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 0.02/0.24 % Computer : n141.star.cs.uiowa.edu 0.02/0.24 % Model : x86_64 x86_64 0.02/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz 0.02/0.24 % Memory : 32218.625MB 0.02/0.24 % OS : Linux 3.10.0-693.2.2.el7.x86_64 0.02/0.24 % CPULimit : 300 0.02/0.24 % DateTime : Sat Jul 14 05:53:10 CDT 2018 0.02/0.24 % CPUTime : 5.60/2.47 % [INFO] Running in sequential loop mode. 6.27/2.69 % [CONFIG] Using configuration: timeout(300) with strategy 6.57/2.77 % [INFO] iprover registered as external prover. 6.57/2.77 % [INFO] e registered as external prover. 6.57/2.77 % [INFO] cvc4 registered as external prover. 6.57/2.78 % [INFO] Parsing finished. Scanning for conjecture ... 6.80/2.85 % [INFO] Found a conjecture and 95 axioms. Running axiom selection ... 7.26/2.94 % [INFO] Axiom selection finished. Selected 95 axioms (removed 0 axioms). 7.64/3.09 % [INFO] Type checking passed. Searching for refutation ... 90.19/25.17 % [INFO] Killing All external provers ... 90.19/25.17 % Time passed: 24830ms 90.19/25.17 % Effective reasoning time: 22684ms 90.19/25.17 % Solved by strategy 90.19/25.17 % Axioms used in derivation (95): ax20, ax52, ax67, ax74, ax24, ax63, ax56, ax4, ax47, ax41, ax90, ax31, ax28, ax9, ax17, ax6, ax45, ax40, ax85, ax35, ax58, ax69, ax13, ax78, ax39, ax89, ax27, ax66, ax8, ax91, ax73, ax51, ax48, ax21, ax88, ax62, ax10, ax55, ax32, ax95, ax16, ax80, ax59, ax1, ax7, ax77, ax38, ax44, ax84, ax92, ax94, ax33, ax26, ax61, ax11, ax50, ax87, ax72, ax65, ax22, ax15, ax81, ax76, ax43, ax83, ax19, ax2, ax70, ax37, ax54, ax49, ax14, ax12, ax46, ax34, ax23, ax86, ax25, ax60, ax71, ax57, ax68, ax30, ax42, ax82, ax18, ax3, ax5, ax36, ax64, ax29, ax75, ax53, ax93, ax79 90.19/25.17 % No. of inferences in proof: 258 90.19/25.17 % No. of processed clauses: 166 90.19/25.17 % No. of generated clauses: 5106 90.19/25.17 % No. of forward subsumed clauses: 98 90.19/25.17 % No. of backward subsumed clauses: 1 90.19/25.17 % No. of ground rewrite rules in store: 47 90.19/25.17 % No. of non-ground rewrite rules in store: 0 90.19/25.17 % No. of positive (non-rewrite) units in store: 0 90.19/25.17 % No. of negative (non-rewrite) units in store: 2 90.19/25.17 % No. of choice functions detected: 0 90.19/25.17 % No. of choice instantiations: 0 90.19/25.17 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 24830 ms resp. 22684 ms w/o parsing 90.23/25.32 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 90.23/25.32 thf(ssList_type, type, ssList: ($i > $o)). 90.23/25.32 thf(nil_type, type, nil: $i). 90.23/25.32 thf(neq_type, type, neq: ($i > ($i > $o))). 90.23/25.32 thf(segmentP_type, type, segmentP: ($i > ($i > $o))). 90.23/25.32 thf(strictorderedP_type, type, strictorderedP: ($i > $o)). 90.23/25.32 thf(ssItem_type, type, ssItem: ($i > $o)). 90.23/25.32 thf(lt_type, type, lt: ($i > ($i > $o))). 90.23/25.32 thf(gt_type, type, gt: ($i > ($i > $o))). 90.23/25.32 thf(leq_type, type, leq: ($i > ($i > $o))). 90.23/25.32 thf(geq_type, type, geq: ($i > ($i > $o))). 90.23/25.32 thf(cons_type, type, cons: ($i > ($i > $i))). 90.23/25.32 thf(frontsegP_type, type, frontsegP: ($i > ($i > $o))). 90.23/25.32 thf(memberP_type, type, memberP: ($i > ($i > $o))). 90.23/25.32 thf(hd_type, type, hd: ($i > $i)). 90.23/25.32 thf(totalorderedP_type, type, totalorderedP: ($i > $o)). 90.23/25.32 thf(app_type, type, app: ($i > ($i > $i))). 90.23/25.32 thf(strictorderP_type, type, strictorderP: ($i > $o)). 90.23/25.32 thf(tl_type, type, tl: ($i > $i)). 90.23/25.32 thf(singletonP_type, type, singletonP: ($i > $o)). 90.23/25.32 thf(equalelemsP_type, type, equalelemsP: ($i > $o)). 90.23/25.32 thf(duplicatefreeP_type, type, duplicatefreeP: ($i > $o)). 90.23/25.32 thf(rearsegP_type, type, rearsegP: ($i > ($i > $o))). 90.23/25.32 thf(totalorderP_type, type, totalorderP: ($i > $o)). 90.23/25.32 thf(cyclefreeP_type, type, cyclefreeP: ($i > $o)). 90.23/25.32 thf(sk1_type, type, sk1: $i). 90.23/25.32 thf(sk2_type, type, sk2: $i). 90.23/25.32 thf(sk3_type, type, sk3: $i). 90.23/25.32 thf(sk4_type, type, sk4: $i). 90.23/25.32 thf(sk5_type, type, sk5: $i). 90.23/25.32 thf(sk6_type, type, sk6: $i). 90.23/25.32 thf(sk7_type, type, sk7: ($i > $i)). 90.23/25.32 thf(1,conjecture,((! [A:$i]: ((! [B:$i]: ((! [C:$i]: ((! [D:$i]: ((ssList @ D) => (~ (neq @ B @ nil) | ? [E:$i]: ((neq @ C @ E) & (segmentP @ D @ E) & (strictorderedP @ E) & (segmentP @ E @ C) & (ssList @ E)) | ((segmentP @ B @ A) & (neq @ A @ nil)) | ~ (strictorderedP @ C) | ~ (segmentP @ D @ C) | (A != C) | (D != B)))) <= (ssList @ C))) <= (ssList @ B))) <= (ssList @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1)). 90.23/25.32 thf(2,negated_conjecture,((~ (! [A:$i]: ((! [B:$i]: ((! [C:$i]: ((! [D:$i]: ((ssList @ D) => (~ (neq @ B @ nil) | ? [E:$i]: ((neq @ C @ E) & (segmentP @ D @ E) & (strictorderedP @ E) & (segmentP @ E @ C) & (ssList @ E)) | ((segmentP @ B @ A) & (neq @ A @ nil)) | ~ (strictorderedP @ C) | ~ (segmentP @ D @ C) | (A != C) | (D != B)))) <= (ssList @ C))) <= (ssList @ B))) <= (ssList @ A))))),inference(neg_conjecture,[status(cth)],[1])). 90.23/25.32 thf(98,plain,((~ (! [A:$i]: (! [B:$i]: (! [C:$i]: (! [D:$i]: ((ssList @ D) => (~ (neq @ B @ nil) | ? [E:$i]: ((neq @ C @ E) & (segmentP @ D @ E) & (strictorderedP @ E) & (segmentP @ E @ C) & (ssList @ E)) | ((segmentP @ B @ A) & (neq @ A @ nil)) | ~ (strictorderedP @ C) | ~ (segmentP @ D @ C) | ~ (A = C) | ~ (D = B))) | ~ (ssList @ C)) | ~ (ssList @ B)) | ~ (ssList @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])). 90.23/25.32 thf(101,plain,((neq @ sk2 @ nil)),inference(cnf,[status(esa)],[98])). 90.23/25.32 thf(36,axiom,((! [A:$i]: ((ssList @ A) => (! [B:$i]: ((! [C:$i]: ((((frontsegP @ A @ B) & (frontsegP @ B @ C)) => (frontsegP @ A @ C)) <= (ssList @ C))) <= (ssList @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax40)). 90.23/25.32 thf(234,plain,((! [A:$i]: ((ssList @ A) => (! [B:$i]: (! [C:$i]: ((((frontsegP @ A @ B) & (frontsegP @ B @ C)) => (frontsegP @ A @ C)) | ~ (ssList @ C)) | ~ (ssList @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[36])). 90.23/25.32 thf(95,axiom,((! [A:$i]: ((ssList @ A) => ((duplicatefreeP @ A) <=> (! [B:$i]: ((! [C:$i]: ((ssItem @ C) => (! [D:$i]: ((! [E:$i]: ((! [F:$i]: (((A = (app @ (app @ D @ (cons @ B @ E)) @ (cons @ C @ F))) => (B != C)) <= (ssList @ F))) <= (ssList @ E))) <= (ssList @ D))))) <= (ssItem @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax13)). 