TSTP Solution File: SWV192+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWV192+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 : n010.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 0.21s 0.68s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SWV192+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.00/0.15 % 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 : n010.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 08:27:03 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.21/0.68 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 0.21/0.68
% 0.21/0.68 % SZS status Theorem
% 0.21/0.68
% 0.21/0.68 % SZS output start Proof
% 0.21/0.68 Take the following subset of the input axioms:
% 0.21/0.70 fof(finite_domain_0, axiom, ![X]: ((leq(n0, X) & leq(X, n0)) => X=n0)).
% 0.21/0.70 fof(irreflexivity_gt, axiom, ![X2]: ~gt(X2, X2)).
% 0.21/0.70 fof(leq_succ, axiom, ![Y, X2]: (leq(X2, Y) => leq(X2, succ(Y)))).
% 0.21/0.70 fof(leq_succ_gt_equiv, axiom, ![X2, Y2]: (leq(X2, Y2) <=> gt(succ(Y2), X2))).
% 0.21/0.70 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)))).
% 0.21/0.70 fof(quaternion_ds1_inuse_0003, 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, n0) & (leq(pv5, n998) & (gt(pv5, n0) & (![B2, A2_2]: ((leq(n0, A2_2) & (leq(n0, B2) & (leq(A2_2, n2) & leq(B2, pred(pv5))))) => a_select3(u_defuse, A2_2, B2)=use) & ![C2, D2]: ((leq(n0, C2) & (leq(n0, D2) & (leq(C2, n2) & leq(D2, pred(pv5))))) => a_select3(z_defuse, C2, D2)=use))))))))))))))))))))))))))))))))) => ![E2, F2]: ((leq(n0, E2) & (leq(n0, F2) & (leq(E2, n2) & leq(F2, pred(pv5))))) => ((~(n0=E2 & pv5=F2) & (~(n1=E2 & pv5=F2) & ~(n2=E2 & pv5=F2))) => a_select3(u_defuse, E2, F2)=use))).
% 0.21/0.70 fof(succ_pred, axiom, ![X2]: succ(pred(X2))=X2).
% 0.21/0.70
% 0.21/0.70 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.70 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.70 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.70 fresh(y, y, x1...xn) = u
% 0.21/0.70 C => fresh(s, t, x1...xn) = v
% 0.21/0.70 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.70 variables of u and v.
% 0.21/0.70 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.70 input problem has no model of domain size 1).
% 0.21/0.70
% 0.21/0.70 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.70
% 0.21/0.70 Axiom 1 (quaternion_ds1_inuse_0003_28): leq(n0, pv5) = true3.
% 0.21/0.70 Axiom 2 (quaternion_ds1_inuse_0003_29): leq(n0, f) = true3.
% 0.21/0.70 Axiom 3 (quaternion_ds1_inuse_0003_31): leq(pv5, n0) = true3.
% 0.21/0.70 Axiom 4 (quaternion_ds1_inuse_0003_33): leq(f, pred(pv5)) = true3.
% 0.21/0.70 Axiom 5 (succ_pred): succ(pred(X)) = X.
% 0.21/0.70 Axiom 6 (finite_domain_0): fresh(X, X, Y) = Y.
% 0.21/0.70 Axiom 7 (finite_domain_0): fresh41(X, X, Y) = n0.
% 0.21/0.70 Axiom 8 (finite_domain_0): fresh(leq(n0, X), true3, X) = fresh41(leq(X, n0), true3, X).
% 0.21/0.70 Axiom 9 (leq_succ): fresh34(X, X, Y, Z) = true3.
% 0.21/0.70 Axiom 10 (leq_succ_gt_equiv_1): fresh31(X, X, Y, Z) = true3.
% 0.21/0.70 Axiom 11 (leq_succ): fresh34(leq(X, Y), true3, X, Y) = leq(X, succ(Y)).
