TSTP Solution File: SYN583-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN583-1 : TPTP v8.1.2. Released v2.5.0.
% 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 : n009.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 03:35:20 EDT 2023
% Result : Unsatisfiable 1.86s 0.63s
% Output : Proof 1.86s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.14/0.14 % Problem : SYN583-1 : TPTP v8.1.2. Released v2.5.0.
% 0.14/0.15 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.15/0.37 % Computer : n009.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Sat Aug 26 16:43:50 EDT 2023
% 0.15/0.37 % CPUTime :
% 1.86/0.63 Command-line arguments: --flatten
% 1.86/0.63
% 1.86/0.63 % SZS status Unsatisfiable
% 1.86/0.63
% 1.86/0.64 % SZS output start Proof
% 1.86/0.64 Take the following subset of the input axioms:
% 1.86/0.64 fof(not_p11_9, negated_conjecture, ~p11(f4(f6(c15, c18)), c16)).
% 1.86/0.64 fof(p11_21, negated_conjecture, ![X7, X8, X9, X10]: (p11(X7, X8) | (~p2(X9, X7) | (~p2(X10, X8) | ~p11(X9, X10))))).
% 1.86/0.64 fof(p11_7, negated_conjecture, p11(f4(f6(c15, c13)), c16)).
% 1.86/0.64 fof(p2_14, negated_conjecture, ![X23, X24]: (p2(f4(X23), f4(X24)) | ~p2(X23, X24))).
% 1.86/0.64 fof(p2_2, negated_conjecture, ![X18]: p2(X18, X18)).
% 1.86/0.64 fof(p2_23, negated_conjecture, ![X25, X26, X27, X28]: (p2(f6(X25, X26), f6(X27, X28)) | (~p2(X26, X28) | ~p5(X25, X27)))).
% 1.86/0.64 fof(p2_4, negated_conjecture, p2(c13, c18)).
% 1.86/0.64 fof(p2_6, negated_conjecture, p2(f3(c18), f8(f9(c17)))).
% 1.86/0.64 fof(p5_3, negated_conjecture, ![X31]: p5(X31, X31)).
% 1.86/0.64
% 1.86/0.64 Now clausify the problem and encode Horn clauses using encoding 3 of
% 1.86/0.64 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 1.86/0.64 We repeatedly replace C & s=t => u=v by the two clauses:
% 1.86/0.64 fresh(y, y, x1...xn) = u
% 1.86/0.64 C => fresh(s, t, x1...xn) = v
% 1.86/0.64 where fresh is a fresh function symbol and x1..xn are the free
% 1.86/0.64 variables of u and v.
% 1.86/0.64 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 1.86/0.64 input problem has no model of domain size 1).
% 1.86/0.64
% 1.86/0.64 The encoding turns the above axioms into the following unit equations and goals:
% 1.86/0.64
% 1.86/0.64 Axiom 1 (p5_3): p5(X, X) = true.
% 1.86/0.64 Axiom 2 (p2_2): p2(X, X) = true.
% 1.86/0.64 Axiom 3 (p2_4): p2(c13, c18) = true.
% 1.86/0.64 Axiom 4 (p11_21): fresh29(X, X, Y, Z) = true.
% 1.86/0.64 Axiom 5 (p2_14): fresh11(X, X, Y, Z) = true.
% 1.86/0.64 Axiom 6 (p11_21): fresh15(X, X, Y, Z, W) = p11(Y, Z).
% 1.86/0.64 Axiom 7 (p11_7): p11(f4(f6(c15, c13)), c16) = true.
% 1.86/0.64 Axiom 8 (p2_6): p2(f3(c18), f8(f9(c17))) = true.
% 1.86/0.64 Axiom 9 (p11_21): fresh28(X, X, Y, Z, W, V) = fresh29(p2(W, Y), true, Y, Z).
% 1.86/0.64 Axiom 10 (p2_14): fresh11(p2(X, Y), true, X, Y) = p2(f4(X), f4(Y)).