90.23/25.32 thf(481,plain,((! [A:$i]: ((ssList @ A) => (((duplicatefreeP @ A) => (! [B:$i]: (! [C:$i]: ((ssItem @ C) => (! [D:$i]: (! [E:$i]: (! [F:$i]: (((A = (app @ (app @ D @ (cons @ B @ E)) @ (cons @ C @ F))) => (~ (B = C))) | ~ (ssList @ F)) | ~ (ssList @ E)) | ~ (ssList @ D)))) | ~ (ssItem @ B)))) & ((! [B:$i]: (! [C:$i]: ((ssItem @ C) => (! [D:$i]: (! [E:$i]: (! [F:$i]: (((A = (app @ (app @ D @ (cons @ B @ E)) @ (cons @ C @ F))) => (~ (B = C))) | ~ (ssList @ F)) | ~ (ssList @ E)) | ~ (ssList @ D)))) | ~ (ssItem @ B))) => (duplicatefreeP @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[95])). 90.23/25.32 thf(23,axiom,((! [A:$i]: ((ssList @ A) => (! [B:$i]: ((ssList @ B) => (! [C:$i]: ((ssList @ C) => ((segmentP @ A @ C) <= ((segmentP @ B @ C) & (segmentP @ A @ B)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax53)). 90.23/25.32 thf(170,plain,((! [A:$i]: ((ssList @ A) => (! [B:$i]: ((ssList @ B) => (! [C:$i]: ((ssList @ C) => ((segmentP @ A @ C) | ~ ((segmentP @ B @ C) & (segmentP @ A @ B)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[23])). 90.23/25.32 thf(4,axiom,((! [A:$i]: ((ssItem @ A) => (! [B:$i]: (((~ (gt @ B @ A)) <= (gt @ A @ B)) <= (ssItem @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax94)). 90.23/25.32 thf(114,plain,((! [A:$i]: ((ssItem @ A) => (! [B:$i]: (~ (gt @ B @ A) | ~ (gt @ A @ B) | ~ (ssItem @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])). 90.23/25.32 thf(115,plain,(! [B:$i,A:$i] : ((~ (ssItem @ A)) | (~ (gt @ B @ A)) | (~ (gt @ A @ B)) | (~ (ssItem @ B)))),inference(cnf,[status(esa)],[114])). 90.23/25.32 thf(31,axiom,((! [A:$i]: ((ssList @ A) => (! [B:$i]: ((ssItem @ B) => ((hd @ (cons @ B @ A)) = B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax23)). 90.23/25.32 thf(217,plain,((! [A:$i]: ((ssList @ A) => (! [B:$i]: ((ssItem @ B) => ((hd @ (cons @ B @ A)) = B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[31])). 90.23/25.32 thf(48,axiom,((~ (singletonP @ nil))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax39)). 90.23/25.32 thf(276,plain,((~ (singletonP @ nil))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[48])). 90.23/25.32 thf(7,axiom,((! [A:$i]: ((! [B:$i]: ((ssItem @ B) => ((leq @ B @ A) <=> (geq @ A @ B)))) <= (ssItem @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax32)). 90.23/25.32 thf(120,plain,((! [A:$i]: (! [B:$i]: ((ssItem @ B) => (((leq @ B @ A) => (geq @ A @ B)) & ((geq @ A @ B) => (leq @ B @ A)))) | ~ (ssItem @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])). 90.23/25.32 thf(74,axiom,((! [A:$i]: (((! [B:$i]: ((! [C:$i]: ((! [D:$i]: ((! [E:$i]: ((ssList @ E) => (! [F:$i]: ((((app @ (app @ D @ (cons @ B @ E)) @ (cons @ C @ F)) = A) => (~ ((leq @ C @ B) & (leq @ B @ C)))) <= (ssList @ F))))) <= (ssList @ D))) <= (ssItem @ C))) <= (ssItem @ B))) <=> (cyclefreeP @ A)) <= (ssList @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax8)). 90.23/25.32 thf(379,plain,((! [A:$i]: ((((! [B:$i]: (! [C:$i]: (! [D:$i]: (! [E:$i]: ((ssList @ E) => (! [F:$i]: ((((app @ (app @ D @ (cons @ B @ E)) @ (cons @ C @ F)) = A) => (~ ((leq @ C @ B) & (leq @ B @ C)))) | ~ (ssList @ F)))) | ~ (ssList @ D)) | ~ (ssItem @ C)) | ~ (ssItem @ B))) => (cyclefreeP @ A)) & ((cyclefreeP @ A) => (! [B:$i]: (! [C:$i]: (! [D:$i]: (! [E:$i]: ((ssList @ E) => (! [F:$i]: ((((app @ (app @ D @ (cons @ B @ E)) @ (cons @ C @ F)) = A) => (~ ((leq @ C @ B) & (leq @ B @ C)))) | ~ (ssList @ F)))) | ~ (ssList @ D)) | ~ (ssItem @ C)) | ~ (ssItem @ B))))) | ~ (ssList @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[74])). 90.23/25.32 thf(102,plain,((segmentP @ sk4 @ sk3)),inference(cnf,[status(esa)],[98])). 90.23/25.32 thf(104,plain,((sk1 = sk3)),inference(cnf,[status(esa)],[98])). 90.23/25.32 thf(111,plain,((sk3 = sk1)),inference(lifteq,[status(thm)],[104])). 90.23/25.32 thf(103,plain,((sk4 = sk2)),inference(cnf,[status(esa)],[98])). 90.23/25.32 thf(110,plain,((sk4 = sk2)),inference(lifteq,[status(thm)],[103])). 90.23/25.32 thf(511,plain,((segmentP @ sk2 @ sk1)),inference(rewrite,[status(thm)],[102,111,110])). 90.23/25.32 thf(29,axiom,((! [A:$i]: (((! [B:$i]: ((! [C:$i]: ((! [D:$i]: ((! [E:$i]: ((! [F:$i]: ((ssList @ F) => (((app @ (app @ D @ (cons @ B @ E)) @ (cons @ C @ F)) = A) => ((lt @ C @ B) | (lt @ B @ C))))) <= (ssList @ E))) <= (ssList @ D))) <= (ssItem @ C))) <= (ssItem @ B))) <=> (strictorderP @ A)) <= (ssList @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax10)). 90.23/25.32 thf(201,plain,((! [A:$i]: ((((! [B:$i]: (! [C:$i]: (! [D:$i]: (! [E:$i]: (! [F:$i]: ((ssList @ F) => (((app @ (app @ D @ (cons @ B @ E)) @ (cons @ C @ F)) = A) => ((lt @ C @ B) | (lt @ B @ C)))) | ~ (ssList @ E)) | ~ (ssList @ D)) | ~ (ssItem @ C)) | ~ (ssItem @ B))) => (strictorderP @ A)) & ((strictorderP @ A) => (! [B:$i]: (! [C:$i]: (! [D:$i]: (! [E:$i]: (! [F:$i]: ((ssList @ F) => (((app @ (app @ D @ (cons @ B @ E)) @ (cons @ C @ F)) = A) => ((lt @ C @ B) | (lt @ B @ C)))) | ~ (ssList @ E)) | ~ (ssList @ D)) | ~ (ssItem @ C)) | ~ (ssItem @ B))))) | ~ (ssList @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[29])). 90.23/25.32 thf(202,plain,(! [A:$i] : ((ssItem @ (sk7 @ A)) | (strictorderP @ A) | (~ (ssList @ A)))),inference(cnf,[status(esa)],[201])). 90.23/25.32 thf(92,axiom,((! [A:$i]: ((ssList @ A) => ((A != nil) => ((cons @ (hd @ A) @ (tl @ A)) = A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax78)). 90.23/25.32 thf(472,plain,((! [A:$i]: ((ssList @ A) => ((~ (A = nil)) => ((cons @ (hd @ A) @ (tl @ A)) = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[92])). 90.23/25.32 thf(25,axiom,((! [A:$i]: ((! [B:$i]: ((ssList @ B) => (((nil = B) | ((nil != B) & (leq @ A @ (hd @ B)) & (totalorderedP @ B))) <=> (totalorderedP @ (cons @ A @ B))))) <= (ssItem @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax67)). 90.23/25.32 thf(174,plain,((! [A:$i]: (! [B:$i]: ((ssList @ B) => ((((nil = B) | (~ (nil = B) & (leq @ A @ (hd @ B)) & (totalorderedP @ B))) => (totalorderedP @ (cons @ A @ B))) & ((totalorderedP @ (cons @ A @ B)) => ((nil = B) | (~ (nil = B) & (leq @ A @ (hd @ B)) & (totalorderedP @ B)))))) | ~ (ssItem @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[25])). 90.23/25.32 thf(52,axiom,((! [A:$i]: (((A = nil) <=> (rearsegP @ nil @ A)) <= (ssList @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax52)). 90.23/25.32 thf(288,plain,((! [A:$i]: ((((A = nil) => (rearsegP @ nil @ A)) & ((rearsegP @ nil @ A) => (A = nil))) | ~ (ssList @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[52])). 90.23/25.32 thf(62,axiom,((! [A:$i]: ((ssList @ A) => (! [B:$i]: ((ssList @ (cons @ B @ A)) <= (ssItem @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax16)). 90.23/25.32 thf(320,plain,((! [A:$i]: ((ssList @ A) => (! [B:$i]: ((ssList @ (cons @ B @ A)) | ~ (ssItem @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[62])). 