TSTP Solution File: SYN717-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN717-1 : 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 : 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 03:35:49 EDT 2023
% Result : Unsatisfiable 0.21s 0.72s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN717-1 : 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
% 0.14/0.34 % Computer : n029.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sat Aug 26 21:43:10 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.72 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.21/0.72
% 0.21/0.72 % SZS status Unsatisfiable
% 0.21/0.72
% 0.21/0.72 % SZS output start Proof
% 0.21/0.72 Take the following subset of the input axioms:
% 0.21/0.72 fof(not_p60_107, negated_conjecture, ![X209, X212, X211, X210]: (~p60(f25(c75, X209), f21(c76, X212)) | (~p59(f29(c73, f31(f33(c74, X211), X212)), c72) | ~p59(f29(c73, f31(f33(c74, X209), X210)), c72)))).
% 0.21/0.72 fof(p20_29, negated_conjecture, ![X48]: p20(X48, X48)).
% 0.21/0.72 fof(p22_28, negated_conjecture, ![X55]: p22(X55, X55)).
% 0.21/0.72 fof(p23_36, negated_conjecture, p23(c79, c77)).
% 0.21/0.72 fof(p24_94, negated_conjecture, ![X68, X69, X70, X71]: (p24(f25(X68, X69), f25(X70, X71)) | (~p22(X68, X70) | ~p23(X69, X71)))).
% 0.21/0.72 fof(p59_44, negated_conjecture, p59(f29(c73, f31(f33(c74, c77), c78)), c72)).
% 0.21/0.72 fof(p60_42, negated_conjecture, p60(f25(c75, c79), f21(c76, c78))).
% 0.21/0.72 fof(p60_84, negated_conjecture, ![X186, X187, X189, X188]: (p60(X186, X187) | (~p24(X189, X186) | (~p60(X189, X188) | ~p20(X188, X187))))).
% 0.21/0.72
% 0.21/0.72 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.72 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.72 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.72 fresh(y, y, x1...xn) = u
% 0.21/0.72 C => fresh(s, t, x1...xn) = v
% 0.21/0.72 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.72 variables of u and v.
% 0.21/0.72 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.72 input problem has no model of domain size 1).
% 0.21/0.72
% 0.21/0.72 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.72
% 0.21/0.72 Axiom 1 (p23_36): p23(c79, c77) = true2.
% 0.21/0.72 Axiom 2 (p20_29): p20(X, X) = true2.
% 0.21/0.72 Axiom 3 (p22_28): p22(X, X) = true2.
% 0.21/0.72 Axiom 4 (p60_84): fresh125(X, X, Y, Z) = true2.
% 0.21/0.72 Axiom 5 (p60_84): fresh14(X, X, Y, Z, W) = p60(Y, Z).
% 0.21/0.72 Axiom 6 (p60_42): p60(f25(c75, c79), f21(c76, c78)) = true2.
% 0.21/0.72 Axiom 7 (p60_84): fresh124(X, X, Y, Z, W, V) = fresh125(p24(W, Y), true2, Y, Z).
% 0.21/0.72 Axiom 8 (p24_94): fresh83(X, X, Y, Z, W, V) = p24(f25(Y, Z), f25(W, V)).
% 0.21/0.72 Axiom 9 (p24_94): fresh82(X, X, Y, Z, W, V) = true2.
% 0.21/0.72 Axiom 10 (p59_44): p59(f29(c73, f31(f33(c74, c77), c78)), c72) = true2.
% 0.21/0.72 Axiom 11 (p60_84): fresh124(p60(X, Y), true2, Z, W, X, Y) = fresh14(p20(Y, W), true2, Z, W, X).
% 0.21/0.72 Axiom 12 (p24_94): fresh83(p22(X, Y), true2, X, Z, Y, W) = fresh82(p23(Z, W), true2, X, Z, Y, W).
