0.00/0.03 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.04 % Command : java -Xss128m -Xmx4g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar %s -t %d -p --atp cvc4=/export/starexec/sandbox2/solver/bin/externals/cvc4 --atp e=/export/starexec/sandbox2/solver/bin/externals/eprover --atp iprover=/export/starexec/sandbox2/solver/bin/externals/iprover 0.03/0.23 % Computer : n117.star.cs.uiowa.edu 0.03/0.23 % Model : x86_64 x86_64 0.03/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz 0.03/0.23 % Memory : 32218.625MB 0.03/0.23 % OS : Linux 3.10.0-693.2.2.el7.x86_64 0.03/0.23 % CPULimit : 300 0.03/0.23 % DateTime : Sat Jul 14 04:56:55 CDT 2018 0.03/0.23 % CPUTime : 3.04/1.60 % [INFO] Running in sequential loop mode. 3.75/1.83 % [CONFIG] Using configuration: timeout(300) with strategy 3.96/1.91 % [INFO] iprover registered as external prover. 3.96/1.92 % [INFO] e registered as external prover. 3.96/1.92 % [INFO] cvc4 registered as external prover. 3.96/1.92 % [INFO] Parsing finished. Scanning for conjecture ... 4.29/1.98 % [INFO] Found a conjecture and 64 axioms. Running axiom selection ... 4.52/2.05 % [INFO] Axiom selection finished. Selected 64 axioms (removed 0 axioms). 4.98/2.25 % [INFO] Type checking passed. Searching for refutation ... 11.02/4.18 % [INFO] Killing All external provers ... 11.02/4.18 % Time passed: 3856ms 11.02/4.18 % Effective reasoning time: 2570ms 11.02/4.18 % Solved by strategy 11.02/4.18 % Axioms used in derivation (64): isSomeType1, isFreeVar0, DIFF-empty-bind, EQ-bind, isValue2, isSomeExp0, getSomeExp0, subst4, reduce-INV, T-app, EQ-app, EQ-abs, reduce1, subst5, alpha-equiv-trans, alpha-equiv-subst-abs, DIFF-var-abs, reduce5, lookup1, T-var, getSomeType0, EQ-someExp, T-abs, reduce4, reduce0, T-Weak, EQ-empty, T-subst-abs-2-gen, T-inv, alpha-equiv-sym, EQ-var, EQ-noExp, isFreeVar2, subst-INV, isValue0, subst1, subst2, lookup0, DIFF-noType-someType, reduce3, isSomeType0, alpha-equiv-typing, T-Context-Duplicate, T-Weak-FreeVar, subst3, EQ-noType, isValue1, DIFF-abs-app, EQ-someType, EQ-arrow, isFreeVar1, gensym-is-fresh, reduce2, isSomeExp1, DIFF-var-app, reduce6, alpha-equiv-refl, alpha-equiv-FreeVar, subst0, lookup2, DIFF-noExp-someExp, lookup-INV, T-Strong, T-Context-Swap 11.02/4.18 % No. of inferences in proof: 132 11.02/4.18 % No. of processed clauses: 2 11.02/4.18 % No. of generated clauses: 0 11.02/4.18 % No. of forward subsumed clauses: 0 11.02/4.18 % No. of backward subsumed clauses: 0 11.02/4.18 % No. of ground rewrite rules in store: 2 11.02/4.18 % No. of non-ground rewrite rules in store: 0 11.02/4.18 % No. of positive (non-rewrite) units in store: 0 11.02/4.18 % No. of negative (non-rewrite) units in store: 0 11.02/4.19 % No. of choice functions detected: 0 11.02/4.19 % No. of choice instantiations: 0 11.02/4.19 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3856 ms resp. 2570 ms w/o parsing 11.59/4.28 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 11.59/4.28 thf(vapp_type, type, vapp: ($i > ($i > $i))). 11.59/4.28 thf(vvar_type, type, vvar: ($i > $i)). 11.59/4.28 thf(vgensym_type, type, vgensym: ($i > $i)). 11.59/4.28 thf(vempty_type, type, vempty: $i). 11.59/4.28 thf(visSomeType_type, type, visSomeType: ($i > $o)). 11.59/4.28 thf(vnoType_type, type, vnoType: $i). 11.59/4.28 thf(vlookup_type, type, vlookup: ($i > ($i > $i))). 11.59/4.28 thf(vbind_type, type, vbind: ($i > ($i > ($i > $i)))). 11.59/4.28 thf(vtcheck_type, type, vtcheck: ($i > ($i > ($i > $o)))). 11.59/4.28 thf(vabs_type, type, vabs: ($i > ($i > ($i > $i)))). 11.59/4.28 thf(varrow_type, type, varrow: ($i > ($i > $i))). 11.59/4.28 thf(vnoExp_type, type, vnoExp: $i). 11.59/4.28 thf(visSomeExp_type, type, visSomeExp: ($i > $o)). 11.59/4.28 thf(vgetSomeType_type, type, vgetSomeType: ($i > $i)). 11.59/4.28 thf(vsomeType_type, type, vsomeType: ($i > $i)). 11.59/4.28 thf(valphaEquivalent_type, type, valphaEquivalent: ($i > ($i > $o))). 11.59/4.28 thf(vsomeExp_type, type, vsomeExp: ($i > $i)). 11.59/4.28 thf(visFreeVar_type, type, visFreeVar: ($i > ($i > $o))). 11.59/4.28 thf(vsubst_type, type, vsubst: ($i > ($i > ($i > $i)))). 11.59/4.28 thf(vgetSomeExp_type, type, vgetSomeExp: ($i > $i)). 11.59/4.28 thf(visValue_type, type, visValue: ($i > $o)). 11.59/4.28 thf(vreduce_type, type, vreduce: ($i > $i)). 11.59/4.28 thf(63,axiom,((! [A:$i,B:$i,C:$i]: ((vtcheck @ C @ A @ B) => (? [D:$i]: ((A = (vvar @ D)) & ((vsomeType @ B) = (vlookup @ D @ C))) | ? [D:$i,E:$i,F:$i]: ((vtcheck @ C @ D @ (varrow @ F @ B)) & (vtcheck @ C @ E @ F) & ((vapp @ D @ E) = A)) | ? [D:$i,E:$i,F:$i,G:$i]: ((vtcheck @ (vbind @ D @ F @ C) @ E @ G) & (B = (varrow @ F @ G)) & ((vabs @ D @ F @ E) = A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-inv')). 