresh79(p3(X, Y, Z), true, Z) = l4(Z).
% 22.32/3.22 Axiom 35 (rule_036): fresh394(m0(b, X, Y), true, Y, X) = n1(Y, Y, X).
% 22.32/3.22 Axiom 36 (rule_176): fresh208(m1(X, Y, X), true, Y, X) = p2(Y, X, Y).
% 22.32/3.22 Axiom 37 (rule_179): fresh203(n1(X, X, Y), true, X, Y) = fresh202(k1(Y), true, X).
% 22.32/3.22 Axiom 38 (rule_255): fresh104(q2(X, Y, Z), true, Y, Z, X) = fresh103(n0(X, Y), true, Y, Z).
% 22.32/3.22
% 22.32/3.22 Lemma 39: n3(X) = true.
% 22.32/3.22 Proof:
% 22.32/3.22 n3(X)
% 22.32/3.22 = { by axiom 32 (rule_240) R->L }
% 22.32/3.22 fresh127(p2(X, b, X), true, X)
% 22.32/3.22 = { by axiom 36 (rule_176) R->L }
% 22.32/3.22 fresh127(fresh208(m1(b, X, b), true, X, b), true, X)
% 22.32/3.22 = { by axiom 16 (rule_029) R->L }
% 22.32/3.22 fresh127(fresh208(fresh404(true, true, b, X), true, X, b), true, X)
% 22.32/3.22 = { by axiom 4 (axiom_14) R->L }
% 22.32/3.22 fresh127(fresh208(fresh404(p0(b, X), true, b, X), true, X, b), true, X)
% 22.32/3.22 = { by axiom 29 (rule_029) }
% 22.32/3.22 fresh127(fresh208(fresh403(s0(b), true, b, X), true, X, b), true, X)
% 22.32/3.22 = { by axiom 1 (axiom_5) }
% 22.32/3.22 fresh127(fresh208(fresh403(true, true, b, X), true, X, b), true, X)
% 22.32/3.22 = { by axiom 17 (rule_029) }
% 22.32/3.22 fresh127(fresh208(true, true, X, b), true, X)
% 22.32/3.22 = { by axiom 19 (rule_176) }
% 22.32/3.22 fresh127(true, true, X)
% 22.32/3.22 = { by axiom 11 (rule_240) }
% 22.32/3.22 true
% 22.32/3.22
% 22.32/3.22 Goal 1 (prove_this): s5(b) = true.
% 22.32/3.22 Proof:
% 22.32/3.22 s5(b)
% 22.32/3.22 = { by axiom 14 (rule_329) R->L }
% 22.32/3.22 fresh2(true, true, b)
% 22.32/3.22 = { by axiom 6 (rule_298) R->L }
% 22.32/3.22 fresh2(fresh459(true, true, X), true, b)
% 22.32/3.22 = { by axiom 4 (axiom_14) R->L }
% 22.32/3.22 fresh2(fresh459(p0(b, X), true, X), true, b)
% 22.32/3.22 = { by axiom 25 (rule_298) R->L }
% 22.32/3.22 fresh2(fresh458(true, true, X, b), true, b)
% 22.32/3.22 = { by axiom 22 (rule_255) R->L }
% 22.32/3.22 fresh2(fresh458(fresh103(true, true, e, e), true, X, b), true, b)
% 22.32/3.22 = { by axiom 3 (axiom_30) R->L }
% 22.32/3.22 fresh2(fresh458(fresh103(n0(e, e), true, e, e), true, X, b), true, b)
% 22.32/3.22 = { by axiom 38 (rule_255) R->L }
% 22.32/3.22 fresh2(fresh458(fresh104(q2(e, e, e), true, e, e, e), true, X, b), true, b)
% 22.32/3.22 = { by axiom 20 (rule_179) R->L }
% 22.32/3.22 fresh2(fresh458(fresh104(fresh203(true, true, e, d), true, e, e, e), true, X, b), true, b)
% 22.32/3.22 = { by axiom 18 (rule_036) R->L }
% 22.32/3.23 fresh2(fresh458(fresh104(fresh203(fresh394(true, true, e, d), true, e, d), true, e, e, e), true, X, b), true, b)
% 22.32/3.23 = { by axiom 15 (axiom_19) R->L }
% 22.32/3.23 fresh2(fresh458(fresh104(fresh203(fresh394(m0(b, d, e), true, e, d), true, e, d), true, e, e, e), true, X, b), true, b)
