TSTP Solution File: SYN555-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SYN555-1 : 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 : n015.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 03:35:14 EDT 2023
% Result : Unsatisfiable 0.21s 0.44s
% 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
% 0.00/0.13 % Problem : SYN555-1 : TPTP v8.1.2. Released v2.5.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35 % Computer : n015.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Aug 26 22:08:08 EDT 2023
% 0.21/0.36 % CPUTime :
% 0.21/0.44 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.21/0.44
% 0.21/0.44 % SZS status Unsatisfiable
% 0.21/0.44
% 0.21/0.44 % SZS output start Proof
% 0.21/0.44 Take the following subset of the input axioms:
% 0.21/0.44 fof(not_p4_5, negated_conjecture, ~p4(f5(c7, c10, c8), c8)).
% 0.21/0.44 fof(p4_12, negated_conjecture, ![X21, X22, X23]: (p4(f5(c7, X21, X22), X22) | (~p4(f5(c7, X21, X23), X23) | ~p4(f5(c7, f6(X21, X23, X22), X23), f5(c7, f6(X21, X23, X22), X22))))).
% 0.21/0.44 fof(p4_2, negated_conjecture, ![X12]: p4(X12, X12)).
% 0.21/0.44 fof(p4_4, negated_conjecture, p4(f5(c7, c10, c9), c9)).
% 0.21/0.44 fof(p4_6, negated_conjecture, ![X24]: p4(f5(c7, X24, c8), f5(c7, X24, c9))).
% 0.21/0.44 fof(p4_8, negated_conjecture, ![X13, X14, X12_2]: (p4(X13, X14) | (~p4(X12_2, X13) | ~p4(X12_2, X14)))).
% 0.21/0.44
% 0.21/0.44 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.44 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.44 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.44 fresh(y, y, x1...xn) = u
% 0.21/0.44 C => fresh(s, t, x1...xn) = v
% 0.21/0.44 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.44 variables of u and v.
% 0.21/0.44 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.44 input problem has no model of domain size 1).
% 0.21/0.44
% 0.21/0.44 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.44
% 0.21/0.44 Axiom 1 (p4_2): p4(X, X) = true.
% 0.21/0.44 Axiom 2 (p4_8): fresh(X, X, Y, Z) = true.
% 0.21/0.44 Axiom 3 (p4_12): fresh3(X, X, Y, Z) = true.
% 0.21/0.44 Axiom 4 (p4_8): fresh2(X, X, Y, Z, W) = p4(Y, Z).
% 0.21/0.44 Axiom 5 (p4_12): fresh4(X, X, Y, Z, W) = p4(f5(c7, Y, Z), Z).
% 0.21/0.44 Axiom 6 (p4_4): p4(f5(c7, c10, c9), c9) = true.
% 0.21/0.44 Axiom 7 (p4_8): fresh2(p4(X, Y), true, Z, Y, X) = fresh(p4(X, Z), true, Z, Y).
% 0.21/0.44 Axiom 8 (p4_6): p4(f5(c7, X, c8), f5(c7, X, c9)) = true.
% 0.21/0.44 Axiom 9 (p4_12): fresh4(p4(f5(c7, f6(X, Y, Z), Y), f5(c7, f6(X, Y, Z), Z)), true, X, Z, Y) = fresh3(p4(f5(c7, X, Y), Y), true, X, Z).
% 0.21/0.44
% 0.21/0.44 Goal 1 (not_p4_5): p4(f5(c7, c10, c8), c8) = true.
% 0.21/0.44 Proof:
% 0.21/0.44 p4(f5(c7, c10, c8), c8)
% 0.21/0.44 = { by axiom 5 (p4_12) R->L }
% 0.21/0.44 fresh4(true, true, c10, c8, c9)
% 0.21/0.44 = { by axiom 2 (p4_8) R->L }
% 0.21/0.44 fresh4(fresh(true, true, f5(c7, f6(c10, c9, c8), c9), f5(c7, f6(c10, c9, c8), c8)), true, c10, c8, c9)
% 0.21/0.44 = { by axiom 8 (p4_6) R->L }
% 0.21/0.44 fresh4(fresh(p4(f5(c7, f6(c10, c9, c8), c8), f5(c7, f6(c10, c9, c8), c9)), true, f5(c7, f6(c10, c9, c8), c9), f5(c7, f6(c10, c9, c8), c8)), true, c10, c8, c9)
% 0.21/0.44 = { by axiom 7 (p4_8) R->L }
% 0.21/0.44 fresh4(fresh2(p4(f5(c7, f6(c10, c9, c8), c8), f5(c7, f6(c10, c9, c8), c8)), true, f5(c7, f6(c10, c9, c8), c9), f5(c7, f6(c10, c9, c8), c8), f5(c7, f6(c10, c9, c8), c8)), true, c10, c8, c9)
% 0.21/0.44 = { by axiom 1 (p4_2) }
% 0.21/0.44 fresh4(fresh2(true, true, f5(c7, f6(c10, c9, c8), c9), f5(c7, f6(c10, c9, c8), c8), f5(c7, f6(c10, c9, c8), c8)), true, c10, c8, c9)
% 0.21/0.44 = { by axiom 4 (p4_8) }
% 0.21/0.44 fresh4(p4(f5(c7, f6(c10, c9, c8), c9), f5(c7, f6(c10, c9, c8), c8)), true, c10, c8, c9)
% 0.21/0.44 = { by axiom 9 (p4_12) }
% 0.21/0.44 fresh3(p4(f5(c7, c10, c9), c9), true, c10, c8)
% 0.21/0.44 = { by axiom 6 (p4_4) }
% 0.21/0.44 fresh3(true, true, c10, c8)
% 0.21/0.44 = { by axiom 3 (p4_12) }
% 0.21/0.44 true
% 0.21/0.44 % SZS output end Proof
% 0.21/0.44
% 0.21/0.44 RESULT: Unsatisfiable (the axioms are contradictory).
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