% 0.21/0.70 Axiom 12 (leq_succ_gt_equiv_1): fresh31(leq(X, Y), true3, X, Y) = gt(succ(Y), X).
% 0.21/0.70
% 0.21/0.70 Lemma 13: pv5 = n0.
% 0.21/0.70 Proof:
% 0.21/0.70 pv5
% 0.21/0.70 = { by axiom 6 (finite_domain_0) R->L }
% 0.21/0.70 fresh(true3, true3, pv5)
% 0.21/0.70 = { by axiom 1 (quaternion_ds1_inuse_0003_28) R->L }
% 0.21/0.70 fresh(leq(n0, pv5), true3, pv5)
% 0.21/0.70 = { by axiom 8 (finite_domain_0) }
% 0.21/0.70 fresh41(leq(pv5, n0), true3, pv5)
% 0.21/0.70 = { by axiom 3 (quaternion_ds1_inuse_0003_31) }
% 0.21/0.70 fresh41(true3, true3, pv5)
% 0.21/0.70 = { by axiom 7 (finite_domain_0) }
% 0.21/0.70 n0
% 0.21/0.70
% 0.21/0.70 Goal 1 (irreflexivity_gt): gt(X, X) = true3.
% 0.21/0.70 The goal is true when:
% 0.21/0.70 X = n0
% 0.21/0.70
% 0.21/0.70 Proof:
% 0.21/0.70 gt(n0, n0)
% 0.21/0.70 = { by axiom 7 (finite_domain_0) R->L }
% 0.21/0.70 gt(n0, fresh41(true3, true3, f))
% 0.21/0.70 = { by axiom 9 (leq_succ) R->L }
% 0.21/0.70 gt(n0, fresh41(fresh34(true3, true3, f, pred(pv5)), true3, f))
% 0.21/0.70 = { by axiom 4 (quaternion_ds1_inuse_0003_33) R->L }
% 0.21/0.70 gt(n0, fresh41(fresh34(leq(f, pred(pv5)), true3, f, pred(pv5)), true3, f))
% 0.21/0.70 = { by axiom 11 (leq_succ) }
% 0.21/0.70 gt(n0, fresh41(leq(f, succ(pred(pv5))), true3, f))
% 0.21/0.70 = { by axiom 5 (succ_pred) }
% 0.21/0.70 gt(n0, fresh41(leq(f, pv5), true3, f))
% 0.21/0.70 = { by lemma 13 }
% 0.21/0.70 gt(n0, fresh41(leq(f, n0), true3, f))
% 0.21/0.70 = { by axiom 8 (finite_domain_0) R->L }
% 0.21/0.70 gt(n0, fresh(leq(n0, f), true3, f))
% 0.21/0.70 = { by axiom 2 (quaternion_ds1_inuse_0003_29) }
% 0.21/0.70 gt(n0, fresh(true3, true3, f))
% 0.21/0.70 = { by axiom 6 (finite_domain_0) }
% 0.21/0.70 gt(n0, f)
% 0.21/0.70 = { by lemma 13 R->L }
% 0.21/0.70 gt(pv5, f)
% 0.21/0.70 = { by axiom 5 (succ_pred) R->L }
% 0.21/0.70 gt(succ(pred(pv5)), f)
% 0.21/0.70 = { by axiom 12 (leq_succ_gt_equiv_1) R->L }
% 0.21/0.70 fresh31(leq(f, pred(pv5)), true3, f, pred(pv5))
% 0.21/0.70 = { by axiom 4 (quaternion_ds1_inuse_0003_33) }
% 0.21/0.70 fresh31(true3, true3, f, pred(pv5))
% 0.21/0.70 = { by axiom 10 (leq_succ_gt_equiv_1) }
% 0.21/0.70 true3
% 0.21/0.70 % SZS output end Proof
% 0.21/0.70
% 0.21/0.70 RESULT: Theorem (the conjecture is true).
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