TSTP Solution File: SWV191+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWV191+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 : n020.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 23:02:56 EDT 2023
% Result : Theorem 0.14s 0.58s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.09 % Problem : SWV191+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.07/0.09 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.09/0.29 % Computer : n020.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Tue Aug 29 06:39:28 EDT 2023
% 0.09/0.29 % CPUTime :
% 0.14/0.58 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 0.14/0.58
% 0.14/0.58 % SZS status Theorem
% 0.14/0.58
% 0.14/0.58 % SZS output start Proof
% 0.14/0.58 Take the following subset of the input axioms:
% 0.14/0.59 fof(finite_domain_0, axiom, ![X]: ((leq(n0, X) & leq(X, n0)) => X=n0)).
% 0.14/0.59 fof(irreflexivity_gt, axiom, ![X2]: ~gt(X2, X2)).
% 0.14/0.59 fof(leq_succ, axiom, ![Y, X2]: (leq(X2, Y) => leq(X2, succ(Y)))).
% 0.14/0.59 fof(leq_succ_gt_equiv, axiom, ![X2, Y2]: (leq(X2, Y2) <=> gt(succ(Y2), X2))).
% 0.14/0.59 fof(matrix_symm_joseph_update, axiom, ![C, N, B, M, D, E, F, A2]: ((![I, J]: ((leq(n0, I) & (leq(I, M) & (leq(n0, J) & leq(J, M)))) => a_select3(D, I, J)=a_select3(D, J, I)) & (![I2, J2]: ((leq(n0, I2) & (leq(I2, N) & (leq(n0, J2) & leq(J2, N)))) => a_select3(A2, I2, J2)=a_select3(A2, J2, I2)) & ![I2, J2]: ((leq(n0, I2) & (leq(I2, N) & (leq(n0, J2) & leq(J2, N)))) => a_select3(F, I2, J2)=a_select3(F, J2, I2)))) => ![I2, J2]: ((leq(n0, I2) & (leq(I2, N) & (leq(n0, J2) & leq(J2, N)))) => a_select3(tptp_madd(A2, tptp_mmul(B, tptp_mmul(tptp_madd(tptp_mmul(C, tptp_mmul(D, trans(C))), tptp_mmul(E, tptp_mmul(F, trans(E)))), trans(B)))), I2, J2)=a_select3(tptp_madd(A2, tptp_mmul(B, tptp_mmul(tptp_madd(tptp_mmul(C, tptp_mmul(D, trans(C))), tptp_mmul(E, tptp_mmul(F, trans(E)))), trans(B)))), J2, I2)))).
% 0.14/0.59 fof(quaternion_ds1_inuse_0002, 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)))))))))))))))))))))))))) => ![A, B2]: ((leq(n0, A) & (leq(n0, B2) & (leq(A, n2) & leq(B2, tptp_minus_1)))) => a_select3(z_defuse, A, B2)=use)).
% 0.14/0.59 fof(succ_tptp_minus_1, axiom, succ(tptp_minus_1)=n0).
% 0.14/0.59
% 0.14/0.59 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.14/0.59 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.14/0.59 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.14/0.59 fresh(y, y, x1...xn) = u
% 0.14/0.59 C => fresh(s, t, x1...xn) = v
% 0.14/0.59 where fresh is a fresh function symbol and x1..xn are the free
% 0.14/0.59 variables of u and v.
% 0.14/0.59 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.14/0.59 input problem has no model of domain size 1).
% 0.14/0.59
% 0.14/0.59 The encoding turns the above axioms into the following unit equations and goals:
% 0.14/0.59
% 0.14/0.59 Axiom 1 (quaternion_ds1_inuse_0002_27): leq(n0, b) = true3.
% 0.14/0.59 Axiom 2 (quaternion_ds1_inuse_0002_29): leq(b, tptp_minus_1) = true3.
% 0.14/0.59 Axiom 3 (succ_tptp_minus_1): succ(tptp_minus_1) = n0.
% 0.14/0.59 Axiom 4 (finite_domain_0): fresh(X, X, Y) = Y.
% 0.14/0.59 Axiom 5 (finite_domain_0): fresh39(X, X, Y) = n0.
% 0.14/0.59 Axiom 6 (finite_domain_0): fresh(leq(n0, X), true3, X) = fresh39(leq(X, n0), true3, X).
% 0.14/0.59 Axiom 7 (leq_succ): fresh32(X, X, Y, Z) = true3.
% 0.14/0.59 Axiom 8 (leq_succ_gt_equiv_1): fresh29(X, X, Y, Z) = true3.
% 0.14/0.59 Axiom 9 (leq_succ): fresh32(leq(X, Y), true3, X, Y) = leq(X, succ(Y)).
% 0.14/0.59 Axiom 10 (leq_succ_gt_equiv_1): fresh29(leq(X, Y), true3, X, Y) = gt(succ(Y), X).
% 0.14/0.59
% 0.14/0.59 Goal 1 (irreflexivity_gt): gt(X, X) = true3.
% 0.14/0.59 The goal is true when:
% 0.14/0.59 X = n0
% 0.14/0.59
% 0.14/0.59 Proof:
% 0.14/0.59 gt(n0, n0)
% 0.14/0.59 = { by axiom 5 (finite_domain_0) R->L }
% 0.14/0.59 gt(n0, fresh39(true3, true3, b))
% 0.14/0.59 = { by axiom 7 (leq_succ) R->L }
% 0.14/0.59 gt(n0, fresh39(fresh32(true3, true3, b, tptp_minus_1), true3, b))
% 0.14/0.59 = { by axiom 2 (quaternion_ds1_inuse_0002_29) R->L }
% 0.14/0.59 gt(n0, fresh39(fresh32(leq(b, tptp_minus_1), true3, b, tptp_minus_1), true3, b))
% 0.14/0.59 = { by axiom 9 (leq_succ) }
% 0.14/0.59 gt(n0, fresh39(leq(b, succ(tptp_minus_1)), true3, b))
% 0.14/0.59 = { by axiom 3 (succ_tptp_minus_1) }
% 0.14/0.59 gt(n0, fresh39(leq(b, n0), true3, b))
% 0.14/0.59 = { by axiom 6 (finite_domain_0) R->L }
% 0.14/0.59 gt(n0, fresh(leq(n0, b), true3, b))
% 0.14/0.59 = { by axiom 1 (quaternion_ds1_inuse_0002_27) }
% 0.14/0.59 gt(n0, fresh(true3, true3, b))
% 0.14/0.59 = { by axiom 4 (finite_domain_0) }
% 0.14/0.59 gt(n0, b)
% 0.14/0.59 = { by axiom 3 (succ_tptp_minus_1) R->L }
% 0.14/0.59 gt(succ(tptp_minus_1), b)
% 0.14/0.59 = { by axiom 10 (leq_succ_gt_equiv_1) R->L }
% 0.14/0.59 fresh29(leq(b, tptp_minus_1), true3, b, tptp_minus_1)
% 0.14/0.59 = { by axiom 2 (quaternion_ds1_inuse_0002_29) }
% 0.14/0.59 fresh29(true3, true3, b, tptp_minus_1)
% 0.14/0.59 = { by axiom 8 (leq_succ_gt_equiv_1) }
% 0.14/0.59 true3
% 0.14/0.59 % SZS output end Proof
% 0.14/0.59
% 0.14/0.59 RESULT: Theorem (the conjecture is true).
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