TSTP Solution File: SWV211+1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SWV211+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 : n032.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 23:03:00 EDT 2023
% Result : Theorem 0.13s 0.51s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : SWV211+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.05/0.10 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 300
% 0.10/0.29 % DateTime : Tue Aug 29 09:56:31 EDT 2023
% 0.10/0.29 % CPUTime :
% 0.13/0.51 Command-line arguments: --no-flatten-goal
% 0.13/0.51
% 0.13/0.51 % SZS status Theorem
% 0.13/0.51
% 0.13/0.51 % SZS output start Proof
% 0.13/0.51 Take the following subset of the input axioms:
% 0.13/0.53 fof(quaternion_ds1_symm_0001, conjecture, ![A, B]: ((leq(n0, A) & (leq(n0, B) & (leq(A, n5) & leq(B, n5)))) => ((~(n0=A & n1=B) & (~(n0=A & n2=B) & (~(n0=A & n3=B) & (~(n0=A & n4=B) & (~(n0=A & n5=B) & (~(n0=B & n1=A) & (~(n0=B & n2=A) & (~(n0=B & n3=A) & (~(n0=B & n4=A) & (~(n0=B & n5=A) & (~(n1=A & n1=B) & (~(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) & (n0=A & (n0=B & n1=A))))))))))))))))))))))))))))))))))))) => n0=times(divide(n1, n400), a_select2(sigma, n0))))).
% 0.13/0.53
% 0.13/0.53 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.13/0.53 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.13/0.53 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.13/0.53 fresh(y, y, x1...xn) = u
% 0.13/0.53 C => fresh(s, t, x1...xn) = v
% 0.13/0.53 where fresh is a fresh function symbol and x1..xn are the free
% 0.13/0.53 variables of u and v.
% 0.13/0.53 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.13/0.53 input problem has no model of domain size 1).
% 0.13/0.53
% 0.13/0.53 The encoding turns the above axioms into the following unit equations and goals:
% 0.13/0.53
% 0.13/0.53 Axiom 1 (quaternion_ds1_symm_0001_2): n1 = a.
% 0.13/0.53 Axiom 2 (quaternion_ds1_symm_0001): n0 = b.
% 0.13/0.53 Axiom 3 (quaternion_ds1_symm_0001_1): n0 = a.
% 0.13/0.53
% 0.13/0.53 Lemma 4: b = n1.
% 0.13/0.53 Proof:
% 0.13/0.53 b
% 0.13/0.53 = { by axiom 2 (quaternion_ds1_symm_0001) R->L }
% 0.13/0.53 n0
% 0.13/0.53 = { by axiom 3 (quaternion_ds1_symm_0001_1) }
% 0.13/0.53 a
% 0.13/0.53 = { by axiom 1 (quaternion_ds1_symm_0001_2) R->L }
% 0.13/0.53 n1
% 0.13/0.53
% 0.13/0.53 Goal 1 (quaternion_ds1_symm_0001_18): tuple2(n1, n1) = tuple2(b, a).
% 0.13/0.53 Proof:
% 0.13/0.53 tuple2(n1, n1)
% 0.13/0.53 = { by lemma 4 R->L }
% 0.13/0.53 tuple2(b, n1)
% 0.13/0.53 = { by axiom 1 (quaternion_ds1_symm_0001_2) }
% 0.13/0.53 tuple2(b, a)
% 0.13/0.53
% 0.13/0.53 Goal 2 (quaternion_ds1_symm_0001_13): tuple2(n0, n1) = tuple2(a, b).
% 0.13/0.53 Proof:
% 0.13/0.53 tuple2(n0, n1)
% 0.13/0.53 = { by axiom 2 (quaternion_ds1_symm_0001) }
% 0.13/0.53 tuple2(b, n1)
% 0.13/0.53 = { by lemma 4 }
% 0.13/0.53 tuple2(n1, n1)
% 0.13/0.53 = { by lemma 4 R->L }
% 0.13/0.53 tuple2(n1, b)
% 0.13/0.53 = { by axiom 1 (quaternion_ds1_symm_0001_2) }
% 0.13/0.53 tuple2(a, b)
% 0.13/0.53
% 0.13/0.53 Goal 3 (quaternion_ds1_symm_0001_8): tuple2(n0, n1) = tuple2(b, a).
% 0.13/0.53 Proof:
% 0.13/0.53 tuple2(n0, n1)
% 0.13/0.53 = { by axiom 2 (quaternion_ds1_symm_0001) }
% 0.13/0.53 tuple2(b, n1)
% 0.13/0.53 = { by axiom 1 (quaternion_ds1_symm_0001_2) }
% 0.13/0.53 tuple2(b, a)
% 0.13/0.53 % SZS output end Proof
% 0.13/0.53
% 0.13/0.53 RESULT: Theorem (the conjecture is true).
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