11.59/4.28 thf(555,plain,((! [A:$i,B:$i,C:$i]: ((vtcheck @ C @ A @ B) => (? [D:$i]: ((A = (vvar @ D)) & ((vsomeType @ B) = (vlookup @ D @ C))) | ? [D:$i,E:$i,F:$i]: ((vtcheck @ C @ D @ (varrow @ F @ B)) & (vtcheck @ C @ E @ F) & ((vapp @ D @ E) = A)) | ? [D:$i,E:$i,F:$i,G:$i]: ((vtcheck @ (vbind @ D @ F @ C) @ E @ G) & (B = (varrow @ F @ G)) & ((vabs @ D @ F @ E) = A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[63])). 11.59/4.28 thf(40,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((vabs @ A @ B @ C) = D) => ((vnoExp = E) <= (E = (vreduce @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reduce1)). 11.59/4.28 thf(276,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((vabs @ A @ B @ C) = D) => ((vnoExp = E) | ~ (E = (vreduce @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[40])). 11.59/4.28 thf(29,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((vtcheck @ (vbind @ A @ B @ C) @ D @ E) <= ((vtcheck @ C @ D @ E) & ((vlookup @ A @ C) = vnoType))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-Weak')). 11.59/4.28 thf(202,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((vtcheck @ (vbind @ A @ B @ C) @ D @ E) | ~ ((vtcheck @ C @ D @ E) & ((vlookup @ A @ C) = vnoType))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[29])). 11.59/4.28 thf(62,axiom,((! [A:$i,B:$i,C:$i]: ((B = (vvar @ A)) => ((C = vnoExp) <= ((vreduce @ B) = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reduce0)). 11.59/4.28 thf(550,plain,((! [A:$i,B:$i,C:$i]: ((B = (vvar @ A)) => ((C = vnoExp) | ~ ((vreduce @ B) = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[62])). 11.59/4.28 thf(64,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i]: ((((D = (vreduce @ C)) => ((vsomeExp @ (vsubst @ E @ F @ G)) = D)) <= (((vreduce @ F) = B) & ~ (visSomeExp @ B) & (visValue @ F))) <= (C = (vapp @ (vabs @ E @ A @ G) @ F))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reduce3)). 11.59/4.28 thf(570,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i]: (((D = (vreduce @ C)) => ((vsomeExp @ (vsubst @ E @ F @ G)) = D)) | ~ (((vreduce @ F) = B) & ~ (visSomeExp @ B) & (visValue @ F)) | ~ (C = (vapp @ (vabs @ E @ A @ G) @ F))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[64])). 11.59/4.28 thf(60,axiom,((! [A:$i,B:$i]: ((? [C:$i]: ((vnoExp = B) & ((vvar @ C) = A)) | ? [C:$i,D:$i,E:$i,F:$i,G:$i]: ((A = (vapp @ (vabs @ D @ E @ F) @ C)) & (visSomeExp @ G) & ((vsomeExp @ (vapp @ (vabs @ D @ E @ F) @ (vgetSomeExp @ G))) = B) & (G = (vreduce @ C))) | ? [C:$i,D:$i,E:$i,F:$i,G:$i]: (~ (visSomeExp @ D) & (visValue @ F) & ((vsomeExp @ (vsubst @ E @ F @ G)) = B) & (D = (vreduce @ F)) & (A = (vapp @ (vabs @ E @ C @ G) @ F))) | ? [C:$i,D:$i,E:$i]: ((A = (vapp @ D @ C)) & ! [F:$i,G:$i,H:$i]: (D != (vabs @ F @ G @ H)) & (B = vnoExp) & ~ (visSomeExp @ E) & (E = (vreduce @ D))) | ? [C:$i,D:$i,E:$i]: (((vreduce @ C) = D) & (visSomeExp @ D) & ((vsomeExp @ (vapp @ (vgetSomeExp @ D) @ E)) = B) & ! [F:$i,G:$i,H:$i]: (C != (vabs @ F @ G @ H)) & ((vapp @ C @ E) = A)) | ? [C:$i,D:$i,E:$i,F:$i,G:$i]: (~ (visValue @ G) & (B = vnoExp) & ~ (visSomeExp @ F) & (F = (vreduce @ G)) & (A = (vapp @ (vabs @ C @ D @ E) @ G))) | ? [C:$i,D:$i,E:$i]: ((vnoExp = B) & (A = (vabs @ C @ D @ E)))) <= (B = (vreduce @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','reduce-INV')). 11.59/4.28 thf(460,plain,((! [A:$i,B:$i]: (? [C:$i]: ((vnoExp = B) & ((vvar @ C) = A)) | ? [C:$i,D:$i,E:$i,F:$i,G:$i]: ((A = (vapp @ (vabs @ D @ E @ F) @ C)) & (visSomeExp @ G) & ((vsomeExp @ (vapp @ (vabs @ D @ E @ F) @ (vgetSomeExp @ G))) = B) & (G = (vreduce @ C))) | ? [C:$i,D:$i,E:$i,F:$i,G:$i]: (~ (visSomeExp @ D) & (visValue @ F) & ((vsomeExp @ (vsubst @ E @ F @ G)) = B) & (D = (vreduce @ F)) & (A = (vapp @ (vabs @ E @ C @ G) @ F))) | ? [C:$i,D:$i,E:$i]: ((A = (vapp @ D @ C)) & ! [F:$i,G:$i,H:$i]: ~ (D = (vabs @ F @ G @ H)) & (B = vnoExp) & ~ (visSomeExp @ E) & (E = (vreduce @ D))) | ? [C:$i,D:$i,E:$i]: (((vreduce @ C) = D) & (visSomeExp @ D) & ((vsomeExp @ (vapp @ (vgetSomeExp @ D) @ E)) = B) & ! [F:$i,G:$i,H:$i]: ~ (C = (vabs @ F @ G @ H)) & ((vapp @ C @ E) = A)) | ? [C:$i,D:$i,E:$i,F:$i,G:$i]: (~ (visValue @ G) & (B = vnoExp) & ~ (visSomeExp @ F) & (F = (vreduce @ G)) & (A = (vapp @ (vabs @ C @ D @ E) @ G))) | ? [C:$i,D:$i,E:$i]: ((vnoExp = B) & (A = (vabs @ C @ D @ E))) | ~ (B = (vreduce @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[60])). 