TSTP Solution File: SYN618-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN618-1 : 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 : n012.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 03:35:28 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
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN618-1 : 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
% 0.13/0.34 % Computer : n012.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 19:15:40 EDT 2023
% 0.13/0.34 % 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_p5_17, negated_conjecture, ~p5(f8(f3(c16), c20), f6(f7(c22)))).
% 0.20/0.48 fof(p13_8, negated_conjecture, p13(c23, c21)).
% 0.20/0.48 fof(p13_9, negated_conjecture, p13(c19, c23)).
% 0.20/0.48 fof(p2_12, negated_conjecture, p2(c17, f3(c16))).
% 0.20/0.48 fof(p2_24, negated_conjecture, ![X24, X25, X26]: (p2(X25, X26) | (~p2(X24, X25) | ~p2(X24, X26)))).
% 0.20/0.48 fof(p2_5, negated_conjecture, ![X24_2]: p2(X24_2, X24_2)).
% 0.20/0.48 fof(p5_16, negated_conjecture, p5(f8(f3(c16), c23), f6(f7(c22)))).
% 0.20/0.48 fof(p5_22, negated_conjecture, ![X34, X35, X36]: (p5(X35, X36) | (~p5(X34, X35) | ~p5(X34, X36)))).
% 0.20/0.48 fof(p5_3, negated_conjecture, ![X34_2]: p5(X34_2, X34_2)).
% 0.20/0.48 fof(p5_30, negated_conjecture, ![X40, X41, X42, X43]: (p5(f8(X40, X41), f8(X42, X43)) | (~p2(X40, X42) | ~p5(X41, X43)))).
% 0.20/0.48 fof(p5_31, negated_conjecture, ![X37]: (p5(X37, c20) | (~p13(X37, c21) | (~p13(c19, X37) | ~p5(f8(c17, X37), f6(f7(c22))))))).
% 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 (p5_3): p5(X, X) = true.
% 0.20/0.48 Axiom 2 (p2_5): p2(X, X) = true.
% 0.20/0.48 Axiom 3 (p13_9): p13(c19, c23) = true.
% 0.20/0.48 Axiom 4 (p13_8): p13(c23, c21) = true.
% 0.20/0.48 Axiom 5 (p2_12): p2(c17, f3(c16)) = true.
% 0.20/0.48 Axiom 6 (p5_31): fresh31(X, X, Y) = p5(Y, c20).
% 0.20/0.48 Axiom 7 (p5_31): fresh4(X, X, Y) = true.
% 0.20/0.48 Axiom 8 (p2_24): fresh14(X, X, Y, Z) = true.
% 0.20/0.48 Axiom 9 (p5_22): fresh8(X, X, Y, Z) = true.
% 0.20/0.48 Axiom 10 (p5_31): fresh30(X, X, Y) = fresh31(p13(Y, c21), true, Y).
% 0.20/0.48 Axiom 11 (p2_24): fresh15(X, X, Y, Z, W) = p2(Y, Z).
% 0.20/0.48 Axiom 12 (p5_22): fresh9(X, X, Y, Z, W) = p5(Y, Z).
% 0.20/0.48 Axiom 13 (p5_30): fresh6(X, X, Y, Z, W, V) = p5(f8(Y, Z), f8(W, V)).
% 0.20/0.48 Axiom 14 (p5_30): fresh5(X, X, Y, Z, W, V) = true.
% 0.20/0.48 Axiom 15 (p5_16): p5(f8(f3(c16), c23), f6(f7(c22))) = true.
% 0.20/0.48 Axiom 16 (p2_24): fresh15(p2(X, Y), true, Z, Y, X) = fresh14(p2(X, Z), true, Z, Y).
% 0.20/0.48 Axiom 17 (p5_22): fresh9(p5(X, Y), true, Z, Y, X) = fresh8(p5(X, Z), true, Z, Y).
% 0.20/0.48 Axiom 18 (p5_30): fresh6(p2(X, Y), true, X, Z, Y, W) = fresh5(p5(Z, W), true, X, Z, Y, W).
% 0.20/0.48 Axiom 19 (p5_31): fresh30(p13(c19, X), true, X) = fresh4(p5(f8(c17, X), f6(f7(c22))), true, X).
