TSTP Solution File: SYN004-1.007 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN004-1.007 : TPTP v8.1.2. Released v1.0.0.
% 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 : n018.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 03:32:41 EDT 2023
% Result : Unsatisfiable 0.12s 0.38s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SYN004-1.007 : TPTP v8.1.2. Released v1.0.0.
% 0.10/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.33 % Computer : n018.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Aug 26 20:32:30 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.12/0.38 Command-line arguments: --ground-connectedness --complete-subsets
% 0.12/0.38
% 0.12/0.38 % SZS status Unsatisfiable
% 0.12/0.38
% 0.12/0.38 % SZS output start Proof
% 0.12/0.38 Take the following subset of the input axioms:
% 0.12/0.38 fof(base_1, negated_conjecture, p_1).
% 0.12/0.39 fof(base_2, negated_conjecture, q_1).
% 0.12/0.39 fof(base_3, negated_conjecture, ~p_7 | ~q_7).
% 0.12/0.39 fof(pqp_1, negated_conjecture, ~p_1 | (~q_1 | p_2)).
% 0.12/0.39 fof(pqp_2, negated_conjecture, ~p_2 | (~q_2 | p_3)).
% 0.12/0.39 fof(pqp_3, negated_conjecture, ~p_3 | (~q_3 | p_4)).
% 0.12/0.39 fof(pqp_4, negated_conjecture, ~p_4 | (~q_4 | p_5)).
% 0.12/0.39 fof(pqp_5, negated_conjecture, ~p_5 | (~q_5 | p_6)).
% 0.12/0.39 fof(pqp_6, negated_conjecture, ~p_6 | (~q_6 | p_7)).
% 0.12/0.39 fof(pqq_1, negated_conjecture, ~p_1 | (~q_1 | q_2)).
% 0.12/0.39 fof(pqq_2, negated_conjecture, ~p_2 | (~q_2 | q_3)).
% 0.12/0.39 fof(pqq_3, negated_conjecture, ~p_3 | (~q_3 | q_4)).
% 0.12/0.39 fof(pqq_4, negated_conjecture, ~p_4 | (~q_4 | q_5)).
% 0.12/0.39 fof(pqq_5, negated_conjecture, ~p_5 | (~q_5 | q_6)).
% 0.12/0.39 fof(pqq_6, negated_conjecture, ~p_6 | (~q_6 | q_7)).
% 0.12/0.39
% 0.12/0.39 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.12/0.39 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.12/0.39 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.12/0.39 fresh(y, y, x1...xn) = u
% 0.12/0.39 C => fresh(s, t, x1...xn) = v
% 0.12/0.39 where fresh is a fresh function symbol and x1..xn are the free
% 0.12/0.39 variables of u and v.
% 0.12/0.39 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.12/0.39 input problem has no model of domain size 1).
% 0.12/0.39
% 0.12/0.39 The encoding turns the above axioms into the following unit equations and goals:
% 0.12/0.39
% 0.12/0.39 Axiom 1 (base_1): p_1 = true.
% 0.12/0.39 Axiom 2 (base_2): q_1 = true.
% 0.12/0.39 Axiom 3 (pqq_6): fresh(X, X) = true.
% 0.12/0.39 Axiom 4 (pqp_1): fresh24(X, X) = true.
% 0.12/0.39 Axiom 5 (pqp_1): fresh23(X, X) = p_2.
% 0.12/0.39 Axiom 6 (pqp_1): fresh23(q_1, true) = fresh24(p_1, true).
% 0.12/0.39 Axiom 7 (pqp_2): fresh22(X, X) = p_3.
% 0.12/0.39 Axiom 8 (pqp_2): fresh21(X, X) = true.
% 0.12/0.39 Axiom 9 (pqp_2): fresh22(q_2, true) = fresh21(p_2, true).
% 0.12/0.39 Axiom 10 (pqp_3): fresh20(X, X) = p_4.
% 0.12/0.39 Axiom 11 (pqp_3): fresh19(X, X) = true.
% 0.12/0.39 Axiom 12 (pqp_3): fresh20(q_3, true) = fresh19(p_3, true).
% 0.12/0.39 Axiom 13 (pqp_4): fresh18(X, X) = p_5.