% 1.86/0.64 Axiom 11 (p2_23): fresh6(X, X, Y, Z, W, V) = true.
% 1.86/0.64 Axiom 12 (p2_23): fresh7(X, X, Y, Z, W, V) = p2(f6(Y, Z), f6(W, V)).
% 1.86/0.64 Axiom 13 (p11_21): fresh28(p11(X, Y), true, Z, W, X, Y) = fresh15(p2(Y, W), true, Z, W, X).
% 1.86/0.64 Axiom 14 (p2_23): fresh7(p5(X, Y), true, X, Z, Y, W) = fresh6(p2(Z, W), true, X, Z, Y, W).
% 1.86/0.64
% 1.86/0.64 Lemma 15: p2(f3(c18), f8(f9(c17))) = p2(c13, c18).
% 1.86/0.64 Proof:
% 1.86/0.64 p2(f3(c18), f8(f9(c17)))
% 1.86/0.64 = { by axiom 8 (p2_6) }
% 1.86/0.64 true
% 1.86/0.64 = { by axiom 3 (p2_4) R->L }
% 1.86/0.64 p2(c13, c18)
% 1.86/0.64
% 1.86/0.64 Goal 1 (not_p11_9): p11(f4(f6(c15, c18)), c16) = true.
% 1.86/0.64 Proof:
% 1.86/0.64 p11(f4(f6(c15, c18)), c16)
% 1.86/0.64 = { by axiom 6 (p11_21) R->L }
% 1.86/0.64 fresh15(p2(f3(c18), f8(f9(c17))), p2(f3(c18), f8(f9(c17))), f4(f6(c15, c18)), c16, f4(f6(c15, c13)))
% 1.86/0.64 = { by lemma 15 }
% 1.86/0.64 fresh15(p2(c13, c18), p2(f3(c18), f8(f9(c17))), f4(f6(c15, c18)), c16, f4(f6(c15, c13)))
% 1.86/0.64 = { by axiom 3 (p2_4) }
% 1.86/0.64 fresh15(true, p2(f3(c18), f8(f9(c17))), f4(f6(c15, c18)), c16, f4(f6(c15, c13)))
% 1.86/0.64 = { by axiom 2 (p2_2) R->L }
% 1.86/0.64 fresh15(p2(c16, c16), p2(f3(c18), f8(f9(c17))), f4(f6(c15, c18)), c16, f4(f6(c15, c13)))
% 1.86/0.64 = { by lemma 15 }
% 1.86/0.64 fresh15(p2(c16, c16), p2(c13, c18), f4(f6(c15, c18)), c16, f4(f6(c15, c13)))
% 1.86/0.64 = { by axiom 3 (p2_4) }
% 1.86/0.64 fresh15(p2(c16, c16), true, f4(f6(c15, c18)), c16, f4(f6(c15, c13)))
% 1.86/0.64 = { by axiom 13 (p11_21) R->L }
% 1.86/0.64 fresh28(p11(f4(f6(c15, c13)), c16), true, f4(f6(c15, c18)), c16, f4(f6(c15, c13)), c16)
% 1.86/0.64 = { by axiom 3 (p2_4) R->L }
% 1.86/0.64 fresh28(p11(f4(f6(c15, c13)), c16), p2(c13, c18), f4(f6(c15, c18)), c16, f4(f6(c15, c13)), c16)
% 1.86/0.64 = { by lemma 15 R->L }
% 1.86/0.64 fresh28(p11(f4(f6(c15, c13)), c16), p2(f3(c18), f8(f9(c17))), f4(f6(c15, c18)), c16, f4(f6(c15, c13)), c16)
% 1.86/0.64 = { by axiom 7 (p11_7) }
% 1.86/0.64 fresh28(true, p2(f3(c18), f8(f9(c17))), f4(f6(c15, c18)), c16, f4(f6(c15, c13)), c16)
% 1.86/0.64 = { by axiom 3 (p2_4) R->L }
% 1.86/0.64 fresh28(p2(c13, c18), p2(f3(c18), f8(f9(c17))), f4(f6(c15, c18)), c16, f4(f6(c15, c13)), c16)
% 1.86/0.64 = { by lemma 15 R->L }
