TSTP Solution File: SYN626-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN626-1 : 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 : n019.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 03:35:29 EDT 2023
% Result : Unsatisfiable 0.20s 0.47s
% Output : Proof 0.20s
% 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 : SYN626-1 : TPTP v8.1.2. Released v2.5.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.15/0.34 % Computer : n019.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Sat Aug 26 18:25:43 EDT 2023
% 0.15/0.34 % CPUTime :
% 0.20/0.47 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.20/0.47
% 0.20/0.47 % SZS status Unsatisfiable
% 0.20/0.47
% 0.20/0.48 % SZS output start Proof
% 0.20/0.48 Take the following subset of the input axioms:
% 0.20/0.48 fof(not_p15_24, negated_conjecture, ~p15(c22, f12(f13(f8(f5(c20), f9(c23, c24)))))).
% 0.20/0.48 fof(p15_31, negated_conjecture, ![X10, X11, X12, X13]: (p15(X10, X11) | (~p6(X12, X10) | (~p7(X13, X11) | ~p15(X12, X13))))).
% 0.20/0.48 fof(p15_9, negated_conjecture, p15(c22, f8(f5(c20), f9(c23, c24)))).
% 0.20/0.48 fof(p16_8, negated_conjecture, ![X14, X15]: (p16(X14, X15) | ~p15(X14, X15))).
% 0.20/0.48 fof(p6_3, negated_conjecture, ![X47]: p6(X47, X47)).
% 0.20/0.48 fof(p7_15, negated_conjecture, ![X20]: (p7(f12(f13(X20)), X20) | ~p16(c22, X20))).
% 0.20/0.48 fof(p7_17, negated_conjecture, ![X54, X55, X56]: (p7(X55, X56) | (~p7(X54, X55) | ~p7(X54, X56)))).
% 0.20/0.48 fof(p7_2, negated_conjecture, ![X54_2]: p7(X54_2, X54_2)).
% 0.20/0.48
% 0.20/0.48 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.48 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.48 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.48 fresh(y, y, x1...xn) = u
% 0.20/0.48 C => fresh(s, t, x1...xn) = v
% 0.20/0.48 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.48 variables of u and v.
% 0.20/0.48 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.48 input problem has no model of domain size 1).
% 0.20/0.48
% 0.20/0.48 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.48
% 0.20/0.48 Axiom 1 (p7_2): p7(X, X) = true.
% 0.20/0.48 Axiom 2 (p6_3): p6(X, X) = true.
% 0.20/0.48 Axiom 3 (p7_15): fresh5(X, X, Y) = true.
% 0.20/0.48 Axiom 4 (p15_31): fresh37(X, X, Y, Z) = true.
% 0.20/0.48 Axiom 5 (p16_8): fresh22(X, X, Y, Z) = true.
% 0.20/0.48 Axiom 6 (p7_17): fresh3(X, X, Y, Z) = true.
% 0.20/0.48 Axiom 7 (p15_31): fresh25(X, X, Y, Z, W) = p15(Y, Z).
% 0.20/0.48 Axiom 8 (p7_15): fresh5(p16(c22, X), true, X) = p7(f12(f13(X)), X).
% 0.20/0.48 Axiom 9 (p7_17): fresh4(X, X, Y, Z, W) = p7(Y, Z).
% 0.20/0.48 Axiom 10 (p15_31): fresh36(X, X, Y, Z, W, V) = fresh37(p7(V, Z), true, Y, Z).
% 0.20/0.48 Axiom 11 (p16_8): fresh22(p15(X, Y), true, X, Y) = p16(X, Y).
% 0.20/0.48 Axiom 12 (p15_9): p15(c22, f8(f5(c20), f9(c23, c24))) = true.
% 0.20/0.48 Axiom 13 (p7_17): fresh4(p7(X, Y), true, Z, Y, X) = fresh3(p7(X, Z), true, Z, Y).
% 0.20/0.48 Axiom 14 (p15_31): fresh36(p15(X, Y), true, Z, W, X, Y) = fresh25(p6(X, Z), true, Z, W, Y).
% 0.20/0.48
% 0.20/0.48 Goal 1 (not_p15_24): p15(c22, f12(f13(f8(f5(c20), f9(c23, c24))))) = true.