% 0.12/0.39 Axiom 14 (pqp_4): fresh17(X, X) = true.
% 0.12/0.39 Axiom 15 (pqp_4): fresh18(q_4, true) = fresh17(p_4, true).
% 0.12/0.39 Axiom 16 (pqp_5): fresh16(X, X) = p_6.
% 0.12/0.39 Axiom 17 (pqp_5): fresh15(X, X) = true.
% 0.12/0.39 Axiom 18 (pqp_5): fresh16(q_5, true) = fresh15(p_5, true).
% 0.12/0.39 Axiom 19 (pqp_6): fresh14(X, X) = p_7.
% 0.12/0.39 Axiom 20 (pqp_6): fresh13(X, X) = true.
% 0.12/0.39 Axiom 21 (pqp_6): fresh14(q_6, true) = fresh13(p_6, true).
% 0.12/0.39 Axiom 22 (pqq_1): fresh12(X, X) = q_2.
% 0.12/0.39 Axiom 23 (pqq_1): fresh11(X, X) = true.
% 0.12/0.39 Axiom 24 (pqq_1): fresh12(q_1, true) = fresh11(p_1, true).
% 0.12/0.39 Axiom 25 (pqq_2): fresh10(X, X) = q_3.
% 0.12/0.39 Axiom 26 (pqq_2): fresh9(X, X) = true.
% 0.12/0.39 Axiom 27 (pqq_2): fresh10(q_2, true) = fresh9(p_2, true).
% 0.12/0.39 Axiom 28 (pqq_3): fresh8(X, X) = q_4.
% 0.12/0.39 Axiom 29 (pqq_3): fresh7(X, X) = true.
% 0.12/0.39 Axiom 30 (pqq_3): fresh8(q_3, true) = fresh7(p_3, true).
% 0.12/0.39 Axiom 31 (pqq_4): fresh6(X, X) = q_5.
% 0.12/0.39 Axiom 32 (pqq_4): fresh5(X, X) = true.
% 0.12/0.39 Axiom 33 (pqq_4): fresh6(q_4, true) = fresh5(p_4, true).
% 0.12/0.39 Axiom 34 (pqq_5): fresh4(X, X) = q_6.
% 0.12/0.39 Axiom 35 (pqq_5): fresh3(X, X) = true.
% 0.12/0.39 Axiom 36 (pqq_5): fresh4(q_5, true) = fresh3(p_5, true).
% 0.12/0.39 Axiom 37 (pqq_6): fresh2(X, X) = q_7.
% 0.12/0.39 Axiom 38 (pqq_6): fresh2(q_6, true) = fresh(p_6, true).
% 0.12/0.39
% 0.12/0.39 Lemma 39: q_1 = p_1.
% 0.12/0.39 Proof:
% 0.12/0.39 q_1
% 0.12/0.39 = { by axiom 2 (base_2) }
% 0.12/0.39 true
% 0.12/0.39 = { by axiom 1 (base_1) R->L }
% 0.12/0.39 p_1
% 0.12/0.39
% 0.12/0.39 Lemma 40: p_2 = p_1.
% 0.12/0.39 Proof:
% 0.12/0.39 p_2
% 0.12/0.39 = { by axiom 5 (pqp_1) R->L }
% 0.12/0.39 fresh23(p_1, p_1)
% 0.12/0.39 = { by axiom 1 (base_1) }
% 0.12/0.39 fresh23(p_1, true)
% 0.12/0.39 = { by lemma 39 R->L }
% 0.12/0.39 fresh23(q_1, true)
% 0.12/0.39 = { by axiom 6 (pqp_1) }
% 0.12/0.39 fresh24(p_1, true)
% 0.12/0.39 = { by axiom 1 (base_1) R->L }
% 0.12/0.39 fresh24(p_1, p_1)
% 0.12/0.39 = { by axiom 4 (pqp_1) }
% 0.12/0.39 true
% 0.12/0.39 = { by axiom 1 (base_1) R->L }
% 0.12/0.39 p_1
% 0.12/0.39
% 0.12/0.39 Lemma 41: q_2 = p_1.