% 0.21/0.72
% 0.21/0.72 Goal 1 (not_p60_107): tuple(p59(f29(c73, f31(f33(c74, X), Y)), c72), p59(f29(c73, f31(f33(c74, Z), W)), c72), p60(f25(c75, X), f21(c76, W))) = tuple(true2, true2, true2).
% 0.21/0.72 The goal is true when:
% 0.21/0.72 X = c77
% 0.21/0.72 Y = c78
% 0.21/0.72 Z = c77
% 0.21/0.72 W = c78
% 0.21/0.72
% 0.21/0.72 Proof:
% 0.21/0.72 tuple(p59(f29(c73, f31(f33(c74, c77), c78)), c72), p59(f29(c73, f31(f33(c74, c77), c78)), c72), p60(f25(c75, c77), f21(c76, c78)))
% 0.21/0.72 = { by axiom 10 (p59_44) }
% 0.21/0.72 tuple(true2, p59(f29(c73, f31(f33(c74, c77), c78)), c72), p60(f25(c75, c77), f21(c76, c78)))
% 0.21/0.72 = { by axiom 10 (p59_44) }
% 0.21/0.72 tuple(true2, true2, p60(f25(c75, c77), f21(c76, c78)))
% 0.21/0.72 = { by axiom 5 (p60_84) R->L }
% 0.21/0.72 tuple(true2, true2, fresh14(true2, true2, f25(c75, c77), f21(c76, c78), f25(c75, c79)))
% 0.21/0.72 = { by axiom 2 (p20_29) R->L }
% 0.21/0.72 tuple(true2, true2, fresh14(p20(f21(c76, c78), f21(c76, c78)), true2, f25(c75, c77), f21(c76, c78), f25(c75, c79)))
% 0.21/0.72 = { by axiom 11 (p60_84) R->L }
% 0.21/0.72 tuple(true2, true2, fresh124(p60(f25(c75, c79), f21(c76, c78)), true2, f25(c75, c77), f21(c76, c78), f25(c75, c79), f21(c76, c78)))
% 0.21/0.72 = { by axiom 6 (p60_42) }
% 0.21/0.72 tuple(true2, true2, fresh124(true2, true2, f25(c75, c77), f21(c76, c78), f25(c75, c79), f21(c76, c78)))
% 0.21/0.72 = { by axiom 7 (p60_84) }
% 0.21/0.72 tuple(true2, true2, fresh125(p24(f25(c75, c79), f25(c75, c77)), true2, f25(c75, c77), f21(c76, c78)))
% 0.21/0.72 = { by axiom 8 (p24_94) R->L }
% 0.21/0.72 tuple(true2, true2, fresh125(fresh83(true2, true2, c75, c79, c75, c77), true2, f25(c75, c77), f21(c76, c78)))
% 0.21/0.72 = { by axiom 3 (p22_28) R->L }
% 0.21/0.72 tuple(true2, true2, fresh125(fresh83(p22(c75, c75), true2, c75, c79, c75, c77), true2, f25(c75, c77), f21(c76, c78)))
% 0.21/0.72 = { by axiom 12 (p24_94) }
% 0.21/0.72 tuple(true2, true2, fresh125(fresh82(p23(c79, c77), true2, c75, c79, c75, c77), true2, f25(c75, c77), f21(c76, c78)))
% 0.21/0.72 = { by axiom 1 (p23_36) }
% 0.21/0.72 tuple(true2, true2, fresh125(fresh82(true2, true2, c75, c79, c75, c77), true2, f25(c75, c77), f21(c76, c78)))
% 0.21/0.72 = { by axiom 9 (p24_94) }
% 0.21/0.72 tuple(true2, true2, fresh125(true2, true2, f25(c75, c77), f21(c76, c78)))
% 0.21/0.72 = { by axiom 4 (p60_84) }
% 0.21/0.72 tuple(true2, true2, true2)
% 0.21/0.72 % SZS output end Proof
% 0.21/0.72
% 0.21/0.72 RESULT: Unsatisfiable (the axioms are contradictory).
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