% 0.20/0.48 Proof:
% 0.20/0.48 p15(c22, f12(f13(f8(f5(c20), f9(c23, c24)))))
% 0.20/0.48 = { by axiom 7 (p15_31) R->L }
% 0.20/0.48 fresh25(true, true, c22, f12(f13(f8(f5(c20), f9(c23, c24)))), f8(f5(c20), f9(c23, c24)))
% 0.20/0.48 = { by axiom 2 (p6_3) R->L }
% 0.20/0.48 fresh25(p6(c22, c22), true, c22, f12(f13(f8(f5(c20), f9(c23, c24)))), f8(f5(c20), f9(c23, c24)))
% 0.20/0.48 = { by axiom 14 (p15_31) R->L }
% 0.20/0.48 fresh36(p15(c22, f8(f5(c20), f9(c23, c24))), true, c22, f12(f13(f8(f5(c20), f9(c23, c24)))), c22, f8(f5(c20), f9(c23, c24)))
% 0.20/0.48 = { by axiom 12 (p15_9) }
% 0.20/0.48 fresh36(true, true, c22, f12(f13(f8(f5(c20), f9(c23, c24)))), c22, f8(f5(c20), f9(c23, c24)))
% 0.20/0.48 = { by axiom 10 (p15_31) }
% 0.20/0.48 fresh37(p7(f8(f5(c20), f9(c23, c24)), f12(f13(f8(f5(c20), f9(c23, c24))))), true, c22, f12(f13(f8(f5(c20), f9(c23, c24)))))
% 0.20/0.48 = { by axiom 9 (p7_17) R->L }
% 0.20/0.48 fresh37(fresh4(true, true, f8(f5(c20), f9(c23, c24)), f12(f13(f8(f5(c20), f9(c23, c24)))), f12(f13(f8(f5(c20), f9(c23, c24))))), true, c22, f12(f13(f8(f5(c20), f9(c23, c24)))))
% 0.20/0.48 = { by axiom 1 (p7_2) R->L }
% 0.20/0.48 fresh37(fresh4(p7(f12(f13(f8(f5(c20), f9(c23, c24)))), f12(f13(f8(f5(c20), f9(c23, c24))))), true, f8(f5(c20), f9(c23, c24)), f12(f13(f8(f5(c20), f9(c23, c24)))), f12(f13(f8(f5(c20), f9(c23, c24))))), true, c22, f12(f13(f8(f5(c20), f9(c23, c24)))))
% 0.20/0.48 = { by axiom 13 (p7_17) }
% 0.20/0.48 fresh37(fresh3(p7(f12(f13(f8(f5(c20), f9(c23, c24)))), f8(f5(c20), f9(c23, c24))), true, f8(f5(c20), f9(c23, c24)), f12(f13(f8(f5(c20), f9(c23, c24))))), true, c22, f12(f13(f8(f5(c20), f9(c23, c24)))))
% 0.20/0.48 = { by axiom 8 (p7_15) R->L }
% 0.20/0.48 fresh37(fresh3(fresh5(p16(c22, f8(f5(c20), f9(c23, c24))), true, f8(f5(c20), f9(c23, c24))), true, f8(f5(c20), f9(c23, c24)), f12(f13(f8(f5(c20), f9(c23, c24))))), true, c22, f12(f13(f8(f5(c20), f9(c23, c24)))))
% 0.20/0.48 = { by axiom 11 (p16_8) R->L }
% 0.20/0.48 fresh37(fresh3(fresh5(fresh22(p15(c22, f8(f5(c20), f9(c23, c24))), true, c22, f8(f5(c20), f9(c23, c24))), true, f8(f5(c20), f9(c23, c24))), true, f8(f5(c20), f9(c23, c24)), f12(f13(f8(f5(c20), f9(c23, c24))))), true, c22, f12(f13(f8(f5(c20), f9(c23, c24)))))
% 0.20/0.48 = { by axiom 12 (p15_9) }
% 0.20/0.48 fresh37(fresh3(fresh5(fresh22(true, true, c22, f8(f5(c20), f9(c23, c24))), true, f8(f5(c20), f9(c23, c24))), true, f8(f5(c20), f9(c23, c24)), f12(f13(f8(f5(c20), f9(c23, c24))))), true, c22, f12(f13(f8(f5(c20), f9(c23, c24)))))
% 0.20/0.48 = { by axiom 5 (p16_8) }
% 0.20/0.48 fresh37(fresh3(fresh5(true, true, f8(f5(c20), f9(c23, c24))), true, f8(f5(c20), f9(c23, c24)), f12(f13(f8(f5(c20), f9(c23, c24))))), true, c22, f12(f13(f8(f5(c20), f9(c23, c24)))))
% 0.20/0.48 = { by axiom 3 (p7_15) }
% 0.20/0.48 fresh37(fresh3(true, true, f8(f5(c20), f9(c23, c24)), f12(f13(f8(f5(c20), f9(c23, c24))))), true, c22, f12(f13(f8(f5(c20), f9(c23, c24)))))
% 0.20/0.48 = { by axiom 6 (p7_17) }
% 0.20/0.48 fresh37(true, true, c22, f12(f13(f8(f5(c20), f9(c23, c24)))))
% 0.20/0.48 = { by axiom 4 (p15_31) }
% 0.20/0.48 true
% 0.20/0.48 % SZS output end Proof
% 0.20/0.48
% 0.20/0.48 RESULT: Unsatisfiable (the axioms are contradictory).
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