% 0.12/0.39 Proof:
% 0.12/0.39 q_2
% 0.12/0.39 = { by axiom 22 (pqq_1) R->L }
% 0.12/0.39 fresh12(p_1, p_1)
% 0.12/0.39 = { by axiom 1 (base_1) }
% 0.12/0.39 fresh12(p_1, true)
% 0.12/0.39 = { by lemma 39 R->L }
% 0.12/0.39 fresh12(q_1, true)
% 0.12/0.39 = { by axiom 24 (pqq_1) }
% 0.12/0.39 fresh11(p_1, true)
% 0.12/0.39 = { by axiom 1 (base_1) R->L }
% 0.12/0.39 fresh11(p_1, p_1)
% 0.12/0.39 = { by axiom 23 (pqq_1) }
% 0.12/0.39 true
% 0.12/0.39 = { by axiom 1 (base_1) R->L }
% 0.12/0.39 p_1
% 0.12/0.39
% 0.12/0.39 Lemma 42: p_3 = p_1.
% 0.12/0.39 Proof:
% 0.12/0.39 p_3
% 0.12/0.39 = { by axiom 7 (pqp_2) R->L }
% 0.12/0.39 fresh22(p_1, p_1)
% 0.12/0.39 = { by lemma 41 R->L }
% 0.12/0.39 fresh22(q_2, p_1)
% 0.12/0.39 = { by axiom 1 (base_1) }
% 0.12/0.39 fresh22(q_2, true)
% 0.12/0.39 = { by axiom 9 (pqp_2) }
% 0.12/0.39 fresh21(p_2, true)
% 0.12/0.39 = { by lemma 40 }
% 0.12/0.39 fresh21(p_1, true)
% 0.12/0.39 = { by axiom 1 (base_1) R->L }
% 0.12/0.39 fresh21(p_1, p_1)
% 0.12/0.39 = { by axiom 8 (pqp_2) }
% 0.12/0.39 true
% 0.12/0.39 = { by axiom 1 (base_1) R->L }
% 0.12/0.39 p_1
% 0.12/0.39
% 0.12/0.39 Lemma 43: q_3 = p_1.
% 0.12/0.39 Proof:
% 0.12/0.39 q_3
% 0.12/0.39 = { by axiom 25 (pqq_2) R->L }
% 0.12/0.39 fresh10(p_1, p_1)
% 0.12/0.39 = { by axiom 1 (base_1) }
% 0.12/0.39 fresh10(p_1, true)
% 0.12/0.39 = { by lemma 41 R->L }
% 0.12/0.39 fresh10(q_2, true)
% 0.12/0.39 = { by axiom 27 (pqq_2) }
% 0.12/0.39 fresh9(p_2, true)
% 0.12/0.39 = { by lemma 40 }
% 0.12/0.39 fresh9(p_1, true)
% 0.12/0.39 = { by axiom 1 (base_1) R->L }
% 0.12/0.39 fresh9(p_1, p_1)
% 0.12/0.39 = { by axiom 26 (pqq_2) }
% 0.12/0.39 true
% 0.12/0.39 = { by axiom 1 (base_1) R->L }
% 0.12/0.39 p_1
% 0.12/0.39
% 0.12/0.39 Lemma 44: p_4 = p_1.
% 0.12/0.39 Proof:
% 0.12/0.39 p_4
% 0.12/0.39 = { by axiom 10 (pqp_3) R->L }
% 0.12/0.39 fresh20(p_1, p_1)
% 0.12/0.39 = { by lemma 43 R->L }
% 0.12/0.39 fresh20(q_3, p_1)
% 0.12/0.39 = { by axiom 1 (base_1) }
% 0.12/0.39 fresh20(q_3, true)
% 0.12/0.39 = { by axiom 12 (pqp_3) }
% 0.12/0.39 fresh19(p_3, true)
% 0.12/0.39 = { by axiom 1 (base_1) R->L }
% 0.12/0.39 fresh19(p_3, p_1)
% 0.12/0.39 = { by lemma 42 }
% 0.12/0.39 fresh19(p_1, p_1)
% 0.12/0.39 = { by axiom 11 (pqp_3) }
% 0.12/0.39 true
% 0.12/0.39 = { by axiom 1 (base_1) R->L }
% 0.12/0.39 p_1
% 0.12/0.39
% 0.12/0.39 Lemma 45: q_4 = p_1.
