TSTP Solution File: CSR064+1 by Twee---2.4.2
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- Process Solution
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% File : Twee---2.4.2
% Problem : CSR064+1 : TPTP v8.1.2. Released v3.4.0.
% 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 : n016.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 : Wed Aug 30 21:41:36 EDT 2023
% Result : Theorem 0.21s 0.53s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : CSR064+1 : TPTP v8.1.2. Released v3.4.0.
% 0.13/0.15 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.36 % Computer : n016.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Mon Aug 28 08:05:29 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.53 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.21/0.53
% 0.21/0.53 % SZS status Theorem
% 0.21/0.53
% 0.21/0.53 % SZS output start Proof
% 0.21/0.53 Take the following subset of the input axioms:
% 0.21/0.53 fof(just10, axiom, ![ARG1, ARG2]: (genls(ARG1, ARG2) => subsetof(ARG1, ARG2))).
% 0.21/0.53 fof(just11, axiom, ![OBJ, COL1, COL2]: ~(isa(OBJ, COL1) & (isa(OBJ, COL2) & disjointwith(COL1, COL2)))).
% 0.21/0.53 fof(just15, axiom, ![OBJ2, COL1_2, COL2_2]: ~(isa(OBJ2, COL1_2) & (isa(OBJ2, COL2_2) & disjointwith(COL1_2, COL2_2)))).
% 0.21/0.53 fof(just2, axiom, ![OBJ2]: ~(individual(OBJ2) & setorcollection(OBJ2))).
% 0.21/0.53 fof(just3, axiom, individual(f_urlfn(f_urlfn(s_http_wwwahwatukeecomafnentertainmentarticles030423ahtml)))).
% 0.21/0.53 fof(just4, axiom, ![OBJ2, COL1_2, COL2_2]: ~(isa(OBJ2, COL1_2) & (isa(OBJ2, COL2_2) & disjointwith(COL1_2, COL2_2)))).
% 0.21/0.53 fof(just41, axiom, ![INS, ARG2_2]: (subsetof(INS, ARG2_2) => setorcollection(INS))).
% 0.21/0.53 fof(query64, conjecture, ~genls(f_urlfn(f_urlfn(s_http_wwwahwatukeecomafnentertainmentarticles030423ahtml)), c_tptpcol_15_74743)).
% 0.21/0.53
% 0.21/0.53 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.53 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.53 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.53 fresh(y, y, x1...xn) = u
% 0.21/0.53 C => fresh(s, t, x1...xn) = v
% 0.21/0.53 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.53 variables of u and v.
% 0.21/0.53 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.53 input problem has no model of domain size 1).
% 0.21/0.53
% 0.21/0.53 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.53
% 0.21/0.53 Axiom 1 (just41): fresh44(X, X, Y) = true2.
% 0.21/0.53 Axiom 2 (just3): individual(f_urlfn(f_urlfn(s_http_wwwahwatukeecomafnentertainmentarticles030423ahtml))) = true2.
% 0.21/0.53 Axiom 3 (just10): fresh80(X, X, Y, Z) = true2.
% 0.21/0.53 Axiom 4 (query64): genls(f_urlfn(f_urlfn(s_http_wwwahwatukeecomafnentertainmentarticles030423ahtml)), c_tptpcol_15_74743) = true2.
% 0.21/0.53 Axiom 5 (just41): fresh44(subsetof(X, Y), true2, X) = setorcollection(X).
% 0.21/0.53 Axiom 6 (just10): fresh80(genls(X, Y), true2, X, Y) = subsetof(X, Y).
% 0.21/0.53
% 0.21/0.53 Goal 1 (just2): tuple2(individual(X), setorcollection(X)) = tuple2(true2, true2).
% 0.21/0.53 The goal is true when:
% 0.21/0.53 X = f_urlfn(f_urlfn(s_http_wwwahwatukeecomafnentertainmentarticles030423ahtml))
% 0.21/0.53
% 0.21/0.53 Proof:
% 0.21/0.53 tuple2(individual(f_urlfn(f_urlfn(s_http_wwwahwatukeecomafnentertainmentarticles030423ahtml))), setorcollection(f_urlfn(f_urlfn(s_http_wwwahwatukeecomafnentertainmentarticles030423ahtml))))
% 0.21/0.53 = { by axiom 5 (just41) R->L }
% 0.21/0.53 tuple2(individual(f_urlfn(f_urlfn(s_http_wwwahwatukeecomafnentertainmentarticles030423ahtml))), fresh44(subsetof(f_urlfn(f_urlfn(s_http_wwwahwatukeecomafnentertainmentarticles030423ahtml)), c_tptpcol_15_74743), true2, f_urlfn(f_urlfn(s_http_wwwahwatukeecomafnentertainmentarticles030423ahtml))))
% 0.21/0.53 = { by axiom 6 (just10) R->L }
% 0.21/0.53 tuple2(individual(f_urlfn(f_urlfn(s_http_wwwahwatukeecomafnentertainmentarticles030423ahtml))), fresh44(fresh80(genls(f_urlfn(f_urlfn(s_http_wwwahwatukeecomafnentertainmentarticles030423ahtml)), c_tptpcol_15_74743), true2, f_urlfn(f_urlfn(s_http_wwwahwatukeecomafnentertainmentarticles030423ahtml)), c_tptpcol_15_74743), true2, f_urlfn(f_urlfn(s_http_wwwahwatukeecomafnentertainmentarticles030423ahtml))))
% 0.21/0.53 = { by axiom 4 (query64) }
% 0.21/0.53 tuple2(individual(f_urlfn(f_urlfn(s_http_wwwahwatukeecomafnentertainmentarticles030423ahtml))), fresh44(fresh80(true2, true2, f_urlfn(f_urlfn(s_http_wwwahwatukeecomafnentertainmentarticles030423ahtml)), c_tptpcol_15_74743), true2, f_urlfn(f_urlfn(s_http_wwwahwatukeecomafnentertainmentarticles030423ahtml))))
% 0.21/0.53 = { by axiom 3 (just10) }
% 0.21/0.53 tuple2(individual(f_urlfn(f_urlfn(s_http_wwwahwatukeecomafnentertainmentarticles030423ahtml))), fresh44(true2, true2, f_urlfn(f_urlfn(s_http_wwwahwatukeecomafnentertainmentarticles030423ahtml))))
% 0.21/0.53 = { by axiom 1 (just41) }
% 0.21/0.53 tuple2(individual(f_urlfn(f_urlfn(s_http_wwwahwatukeecomafnentertainmentarticles030423ahtml))), true2)
% 0.21/0.53 = { by axiom 2 (just3) }
% 0.21/0.53 tuple2(true2, true2)
% 0.21/0.53 % SZS output end Proof
% 0.21/0.53
% 0.21/0.53 RESULT: Theorem (the conjecture is true).
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