0.02/0.03 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.02/0.04 % 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 : n134.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 : Fri Jul 13 14:54:12 CDT 2018 0.03/0.23 % CPUTime : 3.16/1.64 % [INFO] Running in sequential loop mode. 3.78/1.86 % [CONFIG] Using configuration: timeout(300) with strategy 3.91/1.94 % [INFO] iprover registered as external prover. 3.91/1.94 % [INFO] e registered as external prover. 3.91/1.94 % [INFO] cvc4 registered as external prover. 3.91/1.94 % [INFO] Parsing finished. Scanning for conjecture ... 4.09/2.00 % [INFO] Found a conjecture and 127 axioms. Running axiom selection ... 4.33/2.09 % [INFO] Axiom selection finished. Selected 127 axioms (removed 0 axioms). 4.99/2.46 % [INFO] Type checking passed. Searching for refutation ... 17.57/6.68 % [INFO] Killing All external provers ... 17.57/6.68 % Time passed: 6354ms 17.57/6.68 % Effective reasoning time: 5038ms 17.57/6.68 % Solved by strategy 17.57/6.70 % Axioms used in derivation (127): qu(cond(axiom(41), 0), imp(cond(axiom(41), 0))), qu(cond(axiom(145), 0), imp(cond(axiom(145), 0))), ass(cond(goal(206), 0), 1), qu(cond(axiom(119), 0), imp(cond(axiom(119), 0))), qu(cond(axiom(3), 0), imp(cond(axiom(3), 0))), replace(qu(theu(the(408), 1), imp(the(408)))), qu(cond(axiom(164), 0), imp(cond(axiom(164), 0))), qu(cond(axiom(202), 0), imp(cond(axiom(202), 0))), qu(cond(axiom(19), 0), imp(cond(axiom(19), 0))), qu(cond(axiom(95), 0), imp(cond(axiom(95), 0))), qu(cond(axiom(43), 0), imp(cond(axiom(43), 0))), ass(cond(goal(264), 0), 2), qu(cond(axiom(133), 0), imp(cond(axiom(133), 0))), qu(cond(axiom(21), 0), imp(cond(axiom(21), 0))), qu(cond(axiom(151), 0), imp(cond(axiom(151), 0))), pred(axiom(5), 0), qu(cond(axiom(75), 0), imp(cond(axiom(75), 0))), qu(cond(axiom(194), 0), imp(cond(axiom(194), 0))), qu(cond(axiom(190), 0), imp(cond(axiom(190), 0))), qu(cond(axiom(53), 0), imp(cond(axiom(53), 0))), qu(cond(axiom(89), 0), imp(cond(axiom(89), 0))), replace(replace(and(pred(s2(plural(the(408))), 0), and(pred(s1(plural(the(408))), 0), pred(the(408), 0))))), replace(pred(408, 2)), ass(cond(goal(264), 0), 1), ass(cond(goal(340), 0), 0), qu(cond(axiom(107), 0), imp(cond(axiom(107), 0))), pred(axiom(137), 2), qu(cond(axiom(31), 0), imp(cond(axiom(31), 0))), ass(cond(goal(206), 0), 0), qu(cond(axiom(103), 0), imp(cond(axiom(103), 0))), ass(cond(goal(238), 0), 0), qu(cond(axiom(77), 0), imp(cond(axiom(77), 0))), qu(cond(axiom(113), 0), imp(cond(axiom(113), 0))), qu(cond(axiom(45), 0), imp(cond(axiom(45), 0))), qu(cond(axiom(11), 0), imp(cond(axiom(11), 0))), qu(cond(axiom(176), 0), imp(cond(axiom(176), 0))), qu(cond(axiom(33), 0), imp(cond(axiom(33), 0))), qu(cond(axiom(139), 0), imp(cond(axiom(139), 0))), ass(cond(goal(340), 0), 1), pred(406, 0), qu(cond(axiom(59), 0), imp(cond(axiom(59), 0))), holds(conjunct1(conjunct2(conjunct2(406))), 1412, 0), qu(cond(axiom(35), 0), imp(cond(axiom(35), 0))), qu(cond(axiom(23), 0), imp(cond(axiom(23), 0))), qu(cond(axiom(87), 0), imp(cond(axiom(87), 0))), qu(cond(axiom(1), 0), imp(cond(axiom(1), 