11.59/4.28 thf(10,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((((C = A) & (B = D)) <= ((varrow @ C @ D) = (varrow @ A @ B))) & (((varrow @ A @ B) = (varrow @ C @ D)) <= ((A = C) & (D = B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','EQ-arrow')). 11.59/4.28 thf(93,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((((C = A) & (B = D)) | ~ ((varrow @ C @ D) = (varrow @ A @ B))) & (((varrow @ A @ B) = (varrow @ C @ D)) | ~ ((A = C) & (D = B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[10])). 11.59/4.28 thf(43,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((vtcheck @ B @ (vapp @ C @ D) @ E) <= ((vtcheck @ B @ D @ A) & (vtcheck @ B @ C @ (varrow @ A @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-app')). 11.59/4.28 thf(289,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((vtcheck @ B @ (vapp @ C @ D) @ E) | ~ ((vtcheck @ B @ D @ A) & (vtcheck @ B @ C @ (varrow @ A @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[43])). 11.59/4.28 thf(34,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: (((E = B) & (C = (vabs @ D @ A @ F))) => ((((E != D) & (visFreeVar @ E @ F)) <= (visFreeVar @ B @ C)) & ((visFreeVar @ B @ C) <= ((visFreeVar @ E @ F) & (D != E))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isFreeVar1)). 11.59/4.28 thf(216,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: (((E = B) & (C = (vabs @ D @ A @ F))) => (((~ (E = D) & (visFreeVar @ E @ F)) | ~ (visFreeVar @ B @ C)) & ((visFreeVar @ B @ C) | ~ ((visFreeVar @ E @ F) & ~ (D = E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[34])). 11.59/4.28 thf(23,axiom,((! [A:$i,B:$i,C:$i]: (((C = B) <= ((vgetSomeExp @ A) = B)) <= ((vsomeExp @ C) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',getSomeExp0)). 11.59/4.28 thf(164,plain,((! [A:$i,B:$i,C:$i]: ((C = B) | ~ ((vgetSomeExp @ A) = B) | ~ ((vsomeExp @ C) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[23])). 11.59/4.28 thf(56,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((vapp @ D @ E) != (vabs @ A @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','DIFF-abs-app')). 11.59/4.28 thf(443,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ~ ((vapp @ D @ E) = (vabs @ A @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[56])). 11.59/4.28 thf(32,axiom,((! [A:$i,B:$i]: ((visSomeExp @ B) <= (B = (vsomeExp @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isSomeExp1)). 11.59/4.28 thf(211,plain,((! [A:$i,B:$i]: ((visSomeExp @ B) | ~ (B = (vsomeExp @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[32])). 11.59/4.28 thf(65,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((((vapp @ C @ D) = (vapp @ A @ B)) => ((C = A) & (B = D))) & (((D = B) & (A = C)) => ((vapp @ A @ B) = (vapp @ C @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','EQ-app')). 11.59/4.28 thf(574,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((((vapp @ C @ D) = (vapp @ A @ B)) => ((C = A) & (B = D))) & (((D = B) & (A = C)) => ((vapp @ A @ B) = (vapp @ C @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[65])). 11.59/4.28 thf(47,axiom,((! [A:$i,B:$i]: ((((vvar @ B) = (vvar @ A)) => (A = B)) & ((B = A) => ((vvar @ A) = (vvar @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','EQ-var')). 11.59/4.28 thf(397,plain,((! [A:$i,B:$i]: ((((vvar @ B) = (vvar @ A)) => (A = B)) & ((B = A) => ((vvar @ A) = (vvar @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[47])). 11.59/4.28 thf(9,axiom,((! [A:$i,B:$i,C:$i]: (((B = (vgetSomeType @ A)) => (C = B)) <= (A = (vsomeType @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',getSomeType0)). 11.59/4.28 thf(89,plain,((! [A:$i,B:$i,C:$i]: (((B = (vgetSomeType @ A)) => (C = B)) | ~ (A = (vsomeType @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[9])). 11.59/4.28 thf(13,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((vtcheck @ C @ D @ E) <= (~ (visFreeVar @ A @ D) & (vtcheck @ (vbind @ A @ B @ C) @ D @ E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-Strong')). 11.59/4.28 thf(116,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((vtcheck @ C @ D @ E) | ~ (~ (visFreeVar @ A @ D) & (vtcheck @ (vbind @ A @ B @ C) @ D @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[13])). 11.59/4.28 thf(37,axiom,((! [A:$i]: (vnoType != (vsomeType @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','DIFF-noType-someType')). 11.59/4.28 thf(233,plain,((! [A:$i]: ~ (vnoType = (vsomeType @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[37])). 11.59/4.28 thf(61,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i]: (((A = D) & (E = (vvar @ G)) & (C = B)) => ((G != B) => (((vsubst @ C @ D @ E) = F) => ((vvar @ G) = F)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subst1)). 