90.23/25.32 thf(9,axiom,((? [A:$i]: (? [B:$i]: ((A != B) & (ssItem @ B)) & (ssItem @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2)). 90.23/25.32 thf(126,plain,((? [A:$i]: (? [B:$i]: (~ (A = B) & (ssItem @ B)) & (ssItem @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[9])). 90.23/25.32 thf(127,plain,((ssItem @ sk5)),inference(cnf,[status(esa)],[126])). 90.23/25.32 thf(3,axiom,((! [A:$i]: ((ssItem @ A) => (~ (lt @ A @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax90)). 90.23/25.32 thf(112,plain,((! [A:$i]: ((ssItem @ A) => (~ (lt @ A @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])). 90.23/25.32 thf(113,plain,(! [A:$i] : ((~ (ssItem @ A)) | (~ (lt @ A @ A)))),inference(cnf,[status(esa)],[112])). 90.23/25.32 thf(564,plain,(! [A:$i] : ((~ (lt @ A @ A)) | ((ssItem @ sk5) != (ssItem @ A)))),inference(paramod_ordered,[status(thm)],[127,113])). 90.23/25.32 thf(565,plain,((~ (lt @ sk5 @ sk5))),inference(pattern_uni,[status(thm)],[564:[bind(A, $thf(sk5))]])). 90.23/25.32 thf(109,plain,((ssList @ sk2)),inference(cnf,[status(esa)],[98])). 90.23/25.32 thf(586,plain,(! [A:$i] : ((ssItem @ (sk7 @ A)) | (strictorderP @ A) | ((ssList @ sk2) != (ssList @ A)))),inference(paramod_ordered,[status(thm)],[109,202])). 90.23/25.32 thf(587,plain,((ssItem @ (sk7 @ sk2)) | (strictorderP @ sk2)),inference(pattern_uni,[status(thm)],[586:[bind(A, $thf(sk2))]])). 90.23/25.32 thf(70,axiom,((! [A:$i]: ((ssList @ A) => ((! [B:$i]: ((ssItem @ B) => (! [C:$i]: ((! [D:$i]: ((ssList @ D) => (! [E:$i]: ((! [F:$i]: (((leq @ B @ C) <= ((app @ (app @ D @ (cons @ B @ E)) @ (cons @ C @ F)) = A)) <= (ssList @ F))) <= (ssList @ E))))) <= (ssItem @ C))))) <=> (totalorderedP @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax11)). 90.23/25.32 thf(357,plain,((! [A:$i]: ((ssList @ A) => (((! [B:$i]: ((ssItem @ B) => (! [C:$i]: (! [D:$i]: ((ssList @ D) => (! [E:$i]: (! [F:$i]: ((leq @ B @ C) | ~ ((app @ (app @ D @ (cons @ B @ E)) @ (cons @ C @ F)) = A) | ~ (ssList @ F)) | ~ (ssList @ E)))) | ~ (ssItem @ C))))) => (totalorderedP @ A)) & ((totalorderedP @ A) => (! [B:$i]: ((ssItem @ B) => (! [C:$i]: (! [D:$i]: ((ssList @ D) => (! [E:$i]: (! [F:$i]: ((leq @ B @ C) | ~ ((app @ (app @ D @ (cons @ B @ E)) @ (cons @ C @ F)) = A) | ~ (ssList @ F)) | ~ (ssList @ E)))) | ~ (ssItem @ C)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[70])). 90.23/25.32 thf(89,axiom,((! [A:$i]: ((! [B:$i]: ((ssList @ B) => (! [C:$i]: (((app @ (app @ A @ B) @ C) = (app @ A @ (app @ B @ C))) <= (ssList @ C))))) <= (ssList @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax82)). 90.23/25.32 thf(460,plain,((! [A:$i]: (! [B:$i]: ((ssList @ B) => (! [C:$i]: (((app @ (app @ A @ B) @ C) = (app @ A @ (app @ B @ C))) | ~ (ssList @ C)))) | ~ (ssList @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[89])). 90.23/25.32 thf(19,axiom,((! [A:$i]: ((! [B:$i]: ((ssItem @ B) => (! [C:$i]: (((lt @ A @ C) <= ((lt @ B @ C) & (leq @ A @ B))) <= (ssItem @ C))))) <= (ssItem @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax91)). 90.23/25.32 thf(157,plain,((! [A:$i]: (! [B:$i]: ((ssItem @ B) => (! [C:$i]: ((lt @ A @ C) | ~ ((lt @ B @ C) & (leq @ A @ B)) | ~ (ssItem @ C)))) | ~ (ssItem @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[19])). 90.23/25.32 thf(93,axiom,((! [A:$i]: ((ssList @ A) => (! [B:$i]: ((ssList @ B) => (((hd @ A) = (hd @ (app @ A @ B))) <= (nil != A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax85)). 90.23/25.32 thf(475,plain,((! [A:$i]: ((ssList @ A) => (! [B:$i]: ((ssList @ B) => (((hd @ A) = (hd @ (app @ A @ B))) | (nil = A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[93])). 90.23/25.32 thf(85,axiom,((! [A:$i]: ((rearsegP @ A @ A) <= (ssList @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax49)). 90.23/25.32 thf(443,plain,((! [A:$i]: ((rearsegP @ A @ A) | ~ (ssList @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[85])). 90.23/25.32 thf(73,axiom,((! [A:$i]: ((! [B:$i]: ((A = (tl @ (cons @ B @ A))) <= (ssItem @ B))) <= (ssList @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax25)). 90.23/25.32 thf(376,plain,((! [A:$i]: (! [B:$i]: ((A = (tl @ (cons @ B @ A))) | ~ (ssItem @ B)) | ~ (ssList @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[73])). 90.23/25.32 thf(41,axiom,((! [A:$i]: ((ssList @ A) => (segmentP @ A @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax55)). 90.23/25.32 thf(253,plain,((! [A:$i]: ((ssList @ A) => (segmentP @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[41])). 90.23/25.32 thf(38,axiom,((! [A:$i]: (((A != nil) => (? [B:$i]: (((tl @ A) = B) & (ssList @ B)))) <= (ssList @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax76)). 90.23/25.32 thf(238,plain,((! [A:$i]: (((~ (A = nil)) => (? [B:$i]: (((tl @ A) = B) & (ssList @ B)))) | ~ (ssList @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[38])). 90.23/25.32 thf(17,axiom,((! [A:$i]: ((! [B:$i]: ((((geq @ B @ A) & (geq @ A @ B)) => (B = A)) <= (ssItem @ B))) <= (ssItem @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax87)). 90.23/25.32 thf(147,plain,((! [A:$i]: (! [B:$i]: ((((geq @ B @ A) & (geq @ A @ B)) => (B = A)) | ~ (ssItem @ B)) | ~ (ssItem @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[17])). 90.23/25.32 thf(11,axiom,((! [A:$i]: ((ssItem @ A) => (! [B:$i]: ((ssItem @ B) => ((~ (lt @ B @ A)) <= (lt @ A @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax33)). 90.23/25.32 thf(133,plain,((! [A:$i]: ((ssItem @ A) => (! [B:$i]: ((ssItem @ B) => (~ (lt @ B @ A) | ~ (lt @ A @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[11])). 90.23/25.32 thf(80,axiom,((totalorderP @ nil)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax62)). 90.23/25.32 thf(411,plain,((totalorderP @ nil)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[80])). 90.23/25.32 thf(5,axiom,((! [A:$i]: ((ssItem @ A) => (! [B:$i]: ((! [C:$i]: (((lt @ A @ C) <= ((lt @ A @ B) & (lt @ B @ C))) <= (ssItem @ C))) <= (ssItem @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax34)). 90.23/25.32 thf(116,plain,((! [A:$i]: ((ssItem @ A) => (! [B:$i]: (! [C:$i]: ((lt @ A @ C) | ~ ((lt @ A @ B) & (lt @ B @ C)) | ~ (ssItem @ C)) | ~ (ssItem @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])). 90.23/25.32 thf(39,axiom,((! [A:$i]: ((! [B:$i]: ((ssItem @ B) => ((memberP @ A @ B) <=> (? [C:$i]: ((ssList @ C) & ? [D:$i]: ((ssList @ D) & (A = (app @ C @ (cons @ B @ D))))))))) <= (ssList @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3)). 90.23/25.32 thf(243,plain,((! [A:$i]: (! [B:$i]: ((ssItem @ B) => (((memberP @ A @ B) => (? [C:$i]: ((ssList @ C) & ? [D:$i]: ((ssList @ D) & (A = (app @ C @ (cons @ B @ D))))))) & ((? [C:$i]: ((ssList @ C) & ? [D:$i]: ((ssList @ D) & (A = (app @ C @ (cons @ B @ D)))))) => (memberP @ A @ B)))) | ~ (ssList @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[39])). 