TSTP Solution File: SWV214+1 by Twee---2.4.2
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- Process Solution
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% File : Twee---2.4.2
% Problem : SWV214+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 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 : Thu Aug 31 23:03:01 EDT 2023
% Result : Theorem 0.20s 0.57s
% 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
% 0.00/0.12 % Problem : SWV214+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.16/0.35 % Computer : n012.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Tue Aug 29 06:00:09 EDT 2023
% 0.16/0.35 % CPUTime :
% 0.20/0.57 Command-line arguments: --ground-connectedness --complete-subsets
% 0.20/0.57
% 0.20/0.57 % SZS status Theorem
% 0.20/0.57
% 0.20/0.59 % SZS output start Proof
% 0.20/0.59 Take the following subset of the input axioms:
% 0.20/0.62 fof(quaternion_ds1_symm_0121, conjecture, ![A, B]: ((leq(n0, A) & (leq(n0, B) & (leq(A, n5) & leq(B, n5)))) => ((~(n0=A & n2=B) & (~(n0=A & n3=B) & (~(n0=A & n4=B) & (~(n0=A & n5=B) & (~(n0=B & n3=A) & (~(n0=B & n4=A) & (~(n0=B & n5=A) & (~(n1=A & n2=B) & (~(n1=A & n3=B) & (~(n1=A & n4=B) & (~(n1=A & n5=B) & (~(n1=B & n2=A) & (~(n1=B & n3=A) & (~(n1=B & n4=A) & (~(n1=B & n5=A) & (~(n2=A & n2=B) & (~(n2=A & n3=B) & (~(n2=A & n4=B) & (~(n2=A & n5=B) & (~(n2=B & n3=A) & (~(n2=B & n4=A) & (~(n2=B & n5=A) & (~(n3=A & n3=B) & (~(n3=A & n4=B) & (~(n3=A & n5=B) & (~(n3=B & n4=A) & (~(n3=B & n5=A) & (~(n4=A & n4=B) & (~(n4=A & n5=B) & (~(n4=B & n5=A) & (~(n5=A & n5=B) & (n1=A & (n1=B & (n2=A & n5=B)))))))))))))))))))))))))))))))))) => n0=times(divide(n1, n400), a_select2(sigma, n1))))).
% 0.20/0.62
% 0.20/0.62 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.62 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.62 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.62 fresh(y, y, x1...xn) = u
% 0.20/0.62 C => fresh(s, t, x1...xn) = v
% 0.20/0.62 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.62 variables of u and v.
% 0.20/0.62 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.62 input problem has no model of domain size 1).
% 0.20/0.62
% 0.20/0.62 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.62
% 0.20/0.62 Axiom 1 (quaternion_ds1_symm_0121): n1 = b.
% 0.20/0.62 Axiom 2 (quaternion_ds1_symm_0121_3): n5 = b.
% 0.20/0.62 Axiom 3 (quaternion_ds1_symm_0121_2): n2 = a.
% 0.20/0.62 Axiom 4 (quaternion_ds1_symm_0121_1): n1 = a.
% 0.20/0.62
% 0.20/0.62 Lemma 5: n1 = n2.
% 0.20/0.62 Proof:
% 0.20/0.62 n1
% 0.20/0.62 = { by axiom 4 (quaternion_ds1_symm_0121_1) }
% 0.20/0.62 a
% 0.20/0.62 = { by axiom 3 (quaternion_ds1_symm_0121_2) R->L }
% 0.20/0.62 n2
% 0.20/0.62
% 0.20/0.62 Lemma 6: n5 = n1.
% 0.20/0.62 Proof:
% 0.20/0.62 n5
% 0.20/0.62 = { by axiom 2 (quaternion_ds1_symm_0121_3) }
% 0.20/0.62 b
% 0.20/0.62 = { by axiom 1 (quaternion_ds1_symm_0121) R->L }
% 0.20/0.62 n1
% 0.20/0.62
% 0.20/0.62 Goal 1 (quaternion_ds1_symm_0121_39): tuple2(n5, n5) = tuple2(b, a).
% 0.20/0.62 Proof:
% 0.20/0.62 tuple2(n5, n5)
% 0.20/0.62 = { by lemma 6 }
% 0.20/0.62 tuple2(n1, n5)
% 0.20/0.62 = { by lemma 6 }
% 0.20/0.62 tuple2(n1, n1)
% 0.20/0.62 = { by lemma 5 }
% 0.20/0.63 tuple2(n2, n1)
% 0.20/0.63 = { by lemma 5 }
% 0.20/0.63 tuple2(n2, n2)
% 0.20/0.63 = { by lemma 5 R->L }
% 0.20/0.63 tuple2(n1, n2)
% 0.20/0.63 = { by axiom 3 (quaternion_ds1_symm_0121_2) }
% 0.20/0.63 tuple2(n1, a)
% 0.20/0.63 = { by axiom 1 (quaternion_ds1_symm_0121) }
% 0.20/0.63 tuple2(b, a)
% 0.20/0.63
% 0.20/0.63 Goal 2 (quaternion_ds1_symm_0121_30): tuple2(n2, n5) = tuple2(a, b).