0))), qu(cond(axiom(121), 0), imp(cond(axiom(121), 0))), qu(cond(axiom(83), 0), imp(cond(axiom(83), 0))), qu(cond(axiom(109), 0), imp(cond(axiom(109), 0))), qu(cond(axiom(79), 0), imp(cond(axiom(79), 0))), ass(cond(goal(382), 0), 0), qu(cond(axiom(55), 0), imp(cond(axiom(55), 0))), qu(cond(axiom(81), 0), imp(cond(axiom(81), 0))), qu(cond(axiom(13), 0), imp(cond(axiom(13), 0))), qu(cond(axiom(143), 0), imp(cond(axiom(143), 0))), ass(cond(156, 0), 0), qu(cond(axiom(184), 0), imp(cond(axiom(184), 0))), qu(cond(axiom(188), 0), imp(cond(axiom(188), 0))), qu(cond(axiom(99), 0), imp(cond(axiom(99), 0))), holds(conjunct2(conjunct2(conjunct2(406))), 1413, 0), qu(cond(axiom(71), 0), imp(cond(axiom(71), 0))), holds(407, 1414, 0), ass(cond(goal(238), 0), 1), qu(cond(axiom(57), 0), imp(cond(axiom(57), 0))), qu(cond(axiom(65), 0), imp(cond(axiom(65), 0))), qu(cond(axiom(174), 0), imp(cond(axiom(174), 0))), and(pred(s2(plural(the(409))), 0), and(pred(s1(plural(the(409))), 0), pred(the(409), 0))), qu(cond(axiom(61), 0), imp(cond(axiom(61), 0))), qu(cond(axiom(9), 0), imp(cond(axiom(9), 0))), and(pred(conjunct2(405), 5), and(pred(s2(plural(conjunct2(405))), 0), and(pred(s1(plural(conjunct2(405))), 0), and(pred(conjunct2(405), 1), and(pred(conjunct1(405), 9), and(pred(conjunct1(405), 8), and(pred(conjunct1(405), 7), and(qe(s3(plural(405))), and(qe(s2(plural(405))), qe(s1(plural(405)))))))))))), qu(cond(axiom(182), 0), imp(cond(axiom(182), 0))), qu(cond(axiom(117), 0), imp(cond(axiom(117), 0))), qu(cond(axiom(172), 0), imp(cond(axiom(172), 0))), qu(cond(axiom(115), 0), imp(cond(axiom(115), 0))), qu(cond(axiom(131), 0), imp(cond(axiom(131), 0))), qu(cond(axiom(196), 0), imp(cond(axiom(196), 0))), qu(cond(axiom(186), 0), imp(cond(axiom(186), 0))), qu(cond(axiom(127), 0), imp(cond(axiom(127), 0))), qu(cond(axiom(123), 0), imp(cond(axiom(123), 0))), qu(cond(axiom(25), 0), imp(cond(axiom(25), 0))), qu(cond(axiom(101), 0), imp(cond(axiom(101), 0))), qu(cond(axiom(125), 0), imp(cond(axiom(125), 0))), qu(cond(axiom(170), 0), imp(cond(axiom(170), 0))), qu(cond(axiom(111), 0), imp(cond(axiom(111), 0))), qu(cond(axiom(166), 0), imp(cond(axiom(166), 0))), qu(cond(axiom(105), 0), imp(cond(axiom(105), 0))), qu(cond(axiom(37), 0), imp(cond(axiom(37), 0))), ass(cond(goal(264), 0), 0), qu(cond(axiom(63), 0), imp(cond(axiom(63), 0))), qu(cond(axiom(192), 0), imp(cond(axiom(192), 0))), ass(cond(goal(219), 0), 0), pred(axiom(137), 1), ass(cond(goal(206), 0), 2), qu(cond(axiom(29), 0), imp(cond(axiom(29), 0))), qu(cond(axiom(39), 0), imp(cond(axiom(39), 0))), qu(cond(axiom(129), 0), imp(cond(axiom(129), 0))), qu(cond(axiom(73), 0), imp(cond(axiom(73), 0))), qu(cond(axiom(15), 0), imp(cond(axiom(15), 0))), qu(cond(axiom(85), 0), imp(cond(axiom(85), 0))), holds(conjunct1(406), 1410, 0), ass(cond(goal(238), 0), 2), qu(cond(axiom(200), 0), imp(cond(axiom(200), 0))), qu(cond(axiom(27), 0), imp(cond(axiom(27), 0))), qu(cond(axiom(91), 0), imp(cond(axiom(91), 0))), ass(cond(goal(219), 0), 1), qu(cond(axiom(49), 0), imp(cond(axiom(49), 0))), qu(cond(axiom(149), 0), imp(cond(axiom(149), 0))), qu(cond(axiom(7), 