90.23/25.32 thf(44,axiom,((! [A:$i]: ((ssItem @ A) => (totalorderedP @ (cons @ A @ nil))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax65)). 90.23/25.32 thf(265,plain,((! [A:$i]: ((ssItem @ A) => (totalorderedP @ (cons @ A @ nil))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[44])). 90.23/25.32 thf(58,axiom,((! [A:$i]: ((ssItem @ A) => (! [B:$i]: ((ssList @ B) => (! [C:$i]: ((ssList @ C) => (((memberP @ C @ A) | (memberP @ B @ A)) <=> (memberP @ (app @ B @ C) @ A))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax36)). 90.23/25.32 thf(307,plain,((! [A:$i]: ((ssItem @ A) => (! [B:$i]: ((ssList @ B) => (! [C:$i]: ((ssList @ C) => ((((memberP @ C @ A) | (memberP @ B @ A)) => (memberP @ (app @ B @ C) @ A)) & ((memberP @ (app @ B @ C) @ A) => ((memberP @ C @ A) | (memberP @ B @ A))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[58])). 90.23/25.32 thf(47,axiom,((! [A:$i]: ((ssItem @ A) => (! [B:$i]: ((ssItem @ B) => ((B != A) <=> (neq @ A @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1)). 90.23/25.32 thf(270,plain,((! [A:$i]: ((ssItem @ A) => (! [B:$i]: ((ssItem @ B) => (((~ (B = A)) => (neq @ A @ B)) & ((neq @ A @ B) => (~ (B = A))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[47])). 90.23/25.32 thf(32,axiom,((! [A:$i]: ((! [B:$i]: ((A != (cons @ B @ A)) <= (ssItem @ B))) <= (ssList @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax18)). 90.23/25.32 thf(220,plain,((! [A:$i]: (! [B:$i]: (~ (A = (cons @ B @ A)) | ~ (ssItem @ B)) | ~ (ssList @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[32])). 90.23/25.32 thf(64,axiom,((! [A:$i]: ((ssItem @ A) => (cyclefreeP @ (cons @ A @ nil))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax59)). 90.23/25.32 thf(334,plain,((! [A:$i]: ((ssItem @ A) => (cyclefreeP @ (cons @ A @ nil))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[64])). 90.23/25.32 thf(56,axiom,((! [A:$i]: ((ssItem @ A) => (totalorderP @ (cons @ A @ nil))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax61)). 90.23/25.32 thf(302,plain,((! [A:$i]: ((ssItem @ A) => (totalorderP @ (cons @ A @ nil))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[56])). 90.23/25.32 thf(75,axiom,((! [A:$i]: (((A = nil) | ? [B:$i]: ((ssList @ B) & ? [C:$i]: ((ssItem @ C) & ((cons @ C @ B) = A)))) <= (ssList @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax20)). 90.23/25.32 thf(392,plain,((! [A:$i]: ((A = nil) | ? [B:$i]: ((ssList @ B) & ? [C:$i]: ((ssItem @ C) & ((cons @ C @ B) = A))) | ~ (ssList @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[75])). 90.23/25.32 thf(54,axiom,((! [A:$i]: ((ssList @ A) => (! [B:$i]: ((! [C:$i]: ((ssList @ C) => ((frontsegP @ A @ B) => (frontsegP @ (app @ A @ C) @ B)))) <= (ssList @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax43)). 90.23/25.32 thf(297,plain,((! [A:$i]: ((ssList @ A) => (! [B:$i]: (! [C:$i]: ((ssList @ C) => ((frontsegP @ A @ B) => (frontsegP @ (app @ A @ C) @ B))) | ~ (ssList @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[54])). 90.23/25.32 thf(87,axiom,((! [A:$i]: (((nil = A) <=> (frontsegP @ nil @ A)) <= (ssList @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax46)). 90.23/25.32 thf(451,plain,((! [A:$i]: ((((nil = A) => (frontsegP @ nil @ A)) & ((frontsegP @ nil @ A) => (nil = A))) | ~ (ssList @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[87])). 90.23/25.32 thf(452,plain,(! [A:$i] : ((~ (nil = A)) | (frontsegP @ nil @ A) | (~ (ssList @ A)))),inference(cnf,[status(esa)],[451])). 90.23/25.32 thf(454,plain,(! [A:$i] : ((nil != A) | (frontsegP @ nil @ A) | (~ (ssList @ A)))),inference(lifteq,[status(thm)],[452])). 90.23/25.32 thf(455,plain,((frontsegP @ nil @ nil) | (~ (ssList @ nil))),inference(simp,[status(thm)],[454])). 90.23/25.32 thf(81,axiom,((ssList @ nil)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17)). 90.23/25.32 thf(412,plain,((ssList @ nil)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[81])). 90.23/25.32 thf(629,plain,((frontsegP @ nil @ nil) | ~ ($true)),inference(rewrite,[status(thm)],[455,412])). 90.23/25.32 thf(630,plain,((frontsegP @ nil @ nil)),inference(simp,[status(thm)],[629])). 90.23/25.32 thf(13,axiom,((! [A:$i]: ((ssItem @ A) => (leq @ A @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax31)). 90.23/25.32 thf(137,plain,((! [A:$i]: ((ssItem @ A) => (leq @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[13])). 90.23/25.32 thf(61,axiom,((! [A:$i]: (((A != nil) => (ssList @ (tl @ A))) <= (ssList @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax24)). 90.23/25.32 thf(317,plain,((! [A:$i]: (((~ (A = nil)) => (ssList @ (tl @ A))) | ~ (ssList @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[61])). 90.23/25.32 thf(26,axiom,((! [A:$i]: ((! [B:$i]: ((ssList @ B) => (ssList @ (app @ A @ B)))) <= (ssList @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax26)). 90.23/25.32 thf(188,plain,((! [A:$i]: (! [B:$i]: ((ssList @ B) => (ssList @ (app @ A @ B))) | ~ (ssList @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[26])). 90.23/25.32 thf(108,plain,((ssList @ sk1)),inference(cnf,[status(esa)],[98])). 90.23/25.32 thf(592,plain,(! [A:$i] : ((ssItem @ (sk7 @ A)) | (strictorderP @ A) | ((ssList @ sk1) != (ssList @ A)))),inference(paramod_ordered,[status(thm)],[108,202])). 90.23/25.32 thf(593,plain,((ssItem @ (sk7 @ sk1)) | (strictorderP @ sk1)),inference(pattern_uni,[status(thm)],[592:[bind(A, $thf(sk1))]])). 90.23/25.32 thf(15,axiom,((! [A:$i]: ((! [B:$i]: ((ssItem @ B) => ((lt @ B @ A) <=> (gt @ A @ B)))) <= (ssItem @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax35)). 90.23/25.32 thf(141,plain,((! [A:$i]: (! [B:$i]: ((ssItem @ B) => (((lt @ B @ A) => (gt @ A @ B)) & ((gt @ A @ B) => (lt @ B @ A)))) | ~ (ssItem @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[15])). 90.23/25.32 thf(34,axiom,((! [A:$i]: (((singletonP @ A) <=> (? [B:$i]: (((cons @ B @ nil) = A) & (ssItem @ B)))) <= (ssList @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4)). 90.23/25.32 thf(225,plain,((! [A:$i]: ((((singletonP @ A) => (? [B:$i]: (((cons @ B @ nil) = A) & (ssItem @ B)))) & ((? [B:$i]: (((cons @ B @ nil) = A) & (ssItem @ B))) => (singletonP @ A))) | ~ (ssList @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[34])). 90.23/25.32 thf(67,axiom,((! [A:$i]: ((! [B:$i]: (((B = A) <= ((rearsegP @ B @ A) & (rearsegP @ A @ B))) <= (ssList @ B))) <= (ssList @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax48)). 