% 22.32/3.23 = { by axiom 35 (rule_036) }
% 22.32/3.23 fresh2(fresh458(fresh104(fresh203(n1(e, e, d), true, e, d), true, e, e, e), true, X, b), true, b)
% 22.32/3.23 = { by axiom 37 (rule_179) }
% 22.32/3.23 fresh2(fresh458(fresh104(fresh202(k1(d), true, e), true, e, e, e), true, X, b), true, b)
% 22.32/3.23 = { by axiom 26 (rule_001) R->L }
% 22.32/3.23 fresh2(fresh458(fresh104(fresh202(fresh440(n0(c, d), true, d), true, e), true, e, e, e), true, X, b), true, b)
% 22.32/3.23 = { by axiom 2 (axiom_34) }
% 22.32/3.23 fresh2(fresh458(fresh104(fresh202(fresh440(true, true, d), true, e), true, e, e, e), true, X, b), true, b)
% 22.32/3.23 = { by axiom 7 (rule_001) }
% 22.32/3.23 fresh2(fresh458(fresh104(fresh202(true, true, e), true, e, e, e), true, X, b), true, b)
% 22.32/3.23 = { by axiom 10 (rule_179) }
% 22.32/3.23 fresh2(fresh458(fresh104(true, true, e, e, e), true, X, b), true, b)
% 22.32/3.23 = { by axiom 27 (rule_255) }
% 22.32/3.23 fresh2(fresh458(q3(e, e), true, X, b), true, b)
% 22.32/3.23 = { by axiom 28 (rule_298) }
% 22.32/3.23 fresh2(fresh47(n3(X), true, X, b), true, b)
% 22.32/3.23 = { by lemma 39 }
% 22.32/3.23 fresh2(fresh47(true, true, X, b), true, b)
% 22.32/3.23 = { by axiom 23 (rule_298) }
% 22.32/3.23 fresh2(r4(X), true, b)
% 22.32/3.23 = { by axiom 24 (rule_329) }
% 22.32/3.23 fresh(l4(b), true, b)
% 22.32/3.23 = { by axiom 34 (rule_277) R->L }
% 22.32/3.23 fresh(fresh79(p3(b, b, b), true, b), true, b)
% 22.32/3.23 = { by axiom 21 (rule_248) R->L }
% 22.32/3.23 fresh(fresh79(fresh117(true, true, b, b), true, b), true, b)
% 22.32/3.23 = { by lemma 39 R->L }
% 22.32/3.23 fresh(fresh79(fresh117(n3(b), true, b, b), true, b), true, b)
% 22.32/3.23 = { by axiom 33 (rule_248) }
% 22.32/3.23 fresh(fresh79(fresh116(p2(b, b, b), true, b), true, b), true, b)
% 22.32/3.23 = { by axiom 31 (rule_154) R->L }
% 22.32/3.23 fresh(fresh79(fresh116(fresh241(q1(b, b, b), true, b), true, b), true, b), true, b)
% 22.32/3.23 = { by axiom 30 (rule_110) R->L }
% 22.32/3.23 fresh(fresh79(fresh116(fresh241(fresh297(m0(Y, d, b), true, b), true, b), true, b), true, b), true, b)
% 22.32/3.23 = { by axiom 15 (axiom_19) }
% 22.32/3.23 fresh(fresh79(fresh116(fresh241(fresh297(true, true, b), true, b), true, b), true, b), true, b)
% 22.32/3.23 = { by axiom 8 (rule_110) }
% 22.32/3.23 fresh(fresh79(fresh116(fresh241(true, true, b), true, b), true, b), true, b)
% 22.32/3.23 = { by axiom 9 (rule_154) }
% 22.32/3.23 fresh(fresh79(fresh116(true, true, b), true, b), true, b)
% 22.32/3.23 = { by axiom 12 (rule_248) }
% 22.32/3.23 fresh(fresh79(true, true, b), true, b)
% 22.32/3.23 = { by axiom 13 (rule_277) }
% 22.32/3.23 fresh(true, true, b)
% 22.32/3.23 = { by axiom 5 (rule_329) }
% 22.32/3.23 true
% 22.32/3.23 % SZS output end Proof
% 22.32/3.23
% 22.32/3.23 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------