0), imp(cond(axiom(7), 0))), qu(cond(axiom(17), 0), imp(cond(axiom(17), 0))), qu(cond(axiom(51), 0), imp(cond(axiom(51), 0))), holds(conjunct1(conjunct2(406)), 1411, 0), qu(cond(axiom(141), 0), imp(cond(axiom(141), 0))), qu(cond(axiom(135), 0), imp(cond(axiom(135), 0))), qu(cond(axiom(47), 0), imp(cond(axiom(47), 0))), qu(cond(axiom(69), 0), imp(cond(axiom(69), 0))), qu(cond(axiom(147), 0), imp(cond(axiom(147), 0))), qu(cond(axiom(168), 0), imp(cond(axiom(168), 0))), qu(cond(axiom(204), 0), imp(cond(axiom(204), 0))), qu(cond(axiom(97), 0), imp(cond(axiom(97), 0))), qu(cond(axiom(162), 0), imp(cond(axiom(162), 0))), qu(cond(axiom(180), 0), imp(cond(axiom(180), 0))), qu(cond(axiom(153), 0), imp(cond(axiom(153), 0))), qu(cond(axiom(178), 0), imp(cond(axiom(178), 0))), qu(cond(axiom(160), 0), imp(cond(axiom(160), 0))), qu(cond(axiom(67), 0), imp(cond(axiom(67), 0))), qu(cond(axiom(93), 0), imp(cond(axiom(93), 0))), qu(cond(axiom(198), 0), imp(cond(axiom(198), 0))) 17.57/6.70 % No. of inferences in proof: 258 17.57/6.70 % No. of processed clauses: 10 17.57/6.70 % No. of generated clauses: 6 17.57/6.70 % No. of forward subsumed clauses: 0 17.57/6.70 % No. of backward subsumed clauses: 0 17.57/6.70 % No. of ground rewrite rules in store: 6 17.57/6.70 % No. of non-ground rewrite rules in store: 0 17.57/6.70 % No. of positive (non-rewrite) units in store: 0 17.57/6.70 % No. of negative (non-rewrite) units in store: 3 17.57/6.70 % No. of choice functions detected: 0 17.57/6.70 % No. of choice instantiations: 0 17.57/6.70 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 6354 ms resp. 5038 ms w/o parsing 18.17/7.04 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 18.17/7.04 thf(vd1409_type, type, vd1409: $i). 18.17/7.04 thf(ron_type, type, ron: ($i > ($i > $o))). 18.17/7.04 thf(vd1401_type, type, vd1401: $i). 18.17/7.04 thf(rline_type, type, rline: ($i > $o)). 18.17/7.04 thf(vd1419_type, type, vd1419: $i). 18.17/7.04 thf(vd684_type, type, vd684: $i). 18.17/7.04 thf(rreal_type, type, rreal: ($i > $o)). 18.17/7.04 thf(rR_type, type, rR: ($i > ($i > ($i > $o)))). 18.17/7.04 thf(rpoint_type, type, rpoint: ($i > $o)). 18.17/7.04 thf(vangle_type, type, vangle: ($i > ($i > ($i > $i)))). 18.17/7.04 thf(v0_type, type, v0: $i). 18.17/7.04 thf(vf_type, type, vf: ($i > ($i > $i))). 18.17/7.04 thf(rleq_type, type, rleq: ($i > ($i > $o))). 18.17/7.04 thf(vskolem1120_type, type, vskolem1120: ($i > ($i > ($i > ($i > ($i > ($i > ($i > ($i > $i))))))))). 18.17/7.04 thf(rless_type, type, rless: ($i > ($i > $o))). 18.17/7.04 thf(rcircle_type, type, rcircle: ($i > $o)). 18.17/7.04 thf(rinside_type, type, rinside: ($i > ($i > $o))). 18.17/7.04 thf(vskolem1078_type, type, vskolem1078: ($i > ($i > ($i > ($i > $i))))). 18.17/7.04 thf(vg_type, type, vg: ($i > ($i > ($i > $i)))). 18.17/7.04 thf(vplus_type, type, vplus: ($i > ($i > $i))). 18.17/7.04 thf(vskolem1052_type, type, vskolem1052: ($i > ($i > ($i > ($i > $i))))). 18.17/7.04 thf(rcenter_type, type, rcenter: ($i > ($i > $o))). 18.17/7.04 thf(vd14_type, type, vd14: $i). 18.17/7.04 thf(vperp_type, type, vperp: $i). 