% 0.20/0.63 Proof:
% 0.20/0.63 tuple2(n2, n5)
% 0.20/0.63 = { by lemma 6 }
% 0.20/0.63 tuple2(n2, n1)
% 0.20/0.63 = { by axiom 3 (quaternion_ds1_symm_0121_2) }
% 0.20/0.63 tuple2(a, n1)
% 0.20/0.63 = { by axiom 1 (quaternion_ds1_symm_0121) }
% 0.20/0.63 tuple2(a, b)
% 0.20/0.63
% 0.20/0.63 Goal 3 (quaternion_ds1_symm_0121_27): tuple2(n2, n5) = tuple2(b, a).
% 0.20/0.63 Proof:
% 0.20/0.63 tuple2(n2, n5)
% 0.20/0.63 = { by lemma 6 }
% 0.20/0.63 tuple2(n2, n1)
% 0.20/0.63 = { by lemma 5 }
% 0.20/0.63 tuple2(n2, n2)
% 0.20/0.63 = { by lemma 5 R->L }
% 0.20/0.63 tuple2(n1, n2)
% 0.20/0.63 = { by axiom 3 (quaternion_ds1_symm_0121_2) }
% 0.20/0.63 tuple2(n1, a)
% 0.20/0.63 = { by axiom 1 (quaternion_ds1_symm_0121) }
% 0.20/0.63 tuple2(b, a)
% 0.20/0.63
% 0.20/0.63 Goal 4 (quaternion_ds1_symm_0121_24): tuple2(n2, n2) = tuple2(b, a).
% 0.20/0.63 Proof:
% 0.20/0.63 tuple2(n2, n2)
% 0.20/0.63 = { by lemma 5 R->L }
% 0.20/0.63 tuple2(n1, n2)
% 0.20/0.63 = { by axiom 3 (quaternion_ds1_symm_0121_2) }
% 0.20/0.63 tuple2(n1, a)
% 0.20/0.63 = { by axiom 1 (quaternion_ds1_symm_0121) }
% 0.20/0.63 tuple2(b, a)
% 0.20/0.63
% 0.20/0.63 Goal 5 (quaternion_ds1_symm_0121_23): tuple2(n1, n5) = tuple2(a, b).
% 0.20/0.63 Proof:
% 0.20/0.63 tuple2(n1, n5)
% 0.20/0.63 = { by lemma 6 }
% 0.20/0.63 tuple2(n1, n1)
% 0.20/0.63 = { by lemma 5 }
% 0.20/0.63 tuple2(n2, n1)
% 0.20/0.63 = { by axiom 3 (quaternion_ds1_symm_0121_2) }
% 0.20/0.63 tuple2(a, n1)
% 0.20/0.63 = { by axiom 1 (quaternion_ds1_symm_0121) }
% 0.20/0.63 tuple2(a, b)
% 0.20/0.63
% 0.20/0.63 Goal 6 (quaternion_ds1_symm_0121_20): tuple2(n1, n2) = tuple2(a, b).
% 0.20/0.63 Proof:
% 0.20/0.63 tuple2(n1, n2)
% 0.20/0.63 = { by lemma 5 }
% 0.20/0.63 tuple2(n2, n2)
% 0.20/0.63 = { by lemma 5 R->L }
% 0.20/0.63 tuple2(n2, n1)
% 0.20/0.63 = { by axiom 3 (quaternion_ds1_symm_0121_2) }
% 0.20/0.63 tuple2(a, n1)
% 0.20/0.63 = { by axiom 1 (quaternion_ds1_symm_0121) }
% 0.20/0.63 tuple2(a, b)
% 0.20/0.63
% 0.20/0.63 Goal 7 (quaternion_ds1_symm_0121_19): tuple2(n1, n5) = tuple2(b, a).
% 0.20/0.63 Proof:
% 0.20/0.63 tuple2(n1, n5)
% 0.20/0.63 = { by lemma 6 }
% 0.20/0.63 tuple2(n1, n1)
% 0.20/0.63 = { by lemma 5 }
% 0.20/0.63 tuple2(n2, n1)
% 0.20/0.63 = { by lemma 5 }
% 0.20/0.63 tuple2(n2, n2)
% 0.20/0.63 = { by lemma 5 R->L }
% 0.20/0.63 tuple2(n1, n2)
% 0.20/0.63 = { by axiom 3 (quaternion_ds1_symm_0121_2) }
% 0.20/0.63 tuple2(n1, a)
% 0.20/0.63 = { by axiom 1 (quaternion_ds1_symm_0121) }
% 0.20/0.63 tuple2(b, a)
% 0.20/0.63
% 0.20/0.63 Goal 8 (quaternion_ds1_symm_0121_16): tuple2(n1, n2) = tuple2(b, a).
% 0.20/0.63 Proof:
% 0.20/0.63 tuple2(n1, n2)
% 0.20/0.63 = { by axiom 3 (quaternion_ds1_symm_0121_2) }
% 0.20/0.63 tuple2(n1, a)
% 0.20/0.63 = { by axiom 1 (quaternion_ds1_symm_0121) }
% 0.20/0.63 tuple2(b, a)
% 0.20/0.63 % SZS output end Proof
% 0.20/0.63
% 0.20/0.63 RESULT: Theorem (the conjecture is true).
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