11.59/4.28 thf(546,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i]: (((A = D) & (E = (vvar @ G)) & (C = B)) => ((~ (G = B)) => (((vsubst @ C @ D @ E) = F) => ((vvar @ G) = F)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[61])). 11.59/4.28 thf(8,axiom,((! [A:$i]: ((vnoExp = A) => (~ (visSomeExp @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isSomeExp0)). 11.59/4.28 thf(85,plain,((! [A:$i]: ((vnoExp = A) => (~ (visSomeExp @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8])). 11.59/4.28 thf(53,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i]: (((E = (vvar @ B)) & (D = G) & (A = C)) => (((G = F) <= ((vsubst @ C @ D @ E) = F)) <= (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subst0)). 11.59/4.28 thf(429,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i]: (((E = (vvar @ B)) & (D = G) & (A = C)) => ((G = F) | ~ ((vsubst @ C @ D @ E) = F) | ~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[53])). 11.59/4.28 thf(59,axiom,((! [A:$i,B:$i,C:$i]: ((~ (visValue @ C)) <= (C = (vapp @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isValue2)). 11.59/4.28 thf(456,plain,((! [A:$i,B:$i,C:$i]: (~ (visValue @ C) | ~ (C = (vapp @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[59])). 11.59/4.28 thf(42,axiom,((! [A:$i,B:$i,C:$i]: ((vapp @ B @ C) != (vvar @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','DIFF-var-app')). 11.59/4.28 thf(285,plain,((! [A:$i,B:$i,C:$i]: ~ ((vapp @ B @ C) = (vvar @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[42])). 11.59/4.28 thf(19,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((vtcheck @ (vbind @ A @ B @ C) @ D @ E) <= (~ (visFreeVar @ A @ D) & (vtcheck @ C @ D @ E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-Weak-FreeVar')). 11.59/4.28 thf(141,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((vtcheck @ (vbind @ A @ B @ C) @ D @ E) | ~ (~ (visFreeVar @ A @ D) & (vtcheck @ C @ D @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[19])). 11.59/4.28 thf(16,axiom,((! [A:$i,B:$i]: ((visSomeType @ B) <= ((vsomeType @ A) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isSomeType1)). 11.59/4.28 thf(124,plain,((! [A:$i,B:$i]: ((visSomeType @ B) | ~ ((vsomeType @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[16])). 11.59/4.28 thf(5,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((D = (vlookup @ B @ C)) => (D = vnoType)) <= ((A = B) & (vempty = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lookup0)). 11.59/4.28 thf(77,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((D = (vlookup @ B @ C)) => (D = vnoType)) | ~ ((A = B) & (vempty = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])). 11.59/4.28 thf(4,axiom,((! [A:$i]: ((~ (visSomeType @ A)) <= (A = vnoType)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isSomeType0)). 11.59/4.28 thf(73,plain,((! [A:$i]: (~ (visSomeType @ A) | ~ (A = vnoType)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])). 11.59/4.28 thf(17,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i]: ((~ (visFreeVar @ E @ D) & (vtcheck @ B @ D @ A) & (vtcheck @ (vbind @ C @ A @ B) @ (vabs @ E @ F @ G) @ H) & (E != C)) => (vtcheck @ B @ (vsubst @ C @ D @ (vabs @ E @ F @ G)) @ H)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-subst-abs-2-gen')). 11.59/4.28 thf(128,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i]: ((~ (visFreeVar @ E @ D) & (vtcheck @ B @ D @ A) & (vtcheck @ (vbind @ C @ A @ B) @ (vabs @ E @ F @ G) @ H) & ~ (E = C)) => (vtcheck @ B @ (vsubst @ C @ D @ (vabs @ E @ F @ G)) @ H)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[17])). 11.59/4.28 thf(38,axiom,((! [A:$i,B:$i,C:$i]: ((C = (vlookup @ A @ B)) => (? [D:$i,E:$i,F:$i,G:$i]: ((F = A) & ((vbind @ E @ D @ G) = B) & (F != E) & (C = (vlookup @ F @ G))) | ? [D:$i,E:$i,F:$i,G:$i]: (((vbind @ F @ G @ D) = B) & ((vsomeType @ G) = C) & (E = F) & (A = E)) | ? [D:$i]: ((A = D) & (C = vnoType) & (vempty = B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','lookup-INV')). 11.59/4.28 thf(237,plain,((! [A:$i,B:$i,C:$i]: ((C = (vlookup @ A @ B)) => (? [D:$i,E:$i,F:$i,G:$i]: ((F = A) & ((vbind @ E @ D @ G) = B) & ~ (F = E) & (C = (vlookup @ F @ G))) | ? [D:$i,E:$i,F:$i,G:$i]: (((vbind @ F @ G @ D) = B) & ((vsomeType @ G) = C) & (E = F) & (A = E)) | ? [D:$i]: ((A = D) & (C = vnoType) & (vempty = B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[38])). 11.59/4.28 thf(11,axiom,((! [A:$i,B:$i]: ((valphaEquivalent @ B @ A) => (valphaEquivalent @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','alpha-equiv-sym')). 