TSTP Solution File: SYN203-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN203-1 : 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 : n023.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 03:33:35 EDT 2023
% Result : Unsatisfiable 24.57s 3.45s
% Output : Proof 24.69s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYN203-1 : TPTP v8.1.2. Released v1.1.0.
% 0.06/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 19:17:11 EDT 2023
% 0.13/0.35 % CPUTime :
% 24.57/3.45 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 24.57/3.45
% 24.57/3.45 % SZS status Unsatisfiable
% 24.57/3.45
% 24.69/3.46 % SZS output start Proof
% 24.69/3.46 Take the following subset of the input axioms:
% 24.69/3.46 fof(axiom_11, axiom, n0(e, b)).
% 24.69/3.46 fof(axiom_14, axiom, ![X]: p0(b, X)).
% 24.69/3.46 fof(axiom_19, axiom, ![Y, X2]: m0(X2, d, Y)).
% 24.69/3.46 fof(axiom_32, axiom, k0(b)).
% 24.69/3.46 fof(prove_this, negated_conjecture, ![X2]: ~s3(X2, b)).
% 24.69/3.46 fof(rule_002, axiom, ![G, H]: (l1(G, G) | ~n0(H, G))).
% 24.69/3.46 fof(rule_085, axiom, ![C, B]: (p1(B, B, B) | ~p0(C, B))).
% 24.69/3.46 fof(rule_125, axiom, ![I]: (s1(I) | ~p0(I, I))).
% 24.69/3.46 fof(rule_177, axiom, ![E, F]: (q2(E, F, F) | (~k0(F) | ~p1(E, E, E)))).
% 24.69/3.46 fof(rule_186, axiom, ![H2, G2]: (q2(G2, G2, H2) | ~l1(H2, G2))).
% 24.69/3.46 fof(rule_189, axiom, ![H2]: (s2(H2) | (~q2(b, H2, b) | ~s1(b)))).
% 24.69/3.46 fof(rule_273, axiom, ![J, A2, I2, B2]: (s3(I2, J) | (~q2(A2, I2, A2) | (~s2(I2) | ~m0(A2, B2, J))))).
% 24.69/3.46
% 24.69/3.46 Now clausify the problem and encode Horn clauses using encoding 3 of
% 24.69/3.46 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 24.69/3.46 We repeatedly replace C & s=t => u=v by the two clauses:
% 24.69/3.46 fresh(y, y, x1...xn) = u
% 24.69/3.46 C => fresh(s, t, x1...xn) = v
% 24.69/3.46 where fresh is a fresh function symbol and x1..xn are the free
% 24.69/3.46 variables of u and v.
% 24.69/3.46 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 24.69/3.46 input problem has no model of domain size 1).
% 24.69/3.46
% 24.69/3.46 The encoding turns the above axioms into the following unit equations and goals:
% 24.69/3.46
% 24.69/3.46 Axiom 1 (axiom_14): p0(b, X) = true2.
% 24.69/3.46 Axiom 2 (axiom_11): n0(e, b) = true2.
% 24.69/3.46 Axiom 3 (axiom_32): k0(b) = true2.
% 24.69/3.46 Axiom 4 (axiom_19): m0(X, d, Y) = true2.
% 24.69/3.46 Axiom 5 (rule_002): fresh441(X, X, Y) = true2.
% 24.69/3.46 Axiom 6 (rule_085): fresh328(X, X, Y) = true2.
% 24.69/3.46 Axiom 7 (rule_125): fresh275(X, X, Y) = true2.
% 24.69/3.46 Axiom 8 (rule_189): fresh192(X, X, Y) = s2(Y).
% 24.69/3.46 Axiom 9 (rule_189): fresh191(X, X, Y) = true2.
% 24.69/3.46 Axiom 10 (rule_273): fresh475(X, X, Y, Z) = true2.
% 24.69/3.46 Axiom 11 (rule_002): fresh441(n0(X, Y), true2, Y) = l1(Y, Y).
% 24.69/3.46 Axiom 12 (rule_085): fresh328(p0(X, Y), true2, Y) = p1(Y, Y, Y).
% 24.69/3.46 Axiom 13 (rule_125): fresh275(p0(X, X), true2, X) = s1(X).
% 24.69/3.46 Axiom 14 (rule_177): fresh207(X, X, Y, Z) = q2(Y, Z, Z).
% 24.69/3.46 Axiom 15 (rule_177): fresh206(X, X, Y, Z) = true2.
% 24.69/3.46 Axiom 16 (rule_186): fresh195(X, X, Y, Z) = true2.
% 24.69/3.46 Axiom 17 (rule_186): fresh195(l1(X, Y), true2, Y, X) = q2(Y, Y, X).
% 24.69/3.46 Axiom 18 (rule_189): fresh192(q2(b, X, b), true2, X) = fresh191(s1(b), true2, X).
% 24.69/3.46 Axiom 19 (rule_273): fresh474(X, X, Y, Z, W, V) = fresh475(m0(W, V, Z), true2, Y, Z).