18.17/7.04 thf(vd1415_type, type, vd1415: $i). 18.17/7.04 thf(vskolem1416_type, type, vskolem1416: $i). 18.17/7.04 thf(rgeq_type, type, rgeq: ($i > ($i > $o))). 18.17/7.04 thf(rtriangle_type, type, rtriangle: ($i > $o)). 18.17/7.04 thf(vtriangle_type, type, vtriangle: ($i > ($i > ($i > $i)))). 18.17/7.04 thf(rS_type, type, rS: ($i > ($i > ($i > $o)))). 18.17/7.04 thf(rintersect_type, type, rintersect: ($i > ($i > $o))). 18.17/7.04 thf(vd1406_type, type, vd1406: $i). 18.17/7.04 thf(vd1400_type, type, vd1400: $i). 18.17/7.04 thf(vd1399_type, type, vd1399: $i). 18.17/7.04 thf(vd1407_type, type, vd1407: $i). 18.17/7.04 thf(91,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i]: (((C = D) & (rS @ G @ C @ A) & (rS @ E @ C @ A) & ~ (ron @ C @ A) & (A = B) & (rline @ B) & (rpoint @ D) & (rpoint @ F) & (rpoint @ H) & (H = G) & (E = F)) => (? [I:$i]: ((I != G) & (I != C) & (rpoint @ I) & (rS @ I @ C @ A) & (E != I)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(37), 0), imp(cond(axiom(37), 0)))')). 18.17/7.04 thf(760,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i]: (((C = D) & (rS @ G @ C @ A) & (rS @ E @ C @ A) & ~ (ron @ C @ A) & (A = B) & (rline @ B) & (rpoint @ D) & (rpoint @ F) & (rpoint @ H) & (H = G) & (E = F)) => (? [I:$i]: (~ (I = G) & ~ (I = C) & (rpoint @ I) & (rS @ I @ C @ A) & ~ (E = I)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[91])). 18.17/7.04 thf(92,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((~ (rinside @ B @ D) & (ron @ A @ C) & ? [E:$i]: ((C = E) & (rcircle @ E)) & ? [E:$i]: ((E = B) & (rpoint @ E)) & ? [E:$i]: ((rpoint @ E) & (A = E)) & ? [E:$i]: ((E = D) & (rcircle @ E)) & ((rinside @ B @ C) | (ron @ B @ C)) & (rinside @ A @ D) & ~ (ron @ B @ D)) => (rintersect @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(133), 0), imp(cond(axiom(133), 0)))')). 18.17/7.04 thf(777,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((~ (rinside @ B @ D) & (ron @ A @ C) & ? [E:$i]: ((C = E) & (rcircle @ E)) & ? [E:$i]: ((E = B) & (rpoint @ E)) & ? [E:$i]: ((rpoint @ E) & (A = E)) & ? [E:$i]: ((E = D) & (rcircle @ E)) & ((rinside @ B @ C) | (ron @ B @ C)) & (rinside @ A @ D) & ~ (ron @ B @ D)) => (rintersect @ C @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[92])). 18.17/7.04 thf(44,axiom,((vd1415 = vskolem1416)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','replace(pred(408, 2))')). 18.17/7.04 thf(352,plain,((vd1415 = vskolem1416)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[44])). 18.17/7.04 thf(65,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i]: (((ron @ A @ G) & (rline @ H) & (F = E) & (D = C) & (rpoint @ D) & (B = A) & (rpoint @ B) & (rpoint @ F) & (G = H) & (A != C) & (A != E) & (ron @ C @ G)) => ((v0 = (vangle @ C @ A @ E)) <=> (~ (rR @ A @ C @ E) & (ron @ E @ G)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(188), 0), imp(cond(axiom(188), 0)))')). 18.17/7.04 thf(523,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i]: (((ron @ A @ G) & (rline @ H) & (F = E) & (D = C) & (rpoint @ D) & (B = A) & (rpoint @ B) & (rpoint @ F) & (G = H) & ~ (A = C) & ~ (A = E) & (ron @ C @ G)) => (((v0 = (vangle @ C @ A @ E)) => (~ (rR @ A @ C @ E) & (ron @ E @ G))) & ((~ (rR @ A @ C @ E) & (ron @ E @ G)) => (v0 = (vangle @ C @ A @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[65])). 