11.59/4.28 thf(105,plain,((! [A:$i,B:$i]: ((valphaEquivalent @ B @ A) => (valphaEquivalent @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[11])). 11.59/4.28 thf(30,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((vtcheck @ B @ C @ D) <= ((vtcheck @ B @ A @ D) & (valphaEquivalent @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','alpha-equiv-typing')). 11.59/4.28 thf(205,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((vtcheck @ B @ C @ D) | ~ ((vtcheck @ B @ A @ D) & (valphaEquivalent @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[30])). 11.59/4.28 thf(52,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i]: (((F = A) & ((vapp @ E @ H) = C) & (G = B)) => ((D = (vapp @ (vsubst @ F @ G @ E) @ (vsubst @ F @ G @ H))) <= (D = (vsubst @ A @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subst2)). 11.59/4.28 thf(425,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i]: (((F = A) & ((vapp @ E @ H) = C) & (G = B)) => ((D = (vapp @ (vsubst @ F @ G @ E) @ (vsubst @ F @ G @ H))) | ~ (D = (vsubst @ A @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[52])). 11.59/4.28 thf(27,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: ((((vbind @ A @ B @ C) = (vbind @ D @ E @ F)) <= ((A = D) & (C = F) & (B = E))) & (((F = C) & (B = E) & (A = D)) <= ((vbind @ A @ B @ C) = (vbind @ D @ E @ F)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','EQ-bind')). 11.59/4.28 thf(180,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: ((((vbind @ A @ B @ C) = (vbind @ D @ E @ F)) | ~ ((A = D) & (C = F) & (B = E))) & (((F = C) & (B = E) & (A = D)) | ~ ((vbind @ A @ B @ C) = (vbind @ D @ E @ F)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[27])). 11.59/4.28 thf(45,axiom,((! [A:$i,B:$i,C:$i]: ((vtcheck @ A @ (vvar @ B) @ C) <= ((vsomeType @ C) = (vlookup @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-var')). 11.59/4.28 thf(296,plain,((! [A:$i,B:$i,C:$i]: ((vtcheck @ A @ (vvar @ B) @ C) | ~ ((vsomeType @ C) = (vlookup @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[45])). 11.59/4.28 thf(26,axiom,((! [A:$i,B:$i,C:$i]: (vempty != (vbind @ A @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','DIFF-empty-bind')). 11.59/4.28 thf(176,plain,((! [A:$i,B:$i,C:$i]: ~ (vempty = (vbind @ A @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[26])). 11.59/4.28 thf(51,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((~ (visFreeVar @ C @ D)) => (valphaEquivalent @ (vabs @ B @ A @ D) @ (vabs @ C @ A @ (vsubst @ B @ (vvar @ C) @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','alpha-equiv-subst-abs')). 11.59/4.28 thf(423,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((~ (visFreeVar @ C @ D)) => (valphaEquivalent @ (vabs @ B @ A @ D) @ (vabs @ C @ A @ (vsubst @ B @ (vvar @ C) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[51])). 11.59/4.28 thf(44,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i]: (((((vreduce @ B) = C) => (C = (vsomeExp @ (vapp @ (vabs @ D @ E @ F) @ (vgetSomeExp @ G))))) <= ((visSomeExp @ G) & ((vreduce @ A) = G))) <= ((vapp @ (vabs @ D @ E @ F) @ A) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reduce2)). 11.59/4.28 thf(291,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i]: ((((vreduce @ B) = C) => (C = (vsomeExp @ (vapp @ (vabs @ D @ E @ F) @ (vgetSomeExp @ G))))) | ~ ((visSomeExp @ G) & ((vreduce @ A) = G)) | ~ ((vapp @ (vabs @ D @ E @ F) @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[44])). 11.59/4.28 thf(14,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i]: (((D = (vbind @ B @ A @ G)) & (C = F)) => ((F != B) => (((vlookup @ C @ D) = E) => ((vlookup @ F @ G) = E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lookup2)). 11.59/4.28 thf(118,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i]: (((D = (vbind @ B @ A @ G)) & (C = F)) => ((~ (F = B)) => (((vlookup @ C @ D) = E) => ((vlookup @ F @ G) = E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[14])). 11.59/4.28 thf(41,axiom,((! [A:$i,B:$i]: ((~ (visFreeVar @ A @ B)) <= ((vgensym @ B) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','gensym-is-fresh')). 11.59/4.28 thf(281,plain,((! [A:$i,B:$i]: (~ (visFreeVar @ A @ B) | ~ ((vgensym @ B) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[41])). 11.59/4.28 thf(25,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i]: ((((vbind @ C @ G @ A) = E) & (D = B)) => (((F = (vsomeType @ G)) <= (F = (vlookup @ D @ E))) <= (B = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lookup1)). 11.59/4.28 thf(172,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i]: ((((vbind @ C @ G @ A) = E) & (D = B)) => ((F = (vsomeType @ G)) | ~ (F = (vlookup @ D @ E)) | ~ (B = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[25])). 