% 0.20/0.48
% 0.20/0.48 Lemma 20: fresh8(p5(f8(f3(c16), c23), X), true, X, f6(f7(c22))) = p5(X, f6(f7(c22))).
% 0.20/0.48 Proof:
% 0.20/0.48 fresh8(p5(f8(f3(c16), c23), X), true, X, f6(f7(c22)))
% 0.20/0.48 = { by axiom 17 (p5_22) R->L }
% 0.20/0.48 fresh9(p5(f8(f3(c16), c23), f6(f7(c22))), true, X, f6(f7(c22)), f8(f3(c16), c23))
% 0.20/0.48 = { by axiom 15 (p5_16) }
% 0.20/0.48 fresh9(true, true, X, f6(f7(c22)), f8(f3(c16), c23))
% 0.20/0.48 = { by axiom 12 (p5_22) }
% 0.20/0.48 p5(X, f6(f7(c22)))
% 0.20/0.48
% 0.20/0.48 Goal 1 (not_p5_17): p5(f8(f3(c16), c20), f6(f7(c22))) = true.
% 0.20/0.48 Proof:
% 0.20/0.48 p5(f8(f3(c16), c20), f6(f7(c22)))
% 0.20/0.48 = { by lemma 20 R->L }
% 0.20/0.48 fresh8(p5(f8(f3(c16), c23), f8(f3(c16), c20)), true, f8(f3(c16), c20), f6(f7(c22)))
% 0.20/0.48 = { by axiom 13 (p5_30) R->L }
% 0.20/0.48 fresh8(fresh6(true, true, f3(c16), c23, f3(c16), c20), true, f8(f3(c16), c20), f6(f7(c22)))
% 0.20/0.48 = { by axiom 2 (p2_5) R->L }
% 0.20/0.48 fresh8(fresh6(p2(f3(c16), f3(c16)), true, f3(c16), c23, f3(c16), c20), true, f8(f3(c16), c20), f6(f7(c22)))
% 0.20/0.48 = { by axiom 18 (p5_30) }
% 0.20/0.48 fresh8(fresh5(p5(c23, c20), true, f3(c16), c23, f3(c16), c20), true, f8(f3(c16), c20), f6(f7(c22)))
% 0.20/0.48 = { by axiom 6 (p5_31) R->L }
% 0.20/0.48 fresh8(fresh5(fresh31(true, true, c23), true, f3(c16), c23, f3(c16), c20), true, f8(f3(c16), c20), f6(f7(c22)))
% 0.20/0.48 = { by axiom 4 (p13_8) R->L }
% 0.20/0.48 fresh8(fresh5(fresh31(p13(c23, c21), true, c23), true, f3(c16), c23, f3(c16), c20), true, f8(f3(c16), c20), f6(f7(c22)))
% 0.20/0.48 = { by axiom 10 (p5_31) R->L }
% 0.20/0.48 fresh8(fresh5(fresh30(true, true, c23), true, f3(c16), c23, f3(c16), c20), true, f8(f3(c16), c20), f6(f7(c22)))
% 0.20/0.48 = { by axiom 3 (p13_9) R->L }
% 0.20/0.48 fresh8(fresh5(fresh30(p13(c19, c23), true, c23), true, f3(c16), c23, f3(c16), c20), true, f8(f3(c16), c20), f6(f7(c22)))
% 0.20/0.48 = { by axiom 19 (p5_31) }
% 0.20/0.48 fresh8(fresh5(fresh4(p5(f8(c17, c23), f6(f7(c22))), true, c23), true, f3(c16), c23, f3(c16), c20), true, f8(f3(c16), c20), f6(f7(c22)))
% 0.20/0.48 = { by lemma 20 R->L }
% 0.20/0.48 fresh8(fresh5(fresh4(fresh8(p5(f8(f3(c16), c23), f8(c17, c23)), true, f8(c17, c23), f6(f7(c22))), true, c23), true, f3(c16), c23, f3(c16), c20), true, f8(f3(c16), c20), f6(f7(c22)))
% 0.20/0.48 = { by axiom 13 (p5_30) R->L }
% 0.20/0.48 fresh8(fresh5(fresh4(fresh8(fresh6(true, true, f3(c16), c23, c17, c23), true, f8(c17, c23), f6(f7(c22))), true, c23), true, f3(c16), c23, f3(c16), c20), true, f8(f3(c16), c20), f6(f7(c22)))