18.17/7.04 thf(74,axiom,(((vangle @ vd1399 @ vd1409 @ vd1401) = (vangle @ vd1399 @ vd1401 @ vd1409))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(407, 1414, 0)')). 18.17/7.04 thf(582,plain,(((vangle @ vd1399 @ vd1409 @ vd1401) = (vangle @ vd1399 @ vd1401 @ vd1409))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[74])). 18.17/7.04 thf(118,axiom,((vd1401 != vd1409)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(conjunct2(conjunct2(conjunct2(406))), 1413, 0)')). 18.17/7.04 thf(1005,plain,((~ (vd1401 = vd1409))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[118])). 18.17/7.04 thf(125,axiom,((! [A:$i,B:$i]: (((rcircle @ B) & (A = B)) => (? [C:$i]: ((rpoint @ C) & (ron @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(41), 0), imp(cond(axiom(41), 0)))')). 18.17/7.04 thf(1068,plain,((! [A:$i,B:$i]: (((rcircle @ B) & (A = B)) => (? [C:$i]: ((rpoint @ C) & (ron @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[125])). 18.17/7.04 thf(78,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: ((((rS @ C @ D @ E) & (rS @ B @ D @ F)) <=> ((vplus @ (vangle @ B @ A @ D) @ (vangle @ D @ A @ C)) = (vangle @ B @ A @ C))) <= (~ (ron @ D @ E) & (A != C) & (B != A) & (ron @ C @ F) & (ron @ B @ E) & ? [G:$i]: ((G = E) & (rline @ G)) & ? [G:$i]: ((G = D) & (rpoint @ G)) & ? [G:$i]: ((G = B) & (rpoint @ G)) & ? [G:$i]: ((A = G) & (rpoint @ G)) & ? [G:$i]: ((rpoint @ G) & (G = C)) & ? [G:$i]: ((rline @ G) & (G = F)) & (ron @ A @ E) & (ron @ A @ F) & ~ (ron @ D @ F) & (E != F))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(190), 0), imp(cond(axiom(190), 0)))')). 18.17/7.04 thf(655,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: (((((rS @ C @ D @ E) & (rS @ B @ D @ F)) => ((vplus @ (vangle @ B @ A @ D) @ (vangle @ D @ A @ C)) = (vangle @ B @ A @ C))) & (((vplus @ (vangle @ B @ A @ D) @ (vangle @ D @ A @ C)) = (vangle @ B @ A @ C)) => ((rS @ C @ D @ E) & (rS @ B @ D @ F)))) | ~ (~ (ron @ D @ E) & ~ (A = C) & ~ (B = A) & (ron @ C @ F) & (ron @ B @ E) & ? [G:$i]: ((G = E) & (rline @ G)) & ? [G:$i]: ((G = D) & (rpoint @ G)) & ? [G:$i]: ((G = B) & (rpoint @ G)) & ? [G:$i]: ((A = G) & (rpoint @ G)) & ? [G:$i]: ((rpoint @ G) & (G = C)) & ? [G:$i]: ((rline @ G) & (G = F)) & (ron @ A @ E) & (ron @ A @ F) & ~ (ron @ D @ F) & ~ (E = F))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[78])). 18.17/7.04 thf(107,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: ((~ (ron @ D @ E) & (E = F) & (B != A) & ? [G:$i]: ((rpoint @ G) & (G = D)) & ? [G:$i]: ((B = G) & (rpoint @ G)) & ? [G:$i]: ((A = G) & (rpoint @ G)) & ? [G:$i]: ((G = C) & (rpoint @ G)) & (C != A) & (D != A) & (C != B) & (B != D) & (C != D) & (rline @ F)) => ((rR @ C @ A @ B) <=> ((vplus @ (vg @ A @ C @ D) @ (vg @ D @ C @ B)) = (vg @ A @ D @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(202), 0), imp(cond(axiom(202), 0)))')). 