11.59/4.28 thf(50,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((vabs @ B @ C @ D) != (vvar @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','DIFF-var-abs')). 11.59/4.28 thf(419,plain,((! [A:$i,B:$i,C:$i,D:$i]: ~ ((vabs @ B @ C @ D) = (vvar @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[50])). 11.59/4.28 thf(36,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i]: (((vtcheck @ (vbind @ C @ D @ (vbind @ A @ B @ E)) @ F @ G) & (C != A)) => (vtcheck @ (vbind @ A @ B @ (vbind @ C @ D @ E)) @ F @ G)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-Context-Swap')). 11.59/4.28 thf(230,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i]: (((vtcheck @ (vbind @ C @ D @ (vbind @ A @ B @ E)) @ F @ G) & ~ (C = A)) => (vtcheck @ (vbind @ A @ B @ (vbind @ C @ D @ E)) @ F @ G)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[36])). 11.59/4.28 thf(58,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((((vreduce @ D) = E) => (E = vnoExp)) <= ((C = (vreduce @ B)) & ~ (visSomeExp @ C))) <= (! [F:$i,G:$i,H:$i]: ((vabs @ F @ G @ H) != B) & ((vapp @ B @ A) = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reduce6)). 11.59/4.28 thf(451,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((((vreduce @ D) = E) => (E = vnoExp)) | ~ ((C = (vreduce @ B)) & ~ (visSomeExp @ C)) | ~ (! [F:$i,G:$i,H:$i]: ~ ((vabs @ F @ G @ H) = B) & ((vapp @ B @ A) = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[58])). 11.59/4.28 thf(28,axiom,((! [A:$i]: ((vsomeExp @ A) != vnoExp))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','DIFF-noExp-someExp')). 11.59/4.28 thf(198,plain,((! [A:$i]: ~ ((vsomeExp @ A) = vnoExp))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[28])). 11.59/4.28 thf(46,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((? [E:$i,F:$i,G:$i]: ((B = E) & ((vvar @ G) = C) & (F != G) & ((vvar @ G) = D) & (A = F)) | ? [E:$i,F:$i,G:$i,H:$i]: ((B = G) & (C = (vapp @ E @ H)) & (D = (vapp @ (vsubst @ F @ G @ E) @ (vsubst @ F @ G @ H))) & (F = A)) | ? [E:$i,F:$i,G:$i,H:$i,I:$i,J:$i]: ((E = A) & (B = F) & (D = (vsubst @ E @ F @ (vabs @ I @ G @ (vsubst @ H @ (vvar @ I) @ J)))) & (I = (vgensym @ (vapp @ (vapp @ F @ J) @ (vvar @ E)))) & (visFreeVar @ H @ F) & (E != H) & ((vabs @ H @ G @ J) = C)) | ? [E:$i,F:$i,G:$i,H:$i,I:$i]: ((A = G) & (B = H) & ~ (visFreeVar @ E @ H) & (D = (vabs @ E @ F @ (vsubst @ G @ H @ I))) & (E != G) & ((vabs @ E @ F @ I) = C)) | ? [E:$i,F:$i,G:$i,H:$i,I:$i]: ((B = E) & (F = G) & (D = (vabs @ G @ H @ I)) & (C = (vabs @ G @ H @ I)) & (F = A)) | ? [E:$i,F:$i,G:$i]: ((G = B) & (D = G) & (E = F) & ((vvar @ F) = C) & (E = A))) <= ((vsubst @ A @ B @ C) = D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','subst-INV')). 11.59/4.28 thf(299,plain,((! [A:$i,B:$i,C:$i,D:$i]: (? [E:$i,F:$i,G:$i]: ((B = E) & ((vvar @ G) = C) & ~ (F = G) & ((vvar @ G) = D) & (A = F)) | ? [E:$i,F:$i,G:$i,H:$i]: ((B = G) & (C = (vapp @ E @ H)) & (D = (vapp @ (vsubst @ F @ G @ E) @ (vsubst @ F @ G @ H))) & (F = A)) | ? [E:$i,F:$i,G:$i,H:$i,I:$i,J:$i]: ((E = A) & (B = F) & (D = (vsubst @ E @ F @ (vabs @ I @ G @ (vsubst @ H @ (vvar @ I) @ J)))) & (I = (vgensym @ (vapp @ (vapp @ F @ J) @ (vvar @ E)))) & (visFreeVar @ H @ F) & ~ (E = H) & ((vabs @ H @ G @ J) = C)) | ? [E:$i,F:$i,G:$i,H:$i,I:$i]: ((A = G) & (B = H) & ~ (visFreeVar @ E @ H) & (D = (vabs @ E @ F @ (vsubst @ G @ H @ I))) & ~ (E = G) & ((vabs @ E @ F @ I) = C)) | ? [E:$i,F:$i,G:$i,H:$i,I:$i]: ((B = E) & (F = G) & (D = (vabs @ G @ H @ I)) & (C = (vabs @ G @ H @ I)) & (F = A)) | ? [E:$i,F:$i,G:$i]: ((G = B) & (D = G) & (E = F) & ((vvar @ F) = C) & (E = A)) | ~ ((vsubst @ A @ B @ C) = D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[46])). 11.59/4.28 thf(35,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i]: ((vtcheck @ (vbind @ C @ D @ E) @ F @ G) <= ((A = C) & (vtcheck @ (vbind @ C @ D @ (vbind @ A @ B @ E)) @ F @ G))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-Context-Duplicate')). 11.59/4.28 thf(226,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i]: ((vtcheck @ (vbind @ C @ D @ E) @ F @ G) | ~ ((A = C) & (vtcheck @ (vbind @ C @ D @ (vbind @ A @ B @ E)) @ F @ G))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[35])). 11.59/4.28 thf(55,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((((C = (vreduce @ B)) => ((vsomeExp @ (vapp @ (vgetSomeExp @ D) @ E)) = C)) <= ((visSomeExp @ D) & (D = (vreduce @ A)))) <= (! [F:$i,G:$i,H:$i]: ((vabs @ F @ G @ H) != A) & ((vapp @ A @ E) = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reduce5)). 