% 1.86/0.64 fresh28(p2(f3(c18), f8(f9(c17))), p2(f3(c18), f8(f9(c17))), f4(f6(c15, c18)), c16, f4(f6(c15, c13)), c16)
% 1.86/0.64 = { by axiom 9 (p11_21) }
% 1.86/0.64 fresh29(p2(f4(f6(c15, c13)), f4(f6(c15, c18))), true, f4(f6(c15, c18)), c16)
% 1.86/0.64 = { by axiom 3 (p2_4) R->L }
% 1.86/0.64 fresh29(p2(f4(f6(c15, c13)), f4(f6(c15, c18))), p2(c13, c18), f4(f6(c15, c18)), c16)
% 1.86/0.64 = { by lemma 15 R->L }
% 1.86/0.64 fresh29(p2(f4(f6(c15, c13)), f4(f6(c15, c18))), p2(f3(c18), f8(f9(c17))), f4(f6(c15, c18)), c16)
% 1.86/0.64 = { by axiom 10 (p2_14) R->L }
% 1.86/0.64 fresh29(fresh11(p2(f6(c15, c13), f6(c15, c18)), true, f6(c15, c13), f6(c15, c18)), p2(f3(c18), f8(f9(c17))), f4(f6(c15, c18)), c16)
% 1.86/0.64 = { by axiom 3 (p2_4) R->L }
% 1.86/0.64 fresh29(fresh11(p2(f6(c15, c13), f6(c15, c18)), p2(c13, c18), f6(c15, c13), f6(c15, c18)), p2(f3(c18), f8(f9(c17))), f4(f6(c15, c18)), c16)
% 1.86/0.64 = { by lemma 15 R->L }
% 1.86/0.64 fresh29(fresh11(p2(f6(c15, c13), f6(c15, c18)), p2(f3(c18), f8(f9(c17))), f6(c15, c13), f6(c15, c18)), p2(f3(c18), f8(f9(c17))), f4(f6(c15, c18)), c16)
% 1.86/0.64 = { by axiom 12 (p2_23) R->L }
% 1.86/0.64 fresh29(fresh11(fresh7(p2(f3(c18), f8(f9(c17))), p2(f3(c18), f8(f9(c17))), c15, c13, c15, c18), p2(f3(c18), f8(f9(c17))), f6(c15, c13), f6(c15, c18)), p2(f3(c18), f8(f9(c17))), f4(f6(c15, c18)), c16)
% 1.86/0.64 = { by lemma 15 }
% 1.86/0.64 fresh29(fresh11(fresh7(p2(c13, c18), p2(f3(c18), f8(f9(c17))), c15, c13, c15, c18), p2(f3(c18), f8(f9(c17))), f6(c15, c13), f6(c15, c18)), p2(f3(c18), f8(f9(c17))), f4(f6(c15, c18)), c16)
% 1.86/0.64 = { by axiom 3 (p2_4) }
% 1.86/0.64 fresh29(fresh11(fresh7(true, p2(f3(c18), f8(f9(c17))), c15, c13, c15, c18), p2(f3(c18), f8(f9(c17))), f6(c15, c13), f6(c15, c18)), p2(f3(c18), f8(f9(c17))), f4(f6(c15, c18)), c16)
% 1.86/0.64 = { by axiom 1 (p5_3) R->L }
% 1.86/0.64 fresh29(fresh11(fresh7(p5(c15, c15), p2(f3(c18), f8(f9(c17))), c15, c13, c15, c18), p2(f3(c18), f8(f9(c17))), f6(c15, c13), f6(c15, c18)), p2(f3(c18), f8(f9(c17))), f4(f6(c15, c18)), c16)
% 1.86/0.64 = { by lemma 15 }
% 1.86/0.64 fresh29(fresh11(fresh7(p5(c15, c15), p2(c13, c18), c15, c13, c15, c18), p2(f3(c18), f8(f9(c17))), f6(c15, c13), f6(c15, c18)), p2(f3(c18), f8(f9(c17))), f4(f6(c15, c18)), c16)
% 1.86/0.64 = { by axiom 3 (p2_4) }
% 1.86/0.64 fresh29(fresh11(fresh7(p5(c15, c15), true, c15, c13, c15, c18), p2(f3(c18), f8(f9(c17))), f6(c15, c13), f6(c15, c18)), p2(f3(c18), f8(f9(c17))), f4(f6(c15, c18)), c16)
% 1.86/0.64 = { by axiom 14 (p2_23) }
% 1.86/0.64 fresh29(fresh11(fresh6(p2(c13, c18), true, c15, c13, c15, c18), p2(f3(c18), f8(f9(c17))), f6(c15, c13), f6(c15, c18)), p2(f3(c18), f8(f9(c17))), f4(f6(c15, c18)), c16)
% 1.86/0.64 = { by axiom 3 (p2_4) R->L }
% 1.86/0.64 fresh29(fresh11(fresh6(p2(c13, c18), p2(c13, c18), c15, c13, c15, c18), p2(f3(c18), f8(f9(c17))), f6(c15, c13), f6(c15, c18)), p2(f3(c18), f8(f9(c17))), f4(f6(c15, c18)), c16)
% 1.86/0.64 = { by lemma 15 R->L }
% 1.86/0.64 fresh29(fresh11(fresh6(p2(c13, c18), p2(f3(c18), f8(f9(c17))), c15, c13, c15, c18), p2(f3(c18), f8(f9(c17))), f6(c15, c13), f6(c15, c18)), p2(f3(c18), f8(f9(c17))), f4(f6(c15, c18)), c16)
% 1.86/0.64 = { by lemma 15 R->L }
% 1.86/0.64 fresh29(fresh11(fresh6(p2(f3(c18), f8(f9(c17))), p2(f3(c18), f8(f9(c17))), c15, c13, c15, c18), p2(f3(c18), f8(f9(c17))), f6(c15, c13), f6(c15, c18)), p2(f3(c18), f8(f9(c17))), f4(f6(c15, c18)), c16)
% 1.86/0.64 = { by axiom 11 (p2_23) }
% 1.86/0.64 fresh29(fresh11(true, p2(f3(c18), f8(f9(c17))), f6(c15, c13), f6(c15, c18)), p2(f3(c18), f8(f9(c17))), f4(f6(c15, c18)), c16)
% 1.86/0.64 = { by axiom 3 (p2_4) R->L }
% 1.86/0.64 fresh29(fresh11(p2(c13, c18), p2(f3(c18), f8(f9(c17))), f6(c15, c13), f6(c15, c18)), p2(f3(c18), f8(f9(c17))), f4(f6(c15, c18)), c16)
% 1.86/0.64 = { by lemma 15 R->L }
% 1.86/0.65 fresh29(fresh11(p2(f3(c18), f8(f9(c17))), p2(f3(c18), f8(f9(c17))), f6(c15, c13), f6(c15, c18)), p2(f3(c18), f8(f9(c17))), f4(f6(c15, c18)), c16)
% 1.86/0.65 = { by axiom 5 (p2_14) }
% 1.86/0.65 fresh29(true, p2(f3(c18), f8(f9(c17))), f4(f6(c15, c18)), c16)
% 1.86/0.65 = { by axiom 3 (p2_4) R->L }
% 1.86/0.65 fresh29(p2(c13, c18), p2(f3(c18), f8(f9(c17))), f4(f6(c15, c18)), c16)
% 1.86/0.65 = { by lemma 15 R->L }
% 1.86/0.65 fresh29(p2(f3(c18), f8(f9(c17))), p2(f3(c18), f8(f9(c17))), f4(f6(c15, c18)), c16)
% 1.86/0.65 = { by axiom 4 (p11_21) }
% 1.86/0.65 true
% 1.86/0.65 % SZS output end Proof
% 1.86/0.65
% 1.86/0.65 RESULT: Unsatisfiable (the axioms are contradictory).
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