18.17/7.04 thf(913,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: ((~ (ron @ D @ E) & (E = F) & ~ (B = A) & ? [G:$i]: ((rpoint @ G) & (G = D)) & ? [G:$i]: ((B = G) & (rpoint @ G)) & ? [G:$i]: ((A = G) & (rpoint @ G)) & ? [G:$i]: ((G = C) & (rpoint @ G)) & ~ (C = A) & ~ (D = A) & ~ (C = B) & ~ (B = D) & ~ (C = D) & (rline @ F)) => (((rR @ C @ A @ B) => ((vplus @ (vg @ A @ C @ D) @ (vg @ D @ C @ B)) = (vg @ A @ D @ B))) & (((vplus @ (vg @ A @ C @ D) @ (vg @ D @ C @ B)) = (vg @ A @ D @ B)) => (rR @ C @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[107])). 18.17/7.04 thf(8,axiom,((! [A:$i,B:$i]: (((rcircle @ B) & (B = A)) => (? [C:$i]: ((rpoint @ C) & (rinside @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(47), 0), imp(cond(axiom(47), 0)))')). 18.17/7.04 thf(153,plain,((! [A:$i,B:$i]: (((rcircle @ B) & (B = A)) => (? [C:$i]: ((rpoint @ C) & (rinside @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8])). 18.17/7.04 thf(128,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((? [E:$i]: ((rcircle @ E) & (D = E)) & ? [E:$i]: ((rcircle @ E) & (E = C)) & ? [E:$i]: ((rpoint @ E) & (B = E)) & ? [E:$i]: ((rpoint @ E) & (E = A)) & ((rinside @ A @ C) | (ron @ A @ C)) & ((ron @ B @ C) | (rinside @ B @ C)) & ~ (? [E:$i]: (rS @ A @ B @ E))) => (? [E:$i]: (rintersect @ E @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(129), 0), imp(cond(axiom(129), 0)))')). 18.17/7.04 thf(1095,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((? [E:$i]: ((rcircle @ E) & (D = E)) & ? [E:$i]: ((rcircle @ E) & (E = C)) & ? [E:$i]: ((rpoint @ E) & (B = E)) & ? [E:$i]: ((rpoint @ E) & (E = A)) & ((rinside @ A @ C) | (ron @ A @ C)) & ((ron @ B @ C) | (rinside @ B @ C)) & ~ (? [E:$i]: (rS @ A @ B @ E))) => (? [E:$i]: (rintersect @ E @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[128])). 18.17/7.04 thf(50,axiom,((! [A:$i,B:$i,C:$i]: ((? [D:$i]: ((B = D) & (rpoint @ D)) & ? [D:$i]: ((rpoint @ D) & (A = D)) & ? [D:$i]: ((rpoint @ D) & (C = D)) & (B != A) & (A != C) & (B != C) & ((vf @ A @ C) = (vf @ A @ B))) => (! [D:$i,E:$i,F:$i,G:$i]: (((G = F) & (rR @ C @ A @ F) & (rR @ B @ A @ D) & (rpoint @ E) & (rpoint @ G) & (D = E)) => ((vangle @ A @ B @ C) = (vangle @ A @ C @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(340), 0), 1)')). 18.17/7.04 thf(404,plain,((! [A:$i,B:$i,C:$i]: ((? [D:$i]: ((B = D) & (rpoint @ D)) & ? [D:$i]: ((rpoint @ D) & (A = D)) & ? [D:$i]: ((rpoint @ D) & (C = D)) & ~ (B = A) & ~ (A = C) & ~ (B = C) & ((vf @ A @ C) = (vf @ A @ B))) => (! [D:$i,E:$i,F:$i,G:$i]: (((G = F) & (rR @ C @ A @ F) & (rR @ B @ A @ D) & (rpoint @ E) & (rpoint @ G) & (D = E)) => ((vangle @ A @ B @ C) = (vangle @ A @ C @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[50])). 18.17/7.04 thf(124,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((ron @ D @ A) & ? [E:$i]: ((rpoint @ E) & (D = E)) & (rcircle @ B) & (B = A) & ? [E:$i]: ((rpoint @ E) & (C = E)) & (ron @ C @ A)) => (? [E:$i]: ((E != D) & (C != E) & (ron @ E @ A) & (rpoint @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(45), 0), imp(cond(axiom(45), 0)))')). 18.17/7.04 thf(1055,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((ron @ D @ A) & ? [E:$i]: