TSTP Solution File: SWV201+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWV201+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 : n028.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 23:02:58 EDT 2023
% Result : Theorem 3.55s 0.83s
% Output : Proof 3.55s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SWV201+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.12/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n028.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 29 07:51:10 EDT 2023
% 0.13/0.34 % CPUTime :
% 3.55/0.83 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 3.55/0.83
% 3.55/0.83 % SZS status Theorem
% 3.55/0.83
% 3.55/0.83 % SZS output start Proof
% 3.55/0.83 Take the following subset of the input axioms:
% 3.55/0.85 fof(quaternion_ds1_inuse_0012, conjecture, (a_select2(rho_defuse, n0)=use & (a_select2(rho_defuse, n1)=use & (a_select2(rho_defuse, n2)=use & (a_select2(sigma_defuse, n0)=use & (a_select2(sigma_defuse, n1)=use & (a_select2(sigma_defuse, n2)=use & (a_select2(sigma_defuse, n3)=use & (a_select2(sigma_defuse, n4)=use & (a_select2(sigma_defuse, n5)=use & (a_select3(u_defuse, n0, n0)=use & (a_select3(u_defuse, n1, n0)=use & (a_select3(u_defuse, n2, n0)=use & (a_select2(xinit_defuse, n3)=use & (a_select2(xinit_defuse, n4)=use & (a_select2(xinit_defuse, n5)=use & (a_select2(xinit_mean_defuse, n0)=use & (a_select2(xinit_mean_defuse, n1)=use & (a_select2(xinit_mean_defuse, n2)=use & (a_select2(xinit_mean_defuse, n3)=use & (a_select2(xinit_mean_defuse, n4)=use & (a_select2(xinit_mean_defuse, n5)=use & (a_select2(xinit_noise_defuse, n0)=use & (a_select2(xinit_noise_defuse, n1)=use & (a_select2(xinit_noise_defuse, n2)=use & (a_select2(xinit_noise_defuse, n3)=use & (a_select2(xinit_noise_defuse, n4)=use & (a_select2(xinit_noise_defuse, n5)=use & (leq(n0, pv5) & (leq(pv5, n998) & (gt(pv5, n0) & (![B, A2]: ((leq(n0, A2) & (leq(n0, B) & (leq(A2, n2) & leq(B, pred(pv5))))) => a_select3(u_defuse, A2, B)=use) & ![C, D]: ((leq(n0, C) & (leq(n0, D) & (leq(C, n2) & leq(D, pred(pv5))))) => a_select3(z_defuse, C, D)=use)))))))))))))))))))))))))))))))) => ![E, F]: ((leq(n0, E) & (leq(n0, F) & (leq(E, n2) & leq(F, pred(pv5))))) => ((~(n0=E & pv5=F) & (~(n1=E & pv5=F) & ~(n2=E & pv5=F))) => a_select3(z_defuse, E, F)=use))).
% 3.55/0.85
% 3.55/0.85 Now clausify the problem and encode Horn clauses using encoding 3 of
% 3.55/0.85 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 3.55/0.85 We repeatedly replace C & s=t => u=v by the two clauses:
% 3.55/0.85 fresh(y, y, x1...xn) = u
% 3.55/0.85 C => fresh(s, t, x1...xn) = v
% 3.55/0.85 where fresh is a fresh function symbol and x1..xn are the free
% 3.55/0.85 variables of u and v.
% 3.55/0.85 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 3.55/0.85 input problem has no model of domain size 1).
% 3.55/0.85
% 3.55/0.85 The encoding turns the above axioms into the following unit equations and goals:
% 3.55/0.85
% 3.55/0.85 Axiom 1 (quaternion_ds1_inuse_0012_29): leq(n0, f) = true3.
% 3.55/0.85 Axiom 2 (quaternion_ds1_inuse_0012_30): leq(n0, e) = true3.
% 3.55/0.85 Axiom 3 (quaternion_ds1_inuse_0012_33): leq(e, n2) = true3.
% 3.55/0.85 Axiom 4 (quaternion_ds1_inuse_0012_32): leq(f, pred(pv5)) = true3.
% 3.55/0.85 Axiom 5 (quaternion_ds1_inuse_0012_39): fresh45(X, X, Y, Z) = use.
% 3.55/0.85 Axiom 6 (quaternion_ds1_inuse_0012_39): fresh11(X, X, Y, Z) = a_select3(z_defuse, Y, Z).
% 3.55/0.85 Axiom 7 (quaternion_ds1_inuse_0012_39): fresh44(X, X, Y, Z) = fresh45(leq(Y, n2), true3, Y, Z).
% 3.55/0.85 Axiom 8 (quaternion_ds1_inuse_0012_39): fresh43(X, X, Y, Z) = fresh44(leq(n0, Y), true3, Y, Z).
% 3.55/0.85 Axiom 9 (quaternion_ds1_inuse_0012_39): fresh43(leq(n0, X), true3, Y, X) = fresh11(leq(X, pred(pv5)), true3, Y, X).
% 3.55/0.85
% 3.55/0.85 Goal 1 (quaternion_ds1_inuse_0012_35): a_select3(z_defuse, e, f) = use.
% 3.55/0.85 Proof:
% 3.55/0.85 a_select3(z_defuse, e, f)
% 3.55/0.85 = { by axiom 6 (quaternion_ds1_inuse_0012_39) R->L }
% 3.55/0.85 fresh11(true3, true3, e, f)
% 3.55/0.85 = { by axiom 4 (quaternion_ds1_inuse_0012_32) R->L }
% 3.55/0.85 fresh11(leq(f, pred(pv5)), true3, e, f)
% 3.55/0.85 = { by axiom 9 (quaternion_ds1_inuse_0012_39) R->L }
% 3.55/0.85 fresh43(leq(n0, f), true3, e, f)
% 3.55/0.85 = { by axiom 1 (quaternion_ds1_inuse_0012_29) }
% 3.55/0.85 fresh43(true3, true3, e, f)
% 3.55/0.85 = { by axiom 8 (quaternion_ds1_inuse_0012_39) }
% 3.55/0.85 fresh44(leq(n0, e), true3, e, f)
% 3.55/0.85 = { by axiom 2 (quaternion_ds1_inuse_0012_30) }
% 3.55/0.85 fresh44(true3, true3, e, f)
% 3.55/0.85 = { by axiom 7 (quaternion_ds1_inuse_0012_39) }
% 3.55/0.85 fresh45(leq(e, n2), true3, e, f)
% 3.55/0.85 = { by axiom 3 (quaternion_ds1_inuse_0012_33) }
% 3.55/0.85 fresh45(true3, true3, e, f)
% 3.55/0.85 = { by axiom 5 (quaternion_ds1_inuse_0012_39) }
% 3.55/0.85 use
% 3.55/0.85 % SZS output end Proof
% 3.55/0.85
% 3.55/0.85 RESULT: Theorem (the conjecture is true).
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