% 0.20/0.48 = { by axiom 8 (p2_24) R->L }
% 0.20/0.48 fresh8(fresh5(fresh4(fresh8(fresh6(fresh14(true, true, f3(c16), c17), true, f3(c16), c23, c17, c23), true, f8(c17, c23), f6(f7(c22))), true, c23), true, f3(c16), c23, f3(c16), c20), true, f8(f3(c16), c20), f6(f7(c22)))
% 0.20/0.48 = { by axiom 5 (p2_12) R->L }
% 0.20/0.48 fresh8(fresh5(fresh4(fresh8(fresh6(fresh14(p2(c17, f3(c16)), true, f3(c16), c17), true, f3(c16), c23, c17, c23), true, f8(c17, c23), f6(f7(c22))), true, c23), true, f3(c16), c23, f3(c16), c20), true, f8(f3(c16), c20), f6(f7(c22)))
% 0.20/0.48 = { by axiom 16 (p2_24) R->L }
% 0.20/0.48 fresh8(fresh5(fresh4(fresh8(fresh6(fresh15(p2(c17, c17), true, f3(c16), c17, c17), true, f3(c16), c23, c17, c23), true, f8(c17, c23), f6(f7(c22))), true, c23), true, f3(c16), c23, f3(c16), c20), true, f8(f3(c16), c20), f6(f7(c22)))
% 0.20/0.48 = { by axiom 2 (p2_5) }
% 0.20/0.48 fresh8(fresh5(fresh4(fresh8(fresh6(fresh15(true, true, f3(c16), c17, c17), true, f3(c16), c23, c17, c23), true, f8(c17, c23), f6(f7(c22))), true, c23), true, f3(c16), c23, f3(c16), c20), true, f8(f3(c16), c20), f6(f7(c22)))
% 0.20/0.48 = { by axiom 11 (p2_24) }
% 0.20/0.48 fresh8(fresh5(fresh4(fresh8(fresh6(p2(f3(c16), c17), true, f3(c16), c23, c17, c23), true, f8(c17, c23), f6(f7(c22))), true, c23), true, f3(c16), c23, f3(c16), c20), true, f8(f3(c16), c20), f6(f7(c22)))
% 0.20/0.48 = { by axiom 18 (p5_30) }
% 0.20/0.48 fresh8(fresh5(fresh4(fresh8(fresh5(p5(c23, c23), true, f3(c16), c23, c17, c23), true, f8(c17, c23), f6(f7(c22))), true, c23), true, f3(c16), c23, f3(c16), c20), true, f8(f3(c16), c20), f6(f7(c22)))
% 0.20/0.48 = { by axiom 1 (p5_3) }
% 0.20/0.48 fresh8(fresh5(fresh4(fresh8(fresh5(true, true, f3(c16), c23, c17, c23), true, f8(c17, c23), f6(f7(c22))), true, c23), true, f3(c16), c23, f3(c16), c20), true, f8(f3(c16), c20), f6(f7(c22)))
% 0.20/0.48 = { by axiom 14 (p5_30) }
% 0.20/0.48 fresh8(fresh5(fresh4(fresh8(true, true, f8(c17, c23), f6(f7(c22))), true, c23), true, f3(c16), c23, f3(c16), c20), true, f8(f3(c16), c20), f6(f7(c22)))
% 0.20/0.48 = { by axiom 9 (p5_22) }
% 0.20/0.48 fresh8(fresh5(fresh4(true, true, c23), true, f3(c16), c23, f3(c16), c20), true, f8(f3(c16), c20), f6(f7(c22)))
% 0.20/0.48 = { by axiom 7 (p5_31) }
% 0.20/0.48 fresh8(fresh5(true, true, f3(c16), c23, f3(c16), c20), true, f8(f3(c16), c20), f6(f7(c22)))
% 0.20/0.48 = { by axiom 14 (p5_30) }
% 0.20/0.48 fresh8(true, true, f8(f3(c16), c20), f6(f7(c22)))
% 0.20/0.48 = { by axiom 9 (p5_22) }
% 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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