% 0.12/0.39 Proof:
% 0.12/0.39 q_4
% 0.12/0.39 = { by axiom 28 (pqq_3) R->L }
% 0.12/0.39 fresh8(p_1, p_1)
% 0.12/0.39 = { by axiom 1 (base_1) }
% 0.12/0.39 fresh8(p_1, true)
% 0.12/0.39 = { by lemma 43 R->L }
% 0.12/0.39 fresh8(q_3, true)
% 0.12/0.39 = { by axiom 30 (pqq_3) }
% 0.12/0.39 fresh7(p_3, true)
% 0.12/0.39 = { by axiom 1 (base_1) R->L }
% 0.12/0.39 fresh7(p_3, p_1)
% 0.12/0.39 = { by lemma 42 }
% 0.12/0.39 fresh7(p_1, p_1)
% 0.12/0.39 = { by axiom 29 (pqq_3) }
% 0.12/0.39 true
% 0.12/0.39 = { by axiom 1 (base_1) R->L }
% 0.12/0.39 p_1
% 0.12/0.39
% 0.12/0.39 Lemma 46: p_5 = p_1.
% 0.12/0.39 Proof:
% 0.12/0.39 p_5
% 0.12/0.39 = { by axiom 13 (pqp_4) R->L }
% 0.12/0.39 fresh18(p_1, p_1)
% 0.12/0.39 = { by lemma 45 R->L }
% 0.12/0.39 fresh18(q_4, p_1)
% 0.12/0.39 = { by axiom 1 (base_1) }
% 0.12/0.39 fresh18(q_4, true)
% 0.12/0.39 = { by axiom 15 (pqp_4) }
% 0.12/0.39 fresh17(p_4, true)
% 0.12/0.39 = { by axiom 1 (base_1) R->L }
% 0.12/0.39 fresh17(p_4, p_1)
% 0.12/0.39 = { by lemma 44 }
% 0.12/0.39 fresh17(p_1, p_1)
% 0.12/0.39 = { by axiom 14 (pqp_4) }
% 0.12/0.39 true
% 0.12/0.39 = { by axiom 1 (base_1) R->L }
% 0.12/0.39 p_1
% 0.12/0.39
% 0.12/0.39 Lemma 47: q_5 = p_1.
% 0.12/0.39 Proof:
% 0.12/0.39 q_5
% 0.12/0.39 = { by axiom 31 (pqq_4) R->L }
% 0.12/0.39 fresh6(p_1, p_1)
% 0.12/0.39 = { by lemma 45 R->L }
% 0.12/0.39 fresh6(q_4, p_1)
% 0.12/0.39 = { by axiom 1 (base_1) }
% 0.12/0.39 fresh6(q_4, true)
% 0.12/0.39 = { by axiom 33 (pqq_4) }
% 0.12/0.39 fresh5(p_4, true)
% 0.12/0.39 = { by axiom 1 (base_1) R->L }
% 0.12/0.39 fresh5(p_4, p_1)
% 0.12/0.39 = { by lemma 44 }
% 0.12/0.39 fresh5(p_1, p_1)
% 0.12/0.39 = { by axiom 32 (pqq_4) }
% 0.12/0.39 true
% 0.12/0.39 = { by axiom 1 (base_1) R->L }
% 0.12/0.39 p_1
% 0.12/0.39
% 0.12/0.39 Lemma 48: p_6 = p_1.
% 0.12/0.39 Proof:
% 0.12/0.39 p_6
% 0.12/0.39 = { by axiom 16 (pqp_5) R->L }
% 0.12/0.39 fresh16(p_1, p_1)
% 0.12/0.39 = { by lemma 47 R->L }
% 0.12/0.39 fresh16(q_5, p_1)
% 0.12/0.39 = { by axiom 1 (base_1) }
% 0.12/0.39 fresh16(q_5, true)
% 0.12/0.39 = { by axiom 18 (pqp_5) }
% 0.12/0.39 fresh15(p_5, true)
% 0.12/0.39 = { by axiom 1 (base_1) R->L }
% 0.12/0.39 fresh15(p_5, p_1)
% 0.12/0.39 = { by lemma 46 }
% 0.12/0.39 fresh15(p_1, p_1)
% 0.12/0.39 = { by axiom 17 (pqp_5) }
% 0.12/0.39 true
% 0.12/0.39 = { by axiom 1 (base_1) R->L }
% 0.12/0.39 p_1
% 0.12/0.39
% 0.12/0.39 Lemma 49: q_6 = p_1.
