TSTP Solution File: SWV230+1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SWV230+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 : n022.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 23:03:05 EDT 2023
% Result : Theorem 1.31s 0.61s
% Output : Proof 1.31s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14 % Problem : SWV230+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.07/0.15 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.15/0.36 % Computer : n022.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Tue Aug 29 04:11:08 EDT 2023
% 0.15/0.36 % CPUTime :
% 1.31/0.61 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 1.31/0.61
% 1.31/0.61 % SZS status Theorem
% 1.31/0.61
% 1.31/0.62 % SZS output start Proof
% 1.31/0.62 Take the following subset of the input axioms:
% 1.31/0.63 fof(quaternion_ds1_symm_0761, conjecture, (![B, A2]: ((leq(n0, A2) & (leq(n0, B) & (leq(A2, n5) & leq(B, n5)))) => a_select3(q_ds1_filter, A2, B)=a_select3(q_ds1_filter, B, A2)) & ![C, D]: ((leq(n0, C) & (leq(n0, D) & (leq(C, n2) & leq(D, n2)))) => a_select3(r_ds1_filter, C, D)=a_select3(r_ds1_filter, D, C))) => ![E, F]: ((leq(n0, E) & (leq(n0, F) & (leq(E, n5) & leq(F, n5)))) => ((~(n0=E & n5=F) & (~(n1=E & n5=F) & (~(n2=E & n5=F) & (~(n2=F & n5=E) & (~(n3=E & n5=F) & (~(n3=F & n5=E) & (~(n4=E & n5=F) & (~(n4=F & n5=E) & (~(n5=E & n5=F) & (n1=F & (n4=E & (n4=F & n5=E)))))))))))) => n0=a_select2(xinit_noise, n4)))).
% 1.31/0.63
% 1.31/0.63 Now clausify the problem and encode Horn clauses using encoding 3 of
% 1.31/0.63 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 1.31/0.63 We repeatedly replace C & s=t => u=v by the two clauses:
% 1.31/0.63 fresh(y, y, x1...xn) = u
% 1.31/0.63 C => fresh(s, t, x1...xn) = v
% 1.31/0.63 where fresh is a fresh function symbol and x1..xn are the free
% 1.31/0.63 variables of u and v.
% 1.31/0.63 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 1.31/0.63 input problem has no model of domain size 1).
% 1.31/0.63
% 1.31/0.63 The encoding turns the above axioms into the following unit equations and goals:
% 1.31/0.63
% 1.31/0.63 Axiom 1 (quaternion_ds1_symm_0761_1): n4 = f.
% 1.31/0.63 Axiom 2 (quaternion_ds1_symm_0761_3): n5 = e.
% 1.31/0.63 Axiom 3 (quaternion_ds1_symm_0761_2): n4 = e.
% 1.31/0.63 Axiom 4 (quaternion_ds1_symm_0761): n1 = f.
% 1.31/0.63
% 1.31/0.63 Lemma 5: n4 = n5.
% 1.31/0.63 Proof:
% 1.31/0.63 n4
% 1.31/0.63 = { by axiom 3 (quaternion_ds1_symm_0761_2) }
% 1.31/0.63 e
% 1.31/0.63 = { by axiom 2 (quaternion_ds1_symm_0761_3) R->L }
% 1.31/0.63 n5
% 1.31/0.63
% 1.31/0.63 Goal 1 (quaternion_ds1_symm_0761_17): tuple2(n5, n5) = tuple2(f, e).
% 1.31/0.63 Proof:
% 1.31/0.63 tuple2(n5, n5)
% 1.31/0.63 = { by lemma 5 R->L }
% 1.31/0.63 tuple2(n4, n5)
% 1.31/0.63 = { by axiom 2 (quaternion_ds1_symm_0761_3) }
% 1.31/0.63 tuple2(n4, e)
% 1.31/0.63 = { by axiom 1 (quaternion_ds1_symm_0761_1) }
% 1.31/0.63 tuple2(f, e)
% 1.31/0.63
% 1.31/0.63 Goal 2 (quaternion_ds1_symm_0761_16): tuple2(n4, n5) = tuple2(e, f).
% 1.31/0.63 Proof:
% 1.31/0.63 tuple2(n4, n5)
% 1.31/0.63 = { by lemma 5 }
% 1.31/0.63 tuple2(n5, n5)
% 1.31/0.63 = { by lemma 5 R->L }
% 1.31/0.63 tuple2(n5, n4)
% 1.31/0.63 = { by axiom 2 (quaternion_ds1_symm_0761_3) }
% 1.31/0.63 tuple2(e, n4)
% 1.31/0.63 = { by axiom 1 (quaternion_ds1_symm_0761_1) }
% 1.31/0.63 tuple2(e, f)
% 1.31/0.63
% 1.31/0.63 Goal 3 (quaternion_ds1_symm_0761_15): tuple2(n4, n5) = tuple2(f, e).
% 1.31/0.63 Proof:
% 1.31/0.63 tuple2(n4, n5)
% 1.31/0.63 = { by axiom 2 (quaternion_ds1_symm_0761_3) }
% 1.31/0.63 tuple2(n4, e)
% 1.31/0.63 = { by axiom 1 (quaternion_ds1_symm_0761_1) }
% 1.31/0.63 tuple2(f, e)
% 1.31/0.63
% 1.31/0.63 Goal 4 (quaternion_ds1_symm_0761_10): tuple2(n1, n5) = tuple2(e, f).
% 1.31/0.63 Proof:
% 1.31/0.63 tuple2(n1, n5)
% 1.31/0.63 = { by axiom 4 (quaternion_ds1_symm_0761) }
% 1.31/0.63 tuple2(f, n5)
% 1.31/0.63 = { by axiom 1 (quaternion_ds1_symm_0761_1) R->L }
% 1.31/0.63 tuple2(n4, n5)
% 1.31/0.63 = { by lemma 5 }
% 1.31/0.63 tuple2(n5, n5)
% 1.31/0.63 = { by lemma 5 R->L }
% 1.31/0.63 tuple2(n5, n4)
% 1.31/0.63 = { by axiom 2 (quaternion_ds1_symm_0761_3) }
% 1.31/0.63 tuple2(e, n4)
% 1.31/0.63 = { by axiom 1 (quaternion_ds1_symm_0761_1) }
% 1.31/0.63 tuple2(e, f)
% 1.31/0.63 % SZS output end Proof
% 1.31/0.63
% 1.31/0.63 RESULT: Theorem (the conjecture is true).
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