% 24.69/3.46 Axiom 20 (rule_177): fresh207(p1(X, X, X), true2, X, Y) = fresh206(k0(Y), true2, X, Y).
% 24.69/3.46 Axiom 21 (rule_273): fresh82(X, X, Y, Z, W, V) = s3(Y, Z).
% 24.69/3.46 Axiom 22 (rule_273): fresh474(s2(X), true2, X, Y, Z, W) = fresh82(q2(Z, X, Z), true2, X, Y, Z, W).
% 24.69/3.46
% 24.69/3.46 Goal 1 (prove_this): s3(X, b) = true2.
% 24.69/3.46 The goal is true when:
% 24.69/3.46 X = b
% 24.69/3.46
% 24.69/3.46 Proof:
% 24.69/3.46 s3(b, b)
% 24.69/3.46 = { by axiom 21 (rule_273) R->L }
% 24.69/3.46 fresh82(true2, true2, b, b, b, d)
% 24.69/3.46 = { by axiom 15 (rule_177) R->L }
% 24.69/3.46 fresh82(fresh206(true2, true2, b, b), true2, b, b, b, d)
% 24.69/3.46 = { by axiom 3 (axiom_32) R->L }
% 24.69/3.46 fresh82(fresh206(k0(b), true2, b, b), true2, b, b, b, d)
% 24.69/3.46 = { by axiom 20 (rule_177) R->L }
% 24.69/3.46 fresh82(fresh207(p1(b, b, b), true2, b, b), true2, b, b, b, d)
% 24.69/3.46 = { by axiom 12 (rule_085) R->L }
% 24.69/3.46 fresh82(fresh207(fresh328(p0(b, b), true2, b), true2, b, b), true2, b, b, b, d)
% 24.69/3.46 = { by axiom 1 (axiom_14) }
% 24.69/3.46 fresh82(fresh207(fresh328(true2, true2, b), true2, b, b), true2, b, b, b, d)
% 24.69/3.46 = { by axiom 6 (rule_085) }
% 24.69/3.46 fresh82(fresh207(true2, true2, b, b), true2, b, b, b, d)
% 24.69/3.46 = { by axiom 14 (rule_177) }
% 24.69/3.46 fresh82(q2(b, b, b), true2, b, b, b, d)
% 24.69/3.46 = { by axiom 22 (rule_273) R->L }
% 24.69/3.46 fresh474(s2(b), true2, b, b, b, d)
% 24.69/3.46 = { by axiom 8 (rule_189) R->L }
% 24.69/3.46 fresh474(fresh192(true2, true2, b), true2, b, b, b, d)
% 24.69/3.46 = { by axiom 16 (rule_186) R->L }
% 24.69/3.46 fresh474(fresh192(fresh195(true2, true2, b, b), true2, b), true2, b, b, b, d)
% 24.69/3.46 = { by axiom 5 (rule_002) R->L }
% 24.69/3.46 fresh474(fresh192(fresh195(fresh441(true2, true2, b), true2, b, b), true2, b), true2, b, b, b, d)
% 24.69/3.46 = { by axiom 2 (axiom_11) R->L }
% 24.69/3.46 fresh474(fresh192(fresh195(fresh441(n0(e, b), true2, b), true2, b, b), true2, b), true2, b, b, b, d)
% 24.69/3.46 = { by axiom 11 (rule_002) }
% 24.69/3.46 fresh474(fresh192(fresh195(l1(b, b), true2, b, b), true2, b), true2, b, b, b, d)
% 24.69/3.46 = { by axiom 17 (rule_186) }
% 24.69/3.46 fresh474(fresh192(q2(b, b, b), true2, b), true2, b, b, b, d)
% 24.69/3.46 = { by axiom 18 (rule_189) }
% 24.69/3.46 fresh474(fresh191(s1(b), true2, b), true2, b, b, b, d)
% 24.69/3.46 = { by axiom 13 (rule_125) R->L }
% 24.69/3.46 fresh474(fresh191(fresh275(p0(b, b), true2, b), true2, b), true2, b, b, b, d)
% 24.69/3.46 = { by axiom 1 (axiom_14) }
% 24.69/3.46 fresh474(fresh191(fresh275(true2, true2, b), true2, b), true2, b, b, b, d)
% 24.69/3.46 = { by axiom 7 (rule_125) }
% 24.69/3.46 fresh474(fresh191(true2, true2, b), true2, b, b, b, d)
% 24.69/3.46 = { by axiom 9 (rule_189) }
% 24.69/3.46 fresh474(true2, true2, b, b, b, d)
% 24.69/3.46 = { by axiom 19 (rule_273) }
% 24.69/3.46 fresh475(m0(b, d, b), true2, b, b)
% 24.69/3.46 = { by axiom 4 (axiom_19) }
% 24.69/3.46 fresh475(true2, true2, b, b)
% 24.69/3.46 = { by axiom 10 (rule_273) }
% 24.69/3.46 true2
% 24.69/3.46 % SZS output end Proof
% 24.69/3.46
% 24.69/3.46 RESULT: Unsatisfiable (the axioms are contradictory).
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