11.59/4.28 thf(438,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((C = (vreduce @ B)) => ((vsomeExp @ (vapp @ (vgetSomeExp @ D) @ E)) = C)) | ~ ((visSomeExp @ D) & (D = (vreduce @ A))) | ~ (! [F:$i,G:$i,H:$i]: ~ ((vabs @ F @ G @ H) = A) & ((vapp @ A @ E) = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[55])). 11.59/4.28 thf(22,axiom,((! [A:$i]: (valphaEquivalent @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','alpha-equiv-refl')). 11.59/4.28 thf(162,plain,((! [A:$i]: (valphaEquivalent @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[22])). 11.59/4.28 thf(21,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: ((((D = A) & (E = B) & (F = C)) => ((vabs @ A @ B @ C) = (vabs @ D @ E @ F))) & (((C = F) & (E = B) & (D = A)) <= ((vabs @ A @ B @ C) = (vabs @ D @ E @ F)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','EQ-abs')). 11.59/4.28 thf(145,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: ((((D = A) & (E = B) & (F = C)) => ((vabs @ A @ B @ C) = (vabs @ D @ E @ F))) & (((C = F) & (E = B) & (D = A)) | ~ ((vabs @ A @ B @ C) = (vabs @ D @ E @ F)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[21])). 11.59/4.28 thf(1,conjecture,((! [A:$i,B:$i,C:$i,D:$i]: ((D = (vgensym @ (vapp @ (vapp @ A @ B) @ (vvar @ C)))) => (D != C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fresh-unequal-var-3')). 11.59/4.28 thf(2,negated_conjecture,((~ (! [A:$i,B:$i,C:$i,D:$i]: ((D = (vgensym @ (vapp @ (vapp @ A @ B) @ (vvar @ C)))) => (D != C))))),inference(neg_conjecture,[status(cth)],[1])). 11.59/4.28 thf(67,plain,((~ (! [A:$i,B:$i,C:$i,D:$i]: ((D = (vgensym @ (vapp @ (vapp @ A @ B) @ (vvar @ C)))) => (~ (D = C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])). 11.59/4.28 thf(66,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((((visFreeVar @ A @ B) <= (D = C)) & ((C = D) <= (visFreeVar @ A @ B))) <= ((B = (vvar @ C)) & (D = A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isFreeVar0)). 11.59/4.28 thf(585,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((((visFreeVar @ A @ B) | ~ (D = C)) & ((C = D) | ~ (visFreeVar @ A @ B))) | ~ ((B = (vvar @ C)) & (D = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[66])). 11.59/4.28 thf(3,axiom,(((($true) <= (vempty = vempty)) & ((vempty = vempty) <= ($true)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','EQ-empty')). 11.59/4.28 thf(72,plain,($true),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])). 11.59/4.28 thf(20,axiom,((! [A:$i,B:$i,C:$i]: ((~ (visFreeVar @ B @ A) & (valphaEquivalent @ A @ C)) => (~ (visFreeVar @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','alpha-equiv-FreeVar')). 11.59/4.28 thf(143,plain,((! [A:$i,B:$i,C:$i]: ((~ (visFreeVar @ B @ A) & (valphaEquivalent @ A @ C)) => (~ (visFreeVar @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[20])). 11.59/4.28 thf(54,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i]: ((((G = vnoExp) <= (G = (vreduce @ F))) <= (~ (visValue @ E) & ~ (visSomeExp @ D) & ((vreduce @ E) = D))) <= (F = (vapp @ (vabs @ A @ B @ C) @ E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reduce4)). 11.59/4.28 thf(433,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i]: ((G = vnoExp) | ~ (G = (vreduce @ F)) | ~ (~ (visValue @ E) & ~ (visSomeExp @ D) & ((vreduce @ E) = D)) | ~ (F = (vapp @ (vabs @ A @ B @ C) @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[54])). 11.59/4.28 thf(31,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i,I:$i]: (((G = B) => ((F = (vsubst @ C @ D @ E)) => ((vabs @ G @ H @ I) = F))) <= ((D = A) & ((vabs @ G @ H @ I) = E) & (C = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subst3)). 11.59/4.28 thf(207,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i,I:$i]: (((G = B) => ((F = (vsubst @ C @ D @ E)) => ((vabs @ G @ H @ I) = F))) | ~ ((D = A) & ((vabs @ G @ H @ I) = E) & (C = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[31])). 11.59/4.28 thf(39,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((visValue @ D) <= (D = (vabs @ A @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isValue0)). 11.59/4.28 thf(272,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((visValue @ D) | ~ (D = (vabs @ A @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[39])). 11.59/4.28 thf(6,axiom,(((($true) <= (vnoType = vnoType)) & (($true) => (vnoType = vnoType)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','EQ-noType')). 11.59/4.28 thf(82,plain,($true),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])). 11.59/4.28 thf(57,axiom,((! [A:$i,B:$i]: (((vvar @ A) = B) => (~ (visValue @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isValue1)). 