% 0.12/0.39 Proof:
% 0.12/0.39 q_6
% 0.12/0.39 = { by axiom 34 (pqq_5) R->L }
% 0.12/0.39 fresh4(p_1, p_1)
% 0.12/0.39 = { by lemma 47 R->L }
% 0.12/0.39 fresh4(q_5, p_1)
% 0.12/0.39 = { by axiom 1 (base_1) }
% 0.12/0.39 fresh4(q_5, true)
% 0.12/0.39 = { by axiom 36 (pqq_5) }
% 0.12/0.39 fresh3(p_5, true)
% 0.12/0.39 = { by axiom 1 (base_1) R->L }
% 0.12/0.39 fresh3(p_5, p_1)
% 0.12/0.39 = { by lemma 46 }
% 0.12/0.39 fresh3(p_1, p_1)
% 0.12/0.39 = { by axiom 35 (pqq_5) }
% 0.12/0.39 true
% 0.12/0.39 = { by axiom 1 (base_1) R->L }
% 0.12/0.39 p_1
% 0.12/0.39
% 0.12/0.39 Goal 1 (base_3): tuple(p_7, q_7) = tuple(true, true).
% 0.12/0.39 Proof:
% 0.12/0.39 tuple(p_7, q_7)
% 0.12/0.39 = { by axiom 19 (pqp_6) R->L }
% 0.12/0.39 tuple(fresh14(p_1, p_1), q_7)
% 0.12/0.39 = { by lemma 49 R->L }
% 0.12/0.39 tuple(fresh14(q_6, p_1), q_7)
% 0.12/0.39 = { by axiom 1 (base_1) }
% 0.12/0.39 tuple(fresh14(q_6, true), q_7)
% 0.12/0.39 = { by axiom 21 (pqp_6) }
% 0.12/0.39 tuple(fresh13(p_6, true), q_7)
% 0.12/0.39 = { by axiom 1 (base_1) R->L }
% 0.12/0.39 tuple(fresh13(p_6, p_1), q_7)
% 0.12/0.39 = { by lemma 48 }
% 0.12/0.39 tuple(fresh13(p_1, p_1), q_7)
% 0.12/0.39 = { by axiom 20 (pqp_6) }
% 0.12/0.39 tuple(true, q_7)
% 0.12/0.39 = { by axiom 1 (base_1) R->L }
% 0.12/0.39 tuple(p_1, q_7)
% 0.12/0.39 = { by axiom 37 (pqq_6) R->L }
% 0.12/0.39 tuple(p_1, fresh2(p_1, p_1))
% 0.12/0.39 = { by lemma 49 R->L }
% 0.12/0.39 tuple(p_1, fresh2(q_6, p_1))
% 0.12/0.39 = { by axiom 1 (base_1) }
% 0.12/0.39 tuple(p_1, fresh2(q_6, true))
% 0.12/0.39 = { by axiom 38 (pqq_6) }
% 0.12/0.39 tuple(p_1, fresh(p_6, true))
% 0.12/0.39 = { by axiom 1 (base_1) R->L }
% 0.12/0.39 tuple(p_1, fresh(p_6, p_1))
% 0.12/0.39 = { by lemma 48 }
% 0.12/0.39 tuple(p_1, fresh(p_1, p_1))
% 0.12/0.39 = { by axiom 3 (pqq_6) }
% 0.12/0.39 tuple(p_1, true)
% 0.12/0.39 = { by axiom 1 (base_1) R->L }
% 0.12/0.39 tuple(p_1, p_1)
% 0.12/0.39 = { by axiom 1 (base_1) }
% 0.12/0.39 tuple(true, p_1)
% 0.12/0.39 = { by axiom 1 (base_1) }
% 0.12/0.39 tuple(true, true)
% 0.12/0.39 % SZS output end Proof
% 0.12/0.39
% 0.12/0.39 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------