90.23/25.32 thf(339,plain,((! [A:$i]: (! [B:$i]: ((B = A) | ~ ((rearsegP @ B @ A) & (rearsegP @ A @ B)) | ~ (ssList @ B)) | ~ (ssList @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[67])). 90.23/25.32 thf(28,axiom,((! [A:$i]: ((ssList @ A) => (! [B:$i]: (((nil = (app @ A @ B)) <=> ((A = nil) & (nil = B))) <= (ssList @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax83)). 90.23/25.32 thf(193,plain,((! [A:$i]: ((ssList @ A) => (! [B:$i]: ((((nil = (app @ A @ B)) => ((A = nil) & (nil = B))) & (((A = nil) & (nil = B)) => (nil = (app @ A @ B)))) | ~ (ssList @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[28])). 90.23/25.32 thf(105,plain,((~ (segmentP @ sk2 @ sk1)) | (~ (neq @ sk1 @ nil))),inference(cnf,[status(esa)],[98])). 90.23/25.32 thf(508,plain,((~ (segmentP @ sk2 @ sk1)) | ((neq @ sk2 @ nil) != (neq @ sk1 @ nil))),inference(paramod_ordered,[status(thm)],[101,105])). 90.23/25.32 thf(509,plain,((~ (segmentP @ sk2 @ sk1)) | (sk2 != sk1) | (nil != nil)),inference(simp,[status(thm)],[508])). 90.23/25.32 thf(510,plain,((~ (segmentP @ sk2 @ sk1)) | (sk2 != sk1)),inference(simp,[status(thm)],[509])). 90.23/25.32 thf(514,plain,(~ ($true) | (sk2 != sk1)),inference(rewrite,[status(thm)],[510,511])). 90.23/25.32 thf(515,plain,((sk2 != sk1)),inference(simp,[status(thm)],[514])). 90.23/25.32 thf(88,axiom,((! [A:$i]: ((! [B:$i]: ((ssList @ B) => (! [C:$i]: ((ssItem @ C) => ((app @ (cons @ C @ B) @ A) = (cons @ C @ (app @ B @ A))))))) <= (ssList @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax27)). 90.23/25.32 thf(457,plain,((! [A:$i]: (! [B:$i]: ((ssList @ B) => (! [C:$i]: ((ssItem @ C) => ((app @ (cons @ C @ B) @ A) = (cons @ C @ (app @ B @ A)))))) | ~ (ssList @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[88])). 90.23/25.32 thf(86,axiom,((! [A:$i]: (((segmentP @ nil @ A) <=> (A = nil)) <= (ssList @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax58)). 90.23/25.32 thf(445,plain,((! [A:$i]: ((((segmentP @ nil @ A) => (A = nil)) & ((A = nil) => (segmentP @ nil @ A))) | ~ (ssList @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[86])). 90.23/25.32 thf(447,plain,(! [A:$i] : ((~ (A = nil)) | (segmentP @ nil @ A) | (~ (ssList @ A)))),inference(cnf,[status(esa)],[445])). 90.23/25.32 thf(449,plain,(! [A:$i] : ((A != nil) | (segmentP @ nil @ A) | (~ (ssList @ A)))),inference(lifteq,[status(thm)],[447])). 90.23/25.32 thf(450,plain,((segmentP @ nil @ nil) | (~ (ssList @ nil))),inference(simp,[status(thm)],[449])). 90.23/25.32 thf(568,plain,((segmentP @ nil @ nil) | ~ ($true)),inference(rewrite,[status(thm)],[450,412])). 90.23/25.32 thf(569,plain,((segmentP @ nil @ nil)),inference(simp,[status(thm)],[568])). 90.23/25.32 thf(128,plain,((ssItem @ sk6)),inference(cnf,[status(esa)],[126])). 90.23/25.32 thf(59,axiom,((! [A:$i]: ((! [B:$i]: (((nil != A) => ((tl @ (app @ A @ B)) = (app @ (tl @ A) @ B))) <= (ssList @ B))) <= (ssList @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax86)). 90.23/25.32 thf(311,plain,((! [A:$i]: (! [B:$i]: (((~ (nil = A)) => ((tl @ (app @ A @ B)) = (app @ (tl @ A) @ B))) | ~ (ssList @ B)) | ~ (ssList @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[59])). 90.23/25.32 thf(512,plain,(~ ($true) | (~ (neq @ sk1 @ nil))),inference(rewrite,[status(thm)],[105,511])). 90.23/25.32 thf(513,plain,((~ (neq @ sk1 @ nil))),inference(simp,[status(thm)],[512])). 90.23/25.32 thf(84,axiom,((! [A:$i]: ((! [B:$i]: ((ssList @ B) => ((strictorderedP @ (cons @ A @ B)) <=> (((B != nil) & (lt @ A @ (hd @ B)) & (strictorderedP @ B)) | (B = nil))))) <= (ssItem @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax70)). 90.23/25.32 thf(430,plain,((! [A:$i]: (! [B:$i]: ((ssList @ B) => (((strictorderedP @ (cons @ A @ B)) => ((~ (B = nil) & (lt @ A @ (hd @ B)) & (strictorderedP @ B)) | (B = nil))) & (((~ (B = nil) & (lt @ A @ (hd @ B)) & (strictorderedP @ B)) | (B = nil)) => (strictorderedP @ (cons @ A @ B))))) | ~ (ssItem @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[84])). 90.23/25.32 thf(21,axiom,((! [A:$i]: ((frontsegP @ A @ nil) <= (ssList @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax45)). 90.23/25.32 thf(161,plain,((! [A:$i]: ((frontsegP @ A @ nil) | ~ (ssList @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[21])). 90.23/25.32 thf(50,axiom,((! [A:$i]: ((! [B:$i]: (((rearsegP @ A @ B) <=> (? [C:$i]: ((ssList @ C) & ((app @ C @ B) = A)))) <= (ssList @ B))) <= (ssList @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax6)). 90.23/25.32 thf(279,plain,((! [A:$i]: (! [B:$i]: ((((rearsegP @ A @ B) => (? [C:$i]: ((ssList @ C) & ((app @ C @ B) = A)))) & ((? [C:$i]: ((ssList @ C) & ((app @ C @ B) = A))) => (rearsegP @ A @ B))) | ~ (ssList @ B)) | ~ (ssList @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[50])). 90.23/25.32 thf(72,axiom,((equalelemsP @ nil)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax74)). 90.23/25.32 thf(375,plain,((equalelemsP @ nil)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[72])). 90.23/25.32 thf(77,axiom,((! [A:$i]: ((! [B:$i]: (((A = B) <= ((frontsegP @ A @ B) & (frontsegP @ B @ A))) <= (ssList @ B))) <= (ssList @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax41)). 90.23/25.32 thf(402,plain,((! [A:$i]: (! [B:$i]: ((A = B) | ~ ((frontsegP @ A @ B) & (frontsegP @ B @ A)) | ~ (ssList @ B)) | ~ (ssList @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[77])). 90.23/25.32 thf(51,axiom,((! [A:$i]: ((ssList @ A) => (segmentP @ A @ nil)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax57)). 90.23/25.32 thf(286,plain,((! [A:$i]: ((ssList @ A) => (segmentP @ A @ nil)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[51])). 90.23/25.32 thf(6,axiom,((! [A:$i]: ((ssItem @ A) => (! [B:$i]: ((! [C:$i]: ((ssItem @ C) => ((leq @ A @ C) <= ((leq @ B @ C) & (leq @ A @ B))))) <= (ssItem @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax30)). 90.23/25.32 thf(118,plain,((! [A:$i]: ((ssItem @ A) => (! [B:$i]: (! [C:$i]: ((ssItem @ C) => ((leq @ A @ C) | ~ ((leq @ B @ C) & (leq @ A @ B)))) | ~ (ssItem @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])). 90.23/25.32 thf(82,axiom,((! [A:$i]: ((! [B:$i]: ((! [C:$i]: ((! [D:$i]: ((((B = A) & (D = C)) <= ((cons @ D @ B) = (cons @ C @ A))) <= (ssItem @ D))) <= (ssItem @ C))) <= (ssList @ B))) <= (ssList @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax19)). 90.23/25.32 thf(413,plain,((! [A:$i]: (! [B:$i]: (! [C:$i]: (! [D:$i]: (((B = A) & (D = C)) | ~ ((cons @ D @ B) = (cons @ C @ A)) | ~ (ssItem @ D)) | ~ (ssItem @ C)) | ~ (ssList @ B)) | ~ (ssList @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[82])). 90.23/25.32 thf(16,axiom,((! [A:$i]: ((ssItem @ A) => (! [B:$i]: ((ssItem @ B) => (((leq @ A @ B) & (leq @ B @ A)) => (B = A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax29)). 