0.07/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.07/0.12	% Command    : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
0.12/0.33	% Computer   : n002.cluster.edu
0.12/0.33	% Model      : x86_64 x86_64
0.12/0.33	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.12/0.33	% Memory     : 8042.1875MB
0.12/0.33	% OS         : Linux 3.10.0-693.el7.x86_64
0.12/0.33	% CPULimit   : 1200
0.12/0.33	% WCLimit    : 120
0.12/0.33	% DateTime   : Tue Jul 13 15:44:03 EDT 2021
0.12/0.34	% CPUTime    : 
10.16/1.68	% SZS status Theorem
10.16/1.68	
10.16/1.69	% SZS output start Proof
10.16/1.69	Take the following subset of the input axioms:
10.16/1.69	  fof(thm_2Ebool_2Ebool__case__thm, axiom, ![A_27a]: (![V2t1_2E0, V3t2_2E0]: s(A_27a, V3t2_2E0)=s(A_27a, c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool, c_2Ebool_2EF_2E0), s(A_27a, V2t1_2E0), s(A_27a, V3t2_2E0))) & ![V0t1_2E0, V1t2_2E0]: s(A_27a, V0t1_2E0)=s(A_27a, c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool, c_2Ebool_2ET_2E0), s(A_27a, V0t1_2E0), s(A_27a, V1t2_2E0))))).
10.16/1.69	  fof(thm_2Einteger_2EINT__LT__CALCULATE, axiom, ![V0n_2E0, V1m_2E0]: (s(tyop_2Emin_2Ebool, c_2Einteger_2Eint__lt_2E2(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum, V0n_2E0))), s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum, V1m_2E0)))))=s(tyop_2Emin_2Ebool, c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum, V0n_2E0), s(tyop_2Enum_2Enum, V1m_2E0))) & (s(tyop_2Emin_2Ebool, c_2Einteger_2Eint__lt_2E2(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum, V0n_2E0))), s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum, V1m_2E0)))))))=s(tyop_2Emin_2Ebool, c_2Ebool_2EF_2E0) & ((p(s(tyop_2Emin_2Ebool, c_2Einteger_2Eint__lt_2E2(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum, V0n_2E0))))), s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum, V1m_2E0)))))) <=> (s(tyop_2Enum_2Enum, V1m_2E0)!=s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0) | s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)!=s(tyop_2Enum_2Enum, V0n_2E0))) & s(tyop_2Emin_2Ebool, c_2Einteger_2Eint__lt_2E2(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum, V0n_2E0))))), s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum, V1m_2E0)))))))=s(tyop_2Emin_2Ebool, c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum, V1m_2E0), s(tyop_2Enum_2Enum, V0n_2E0))))))).
10.16/1.69	  fof(thm_2Einteger_2EINT__NEG__0, axiom, s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))=s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))))).
10.16/1.69	  fof(thm_2Einteger_2ENUM__OF__INT, axiom, ![V0n_2E0]: s(tyop_2Enum_2Enum, V0n_2E0)=s(tyop_2Enum_2Enum, c_2Einteger_2ENum_2E1(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum, V0n_2E0)))))).
10.16/1.69	  fof(thm_2Einteger__word_2Ei2w__0, conjecture, ![A_27a]: s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, A_27a), c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))=s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, A_27a), c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))))).
10.16/1.69	  fof(thm_2Einteger__word_2Ei2w__def, axiom, ![A_27a, V0i_2E0]: s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, A_27a), c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool, c_2Einteger_2Eint__lt_2E2(s(tyop_2Einteger_2Eint, V0i_2E0), s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0))))), s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, A_27a), c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, A_27a), c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum, c_2Einteger_2ENum_2E1(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint, V0i_2E0))))))))), s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, A_27a), c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum, c_2Einteger_2ENum_2E1(s(tyop_2Einteger_2Eint, V0i_2E0)))))))=s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, A_27a), c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint, V0i_2E0)))).