11.59/4.28 thf(447,plain,((! [A:$i,B:$i]: (((vvar @ A) = B) => (~ (visValue @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[57])). 11.59/4.28 thf(24,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i,I:$i]: (((A = G) & ((vabs @ E @ F @ I) = C) & (B = H)) => ((~ (visFreeVar @ E @ H) & (G != E)) => ((D = (vsubst @ A @ B @ C)) => ((vabs @ E @ F @ (vsubst @ G @ H @ I)) = D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subst5)). 11.59/4.28 thf(168,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i,I:$i]: (((A = G) & ((vabs @ E @ F @ I) = C) & (B = H)) => ((~ (visFreeVar @ E @ H) & ~ (G = E)) => ((D = (vsubst @ A @ B @ C)) => ((vabs @ E @ F @ (vsubst @ G @ H @ I)) = D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[24])). 11.59/4.28 thf(48,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((A = D) & ((vapp @ C @ E) = B)) => (((visFreeVar @ A @ B) => ((visFreeVar @ D @ C) | (visFreeVar @ D @ E))) & ((visFreeVar @ A @ B) <= ((visFreeVar @ D @ C) | (visFreeVar @ D @ E))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isFreeVar2)). 11.59/4.28 thf(405,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((A = D) & ((vapp @ C @ E) = B)) => (((visFreeVar @ A @ B) => ((visFreeVar @ D @ C) | (visFreeVar @ D @ E))) & ((visFreeVar @ A @ B) | ~ ((visFreeVar @ D @ C) | (visFreeVar @ D @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[48])). 11.59/4.28 thf(12,axiom,((! [A:$i,B:$i]: (((A = B) => ((vsomeExp @ B) = (vsomeExp @ A))) & (((vsomeExp @ A) = (vsomeExp @ B)) => (B = A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','EQ-someExp')). 11.59/4.28 thf(107,plain,((! [A:$i,B:$i]: (((A = B) => ((vsomeExp @ B) = (vsomeExp @ A))) & (((vsomeExp @ A) = (vsomeExp @ B)) => (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[12])). 11.59/4.28 thf(49,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i,I:$i,J:$i]: ((((I = (vgensym @ (vapp @ (vapp @ F @ J) @ (vvar @ E)))) & (visFreeVar @ H @ F) & (E != H)) => ((D = (vsubst @ E @ F @ (vabs @ I @ G @ (vsubst @ H @ (vvar @ I) @ J)))) <= (D = (vsubst @ A @ B @ C)))) <= ((A = E) & (C = (vabs @ H @ G @ J)) & (B = F))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subst4)). 11.59/4.28 thf(415,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i,I:$i,J:$i]: ((((I = (vgensym @ (vapp @ (vapp @ F @ J) @ (vvar @ E)))) & (visFreeVar @ H @ F) & ~ (E = H)) => ((D = (vsubst @ E @ F @ (vabs @ I @ G @ (vsubst @ H @ (vvar @ I) @ J)))) | ~ (D = (vsubst @ A @ B @ C)))) | ~ ((A = E) & (C = (vabs @ H @ G @ J)) & (B = F))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[49])). 11.59/4.28 thf(18,axiom,((! [A:$i,B:$i]: ((((vsomeType @ B) = (vsomeType @ A)) <= (B = A)) & (((vsomeType @ A) = (vsomeType @ B)) => (B = A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','EQ-someType')). 11.59/4.28 thf(131,plain,((! [A:$i,B:$i]: ((((vsomeType @ B) = (vsomeType @ A)) | ~ (B = A)) & (((vsomeType @ A) = (vsomeType @ B)) => (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[18])). 11.59/4.28 thf(15,axiom,((! [A:$i,B:$i,C:$i]: (((valphaEquivalent @ B @ A) & (valphaEquivalent @ A @ C)) => (valphaEquivalent @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','alpha-equiv-trans')). 11.59/4.28 thf(122,plain,((! [A:$i,B:$i,C:$i]: (((valphaEquivalent @ B @ A) & (valphaEquivalent @ A @ C)) => (valphaEquivalent @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[15])). 11.59/4.28 thf(7,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((vtcheck @ (vbind @ B @ D @ A) @ C @ E) => (vtcheck @ A @ (vabs @ B @ D @ C) @ (varrow @ D @ E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-abs')). 11.59/4.28 thf(83,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((vtcheck @ (vbind @ B @ D @ A) @ C @ E) => (vtcheck @ A @ (vabs @ B @ D @ C) @ (varrow @ D @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])). 11.59/4.28 thf(33,axiom,(((($true) <= (vnoExp = vnoExp)) & ((vnoExp = vnoExp) <= ($true)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','EQ-noExp')). 11.59/4.28 thf(215,plain,($true),inference(defexp_and_simp_and_etaexpand,[status(thm)],[33])). 11.59/4.28 thf(592,plain,($false),inference(cvc4,[status(thm)],[555,276,202,550,570,460,93,289,216,164,443,211,574,397,89,116,233,546,85,429,456,285,141,124,77,73,128,237,105,205,425,180,296,176,423,291,118,281,172,419,230,451,198,299,226,438,162,145,67,585,72,143,433,207,272,82,447,168,405,107,415,131,122,83,215])). 11.59/4.28 % SZS output end CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 11.59/4.28 % [INFO] Killing All external provers ... 11.62/4.32 EOF