90.23/25.32 thf(144,plain,((! [A:$i]: ((ssItem @ A) => (! [B:$i]: ((ssItem @ B) => (((leq @ A @ B) & (leq @ B @ A)) => (B = A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[16])). 90.23/25.32 thf(37,axiom,((! [A:$i]: ((ssList @ A) => (frontsegP @ A @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax42)). 90.23/25.32 thf(236,plain,((! [A:$i]: ((ssList @ A) => (frontsegP @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[37])). 90.23/25.32 thf(100,plain,((strictorderedP @ sk3)),inference(cnf,[status(esa)],[98])). 90.23/25.32 thf(506,plain,((strictorderedP @ sk1)),inference(rewrite,[status(thm)],[100,111])). 90.23/25.32 thf(106,plain,(! [A:$i] : ((~ (neq @ sk3 @ A)) | (~ (segmentP @ sk4 @ A)) | (~ (strictorderedP @ A)) | (~ (segmentP @ A @ sk3)) | (~ (ssList @ A)))),inference(cnf,[status(esa)],[98])). 90.23/25.32 thf(516,plain,(! [A:$i] : ((~ (neq @ sk1 @ A)) | (~ (segmentP @ sk2 @ A)) | (~ (strictorderedP @ A)) | (~ (segmentP @ A @ sk1)) | (~ (ssList @ A)))),inference(rewrite,[status(thm)],[106,111,110])). 90.23/25.32 thf(528,plain,(! [A:$i] : ((~ (neq @ sk1 @ A)) | (~ (segmentP @ sk2 @ A)) | (~ (segmentP @ A @ sk1)) | (~ (ssList @ A)) | ((strictorderedP @ sk1) != (strictorderedP @ A)))),inference(paramod_ordered,[status(thm)],[506,516])). 90.23/25.32 thf(529,plain,((~ (neq @ sk1 @ sk1)) | (~ (segmentP @ sk2 @ sk1)) | (~ (segmentP @ sk1 @ sk1)) | (~ (ssList @ sk1))),inference(pattern_uni,[status(thm)],[528:[bind(A, $thf(sk1))]])). 90.23/25.32 thf(539,plain,((~ (neq @ sk1 @ sk1)) | ~ ($true) | (~ (segmentP @ sk1 @ sk1)) | ~ ($true)),inference(rewrite,[status(thm)],[529,511,108])). 90.23/25.32 thf(540,plain,((~ (neq @ sk1 @ sk1)) | (~ (segmentP @ sk1 @ sk1))),inference(simp,[status(thm)],[539])). 90.23/25.32 thf(20,axiom,((! [A:$i]: ((strictorderedP @ (cons @ A @ nil)) <= (ssItem @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax68)). 90.23/25.32 thf(159,plain,((! [A:$i]: ((strictorderedP @ (cons @ A @ nil)) | ~ (ssItem @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[20])). 90.23/25.32 thf(79,axiom,((! [A:$i]: ((ssList @ A) => ((? [B:$i]: (((hd @ A) = B) & (ssItem @ B))) <= (A != nil))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax75)). 90.23/25.32 thf(406,plain,((! [A:$i]: ((ssList @ A) => (? [B:$i]: (((hd @ A) = B) & (ssItem @ B)) | (A = nil))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[79])). 90.23/25.32 thf(24,axiom,((! [A:$i]: ((ssItem @ A) => (~ (memberP @ nil @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax38)). 90.23/25.32 thf(172,plain,((! [A:$i]: ((ssItem @ A) => (~ (memberP @ nil @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[24])). 90.23/25.32 thf(289,plain,(! [A:$i] : ((~ (A = nil)) | (rearsegP @ nil @ A) | (~ (ssList @ A)))),inference(cnf,[status(esa)],[288])). 90.23/25.32 thf(291,plain,(! [A:$i] : ((A != nil) | (rearsegP @ nil @ A) | (~ (ssList @ A)))),inference(lifteq,[status(thm)],[289])). 90.23/25.32 thf(292,plain,((rearsegP @ nil @ nil) | (~ (ssList @ nil))),inference(simp,[status(thm)],[291])). 90.23/25.32 thf(566,plain,((rearsegP @ nil @ nil) | ~ ($true)),inference(rewrite,[status(thm)],[292,412])). 90.23/25.32 thf(567,plain,((rearsegP @ nil @ nil)),inference(simp,[status(thm)],[566])). 90.23/25.32 thf(96,axiom,((totalorderedP @ nil)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax66)). 90.23/25.32 thf(494,plain,((totalorderedP @ nil)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[96])). 90.23/25.32 thf(40,axiom,((! [A:$i]: ((strictorderP @ (cons @ A @ nil)) <= (ssItem @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax63)). 90.23/25.32 thf(251,plain,((! [A:$i]: ((strictorderP @ (cons @ A @ nil)) | ~ (ssItem @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[40])). 90.23/25.32 thf(129,plain,((~ (sk5 = sk6))),inference(cnf,[status(esa)],[126])). 90.23/25.32 thf(130,plain,((sk6 != sk5)),inference(lifteq,[status(thm)],[129])). 90.23/25.32 thf(76,axiom,((! [A:$i]: ((! [B:$i]: ((! [C:$i]: ((ssList @ C) => ((A = C) <= ((app @ B @ C) = (app @ B @ A))))) <= (ssList @ B))) <= (ssList @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax80)). 90.23/25.32 thf(399,plain,((! [A:$i]: (! [B:$i]: (! [C:$i]: ((ssList @ C) => ((A = C) | ~ ((app @ B @ C) = (app @ B @ A)))) | ~ (ssList @ B)) | ~ (ssList @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[76])). 90.23/25.32 thf(49,axiom,((strictorderP @ nil)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax64)). 90.23/25.32 thf(278,plain,((strictorderP @ nil)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[49])). 90.23/25.32 thf(33,axiom,((! [A:$i]: ((! [B:$i]: ((! [C:$i]: ((ssList @ C) => (! [D:$i]: ((ssList @ D) => ((segmentP @ A @ B) => (segmentP @ (app @ (app @ C @ A) @ D) @ B)))))) <= (ssList @ B))) <= (ssList @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax56)). 90.23/25.32 thf(223,plain,((! [A:$i]: (! [B:$i]: (! [C:$i]: ((ssList @ C) => (! [D:$i]: ((ssList @ D) => ((segmentP @ A @ B) => (segmentP @ (app @ (app @ C @ A) @ D) @ B))))) | ~ (ssList @ B)) | ~ (ssList @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[33])). 90.23/25.32 thf(12,axiom,((! [A:$i]: ((! [B:$i]: ((ssItem @ B) => (! [C:$i]: ((((gt @ B @ C) & (gt @ A @ B)) => (gt @ A @ C)) <= (ssItem @ C))))) <= (ssItem @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax95)). 90.23/25.32 thf(135,plain,((! [A:$i]: (! [B:$i]: ((ssItem @ B) => (! [C:$i]: ((((gt @ B @ C) & (gt @ A @ B)) => (gt @ A @ C)) | ~ (ssItem @ C)))) | ~ (ssItem @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[12])). 90.23/25.32 thf(562,plain,(! [A:$i] : ((~ (lt @ A @ A)) | ((ssItem @ sk6) != (ssItem @ A)))),inference(paramod_ordered,[status(thm)],[128,113])). 90.23/25.32 thf(563,plain,((~ (lt @ sk6 @ sk6))),inference(pattern_uni,[status(thm)],[562:[bind(A, $thf(sk6))]])). 90.23/25.32 thf(55,axiom,((! [A:$i]: ((! [B:$i]: (((cons @ B @ A) = (app @ (cons @ B @ nil) @ A)) <= (ssItem @ B))) <= (ssList @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax81)). 90.23/25.32 thf(299,plain,((! [A:$i]: (! [B:$i]: (((cons @ B @ A) = (app @ (cons @ B @ nil) @ A)) | ~ (ssItem @ B)) | ~ (ssList @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[55])). 90.23/25.32 thf(45,axiom,((duplicatefreeP @ nil)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax72)). 90.23/25.32 thf(267,plain,((duplicatefreeP @ nil)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[45])). 90.23/25.32 thf(42,axiom,((! [A:$i]: ((! [B:$i]: ((ssItem @ B) => (! [C:$i]: ((ssList @ C) => (((memberP @ C @ A) | (B = A)) <=> (memberP @ (cons @ B @ C) @ A)))))) <= (ssItem @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax37)). 