10.16/1.69	
10.16/1.69	Now clausify the problem and encode Horn clauses using encoding 3 of
10.16/1.69	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
10.16/1.69	We repeatedly replace C & s=t => u=v by the two clauses:
10.16/1.69	  fresh(y, y, x1...xn) = u
10.16/1.69	  C => fresh(s, t, x1...xn) = v
10.16/1.69	where fresh is a fresh function symbol and x1..xn are the free
10.16/1.69	variables of u and v.
10.16/1.69	A predicate p(X) is encoded as p(X)=true (this is sound, because the
10.16/1.69	input problem has no model of domain size 1).
10.16/1.69	
10.16/1.69	The encoding turns the above axioms into the following unit equations and goals:
10.16/1.69	
10.16/1.69	Axiom 1 (thm_2Einteger_2ENUM__OF__INT): s(tyop_2Enum_2Enum, X) = s(tyop_2Enum_2Enum, c_2Einteger_2ENum_2E1(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum, X))))).
10.16/1.69	Axiom 2 (thm_2Einteger_2EINT__NEG__0): s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0))) = s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0))))).
10.16/1.69	Axiom 3 (thm_2Ebool_2Ebool__case__thm): s(X, Y) = s(X, c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool, c_2Ebool_2EF_2E0), s(X, Z), s(X, Y))).
10.16/1.69	Axiom 4 (thm_2Einteger_2EINT__LT__CALCULATE): s(tyop_2Emin_2Ebool, c_2Einteger_2Eint__lt_2E2(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum, X))), s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum, Y))))))) = s(tyop_2Emin_2Ebool, c_2Ebool_2EF_2E0).
10.16/1.69	Axiom 5 (thm_2Einteger__word_2Ei2w__def): s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X), c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool, c_2Einteger_2Eint__lt_2E2(s(tyop_2Einteger_2Eint, Y), s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0))))), s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X), c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X), c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum, c_2Einteger_2ENum_2E1(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint, Y))))))))), s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X), c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum, c_2Einteger_2ENum_2E1(s(tyop_2Einteger_2Eint, Y))))))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, X), c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint, Y))).
10.16/1.69	
10.16/1.69	Goal 1 (thm_2Einteger__word_2Ei2w__0): s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, a_27a), c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, a_27a), c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0))))).
10.16/1.69	Proof:
10.16/1.69	  s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, a_27a), c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))
10.16/1.69	= { by axiom 1 (thm_2Einteger_2ENUM__OF__INT) }
10.16/1.69	  s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, a_27a), c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum, c_2Einteger_2ENum_2E1(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))))))
10.16/1.69	= { by axiom 3 (thm_2Ebool_2Ebool__case__thm) }
10.16/1.69	  s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, a_27a), c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool, c_2Ebool_2EF_2E0), s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, a_27a), c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, a_27a), c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum, c_2Einteger_2ENum_2E1(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0))))))))))), s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, a_27a), c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum, c_2Einteger_2ENum_2E1(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))))))))
10.16/1.69	= { by axiom 4 (thm_2Einteger_2EINT__LT__CALCULATE) R->L }
10.16/1.69	  s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, a_27a), c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool, c_2Einteger_2Eint__lt_2E2(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0))), s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0))))))), s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, a_27a), c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, a_27a), c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum, c_2Einteger_2ENum_2E1(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0))))))))))), s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, a_27a), c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum, c_2Einteger_2ENum_2E1(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))))))))
10.16/1.69	= { by axiom 2 (thm_2Einteger_2EINT__NEG__0) R->L }
10.16/1.69	  s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, a_27a), c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool, c_2Einteger_2Eint__lt_2E2(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0))), s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0))))), s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, a_27a), c_2Ewords_2Eword__2comp_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, a_27a), c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum, c_2Einteger_2ENum_2E1(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__neg_2E1(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0))))))))))), s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, a_27a), c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum, c_2Einteger_2ENum_2E1(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))))))))
10.16/1.69	= { by axiom 5 (thm_2Einteger__word_2Ei2w__def) }
10.16/1.69	  s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool, a_27a), c_2Einteger__word_2Ei2w_2E1(s(tyop_2Einteger_2Eint, c_2Einteger_2Eint__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))))
10.16/1.69	% SZS output end Proof
10.16/1.69	
10.16/1.69	RESULT: Theorem (the conjecture is true).
10.16/1.70	EOF