90.23/25.32 thf(255,plain,((! [A:$i]: (! [B:$i]: ((ssItem @ B) => (! [C:$i]: ((ssList @ C) => ((((memberP @ C @ A) | (B = A)) => (memberP @ (cons @ B @ C) @ A)) & ((memberP @ (cons @ B @ C) @ A) => ((memberP @ C @ A) | (B = A))))))) | ~ (ssItem @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[42])). 90.23/25.32 thf(68,axiom,((! [A:$i]: (((totalorderP @ A) <=> (! [B:$i]: ((ssItem @ B) => (! [C:$i]: ((ssItem @ C) => (! [D:$i]: ((ssList @ D) => (! [E:$i]: ((ssList @ E) => (! [F:$i]: ((((leq @ B @ C) | (leq @ C @ B)) <= ((app @ (app @ D @ (cons @ B @ E)) @ (cons @ C @ F)) = A)) <= (ssList @ F)))))))))))) <= (ssList @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax9)). 90.23/25.32 thf(342,plain,((! [A:$i]: ((((totalorderP @ A) => (! [B:$i]: ((ssItem @ B) => (! [C:$i]: ((ssItem @ C) => (! [D:$i]: ((ssList @ D) => (! [E:$i]: ((ssList @ E) => (! [F:$i]: ((leq @ B @ C) | (leq @ C @ B) | ~ ((app @ (app @ D @ (cons @ B @ E)) @ (cons @ C @ F)) = A) | ~ (ssList @ F)))))))))))) & ((! [B:$i]: ((ssItem @ B) => (! [C:$i]: ((ssItem @ C) => (! [D:$i]: ((ssList @ D) => (! [E:$i]: ((ssList @ E) => (! [F:$i]: ((leq @ B @ C) | (leq @ C @ B) | ~ ((app @ (app @ D @ (cons @ B @ E)) @ (cons @ C @ F)) = A) | ~ (ssList @ F))))))))))) => (totalorderP @ A))) | ~ (ssList @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[68])). 90.23/25.32 thf(8,axiom,((! [A:$i]: ((ssItem @ A) => (! [B:$i]: ((((lt @ A @ B) | (A = B)) <= (leq @ A @ B)) <= (ssItem @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax92)). 90.23/25.32 thf(123,plain,((! [A:$i]: ((ssItem @ A) => (! [B:$i]: ((lt @ A @ B) | (A = B) | ~ (leq @ A @ B) | ~ (ssItem @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8])). 90.23/25.32 thf(69,axiom,((! [A:$i]: ((ssList @ A) => (rearsegP @ A @ nil)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax51)). 90.23/25.32 thf(355,plain,((! [A:$i]: ((ssList @ A) => (rearsegP @ A @ nil)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[69])). 90.23/25.32 thf(18,axiom,((! [A:$i]: ((ssItem @ A) => (! [B:$i]: (((lt @ A @ B) <=> ((leq @ A @ B) & (B != A))) <= (ssItem @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax93)). 90.23/25.32 thf(150,plain,((! [A:$i]: ((ssItem @ A) => (! [B:$i]: ((((lt @ A @ B) => ((leq @ A @ B) & ~ (B = A))) & (((leq @ A @ B) & ~ (B = A)) => (lt @ A @ B))) | ~ (ssItem @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[18])). 90.23/25.32 thf(90,axiom,((! [A:$i]: ((ssList @ A) => (! [B:$i]: ((ssList @ B) => (! [C:$i]: ((ssList @ C) => ((rearsegP @ A @ B) => (rearsegP @ (app @ C @ A) @ B))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax50)). 90.23/25.32 thf(463,plain,((! [A:$i]: ((ssList @ A) => (! [B:$i]: ((ssList @ B) => (! [C:$i]: ((ssList @ C) => ((rearsegP @ A @ B) => (rearsegP @ (app @ C @ A) @ B))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[90])). 90.23/25.32 thf(66,axiom,((strictorderedP @ nil)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax69)). 90.23/25.32 thf(338,plain,((strictorderedP @ nil)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[66])). 90.23/25.32 thf(570,plain,((~ (neq @ sk1 @ sk1)) | ((segmentP @ sk1 @ sk1) != (segmentP @ nil @ nil))),inference(paramod_ordered,[status(thm)],[569,540])). 90.23/25.32 thf(573,plain,((~ (neq @ sk1 @ sk1)) | (sk1 != nil) | (sk1 != nil)),inference(simp,[status(thm)],[570])). 90.23/25.32 thf(576,plain,((~ (neq @ sk1 @ sk1)) | (sk1 != nil)),inference(simp,[status(thm)],[573])). 90.23/25.32 thf(65,axiom,((! [A:$i]: ((duplicatefreeP @ (cons @ A @ nil)) <= (ssItem @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax71)). 90.23/25.32 thf(336,plain,((! [A:$i]: ((duplicatefreeP @ (cons @ A @ nil)) | ~ (ssItem @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[65])). 90.23/25.32 thf(60,axiom,((! [A:$i]: ((! [B:$i]: ((ssList @ B) => ((B = A) <= ((segmentP @ B @ A) & (segmentP @ A @ B))))) <= (ssList @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax54)). 90.23/25.32 thf(314,plain,((! [A:$i]: (! [B:$i]: ((ssList @ B) => ((B = A) | ~ ((segmentP @ B @ A) & (segmentP @ A @ B)))) | ~ (ssList @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[60])). 90.23/25.32 thf(91,axiom,((! [A:$i]: ((ssList @ A) => (! [B:$i]: ((ssList @ B) => ((frontsegP @ A @ B) <=> (? [C:$i]: (((app @ B @ C) = A) & (ssList @ C))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax5)). 90.23/25.32 thf(465,plain,((! [A:$i]: ((ssList @ A) => (! [B:$i]: ((ssList @ B) => (((frontsegP @ A @ B) => (? [C:$i]: (((app @ B @ C) = A) & (ssList @ C)))) & ((? [C:$i]: (((app @ B @ C) = A) & (ssList @ C))) => (frontsegP @ A @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[91])). 90.23/25.32 thf(97,axiom,((! [A:$i]: ((ssList @ A) => (! [B:$i]: ((ssList @ B) => ((? [C:$i]: ((ssList @ C) & ? [D:$i]: ((ssList @ D) & ((app @ (app @ C @ B) @ D) = A)))) <=> (segmentP @ A @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax7)). 90.23/25.32 thf(495,plain,((! [A:$i]: ((ssList @ A) => (! [B:$i]: ((ssList @ B) => (((? [C:$i]: ((ssList @ C) & ? [D:$i]: ((ssList @ D) & ((app @ (app @ C @ B) @ D) = A)))) => (segmentP @ A @ B)) & ((segmentP @ A @ B) => (? [C:$i]: ((ssList @ C) & ? [D:$i]: ((ssList @ D) & ((app @ (app @ C @ B) @ D) = A))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[97])). 90.23/25.32 thf(57,axiom,((! [A:$i]: ((ssList @ A) => (! [B:$i]: ((ssList @ B) => (! [C:$i]: ((((app @ C @ B) = (app @ A @ B)) => (C = A)) <= (ssList @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax79)). 90.23/25.32 thf(304,plain,((! [A:$i]: ((ssList @ A) => (! [B:$i]: ((ssList @ B) => (! [C:$i]: ((((app @ C @ B) = (app @ A @ B)) => (C = A)) | ~ (ssList @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[57])). 90.23/25.32 thf(194,plain,(! [B:$i,A:$i] : ((~ (ssList @ A)) | (~ (A = nil)) | (~ (nil = B)) | (nil = (app @ A @ B)) | (~ (ssList @ B)))),inference(cnf,[status(esa)],[193])). 90.23/25.32 thf(197,plain,(! [B:$i,A:$i] : ((A != nil) | (nil != B) | ((app @ A @ B) = nil) | (~ (ssList @ A)) | (~ (ssList @ B)))),inference(lifteq,[status(thm)],[194])). 90.23/25.32 thf(198,plain,(((app @ nil @ nil) = nil) | (~ (ssList @ nil))),inference(simp,[status(thm)],[197])). 90.23/25.32 thf(631,plain,(((app @ nil @ nil) = nil) | ~ ($true)),inference(rewrite,[status(thm)],[198,412])). 90.23/25.32 thf(632,plain,(((app @ nil @ nil) = nil)),inference(simp,[status(thm)],[631])). 90.23/25.32 thf(14,axiom,((! [A:$i]: ((! [B:$i]: ((! [C:$i]: (((geq @ A @ C) <= ((geq @ B @ C) & (geq @ A @ B))) <= (ssItem @ C))) <= (ssItem @ B))) <= (ssItem @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax88)). 90.23/25.32 thf(139,plain,((! [A:$i]: (! [B:$i]: (! [C:$i]: ((geq @ A @ C) | ~ ((geq @ B @ C) & (geq @ A @ B)) | ~ (ssItem @ C)) | ~ (ssItem @ B)) | ~ (ssItem @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[14])). 90.23/25.32 thf(83,axiom,((! [A:$i]: ((ssList @ A) => ((! [B:$i]: ((! [C:$i]: ((! [D:$i]: ((ssList @ D) => (! [E:$i]: ((ssList @ E) => (! [F:$i]: (((A = (app @ (app @ D @ (cons @ B @ E)) @ (cons @ C @ F))) => (lt @ B @ C)) <= (ssList @ F))))))) <= (ssItem @ C))) <= (ssItem @ B))) <=> (strictorderedP @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax12)). 90.23/25.32 thf(418,plain,((! [A:$i]: ((ssList @ A) => (((! [B:$i]: (! [C:$i]: (! [D:$i]: ((ssList @ D) => (! [E:$i]: ((ssList @ E) => (! [F:$i]: (((A = (app @ (app @ D @ (cons @ B @ E)) @ (cons @ C @ F))) => (lt @ B @ C)) | ~ (ssList @ F)))))) | ~ (ssItem @ C)) | ~ (ssItem @ B))) => (strictorderedP @ A)) & ((strictorderedP @ A) => (! [B:$i]: (! [C:$i]: (! [D:$i]: ((ssList @ D) => (! [E:$i]: ((ssList @ E) => (! [F:$i]: (((A = (app @ (app @ D @ (cons @ B @ E)) @ (cons @ C @ F))) => (lt @ B @ C)) | ~ (ssList @ F)))))) | ~ (ssItem @ C)) | ~ (ssItem @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[83])). 90.23/25.32 thf(94,axiom,((! [A:$i]: (((A != nil) => (ssItem @ (hd @ A))) <= (ssList @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax22)). 90.23/25.32 thf(478,plain,((! [A:$i]: (((~ (A = nil)) => (ssItem @ (hd @ A))) | ~ (ssList @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[94])). 90.23/25.32 thf(30,axiom,((! [A:$i]: ((! [B:$i]: ((((nil != A) & ((tl @ B) = (tl @ A)) & ((hd @ A) = (hd @ B)) & (nil != B)) => (B = A)) <= (ssList @ B))) <= (ssList @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax77)). 90.23/25.32 thf(214,plain,((! [A:$i]: (! [B:$i]: (((~ (nil = A) & ((tl @ B) = (tl @ A)) & ((hd @ A) = (hd @ B)) & ~ (nil = B)) => (B = A)) | ~ (ssList @ B)) | ~ (ssList @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[30])). 90.23/25.32 thf(43,axiom,((! [A:$i]: ((ssList @ A) => ((app @ nil @ A) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax28)). 90.23/25.32 thf(262,plain,((! [A:$i]: ((ssList @ A) => ((app @ nil @ A) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[43])). 90.23/25.32 thf(78,axiom,((cyclefreeP @ nil)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax60)). 90.23/25.32 thf(405,plain,((cyclefreeP @ nil)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[78])). 90.23/25.32 thf(27,axiom,((! [A:$i]: ((! [B:$i]: (((cons @ B @ A) != nil) <= (ssItem @ B))) <= (ssList @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax21)). 90.23/25.32 thf(190,plain,((! [A:$i]: (! [B:$i]: (~ ((cons @ B @ A) = nil) | ~ (ssItem @ B)) | ~ (ssList @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[27])). 90.23/25.32 thf(53,axiom,((! [A:$i]: ((ssList @ A) => ((app @ A @ nil) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax84)). 90.23/25.32 thf(294,plain,((! [A:$i]: ((ssList @ A) => ((app @ A @ nil) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[53])). 90.23/25.32 thf(46,axiom,((! [A:$i]: ((ssList @ A) => (! [B:$i]: ((! [C:$i]: (((rearsegP @ A @ C) <= ((rearsegP @ B @ C) & (rearsegP @ A @ B))) <= (ssList @ C))) <= (ssList @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax47)). 90.23/25.32 thf(268,plain,((! [A:$i]: ((ssList @ A) => (! [B:$i]: (! [C:$i]: ((rearsegP @ A @ C) | ~ ((rearsegP @ B @ C) & (rearsegP @ A @ B)) | ~ (ssList @ C)) | ~ (ssList @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[46])). 90.23/25.32 thf(10,axiom,((! [A:$i]: ((geq @ A @ A) <= (ssItem @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax89)). 90.23/25.32 thf(131,plain,((! [A:$i]: ((geq @ A @ A) | ~ (ssItem @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[10])). 90.23/25.32 thf(22,axiom,((! [A:$i]: ((ssItem @ A) => (! [B:$i]: ((ssItem @ B) => (! [C:$i]: ((! [D:$i]: ((ssList @ D) => ((frontsegP @ (cons @ A @ C) @ (cons @ B @ D)) <=> ((B = A) & (frontsegP @ C @ D))))) <= (ssList @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax44)). 90.23/25.32 thf(163,plain,((! [A:$i]: ((ssItem @ A) => (! [B:$i]: ((ssItem @ B) => (! [C:$i]: (! [D:$i]: ((ssList @ D) => (((frontsegP @ (cons @ A @ C) @ (cons @ B @ D)) => ((B = A) & (frontsegP @ C @ D))) & (((B = A) & (frontsegP @ C @ D)) => (frontsegP @ (cons @ A @ C) @ (cons @ B @ D))))) | ~ (ssList @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[22])). 90.23/25.32 thf(277,plain,((~ (singletonP @ nil))),inference(polarity_switch,[status(thm)],[276])). 90.23/25.32 thf(71,axiom,((! [A:$i]: ((ssList @ A) => (! [B:$i]: ((ssList @ B) => ((B != A) <=> (neq @ A @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax15)). 90.23/25.32 thf(369,plain,((! [A:$i]: ((ssList @ A) => (! [B:$i]: ((ssList @ B) => (((~ (B = A)) => (neq @ A @ B)) & ((neq @ A @ B) => (~ (B = A))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[71])). 90.23/25.32 thf(63,axiom,((! [A:$i]: (((! [B:$i]: ((! [C:$i]: ((ssItem @ C) => (! [D:$i]: ((! [E:$i]: ((ssList @ E) => ((C = B) <= (A = (app @ D @ (cons @ B @ (cons @ C @ E))))))) <= (ssList @ D))))) <= (ssItem @ B))) <=> (equalelemsP @ A)) <= (ssList @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax14)). 90.23/25.32 thf(322,plain,((! [A:$i]: ((((! [B:$i]: (! [C:$i]: ((ssItem @ C) => (! [D:$i]: (! [E:$i]: ((ssList @ E) => ((C = B) | ~ (A = (app @ D @ (cons @ B @ (cons @ C @ E)))))) | ~ (ssList @ D)))) | ~ (ssItem @ B))) => (equalelemsP @ A)) & ((equalelemsP @ A) => (! [B:$i]: (! [C:$i]: ((ssItem @ C) => (! [D:$i]: (! [E:$i]: ((ssList @ E) => ((C = B) | ~ (A = (app @ D @ (cons @ B @ (cons @ C @ E)))))) | ~ (ssList @ D)))) | ~ (ssItem @ B))))) | ~ (ssList @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[63])). 90.23/25.32 thf(35,axiom,((! [A:$i]: ((equalelemsP @ (cons @ A @ nil)) <= (ssItem @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax73)). 90.23/25.32 thf(232,plain,((! [A:$i]: ((equalelemsP @ (cons @ A @ nil)) | ~ (ssItem @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[35])). 90.23/25.32 thf(16529,plain,($false),inference(e,[status(thm)],[101,234,481,170,115,217,276,120,379,511,202,472,174,288,320,565,110,587,357,460,157,475,443,376,253,238,147,133,411,116,243,265,307,270,201,220,334,302,392,297,630,137,317,188,593,141,109,225,339,193,515,457,569,128,311,412,513,430,161,279,375,402,286,118,413,445,144,236,540,159,406,172,113,451,567,98,494,251,108,130,399,278,223,135,563,299,267,255,112,516,342,123,355,150,463,127,338,576,336,314,465,495,304,114,632,139,418,478,214,262,405,190,294,126,506,268,131,163,277,369,111,322,232])). 90.23/25.32 % SZS output end CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 90.23/25.32 % [INFO] Killing All external provers ... 90.58/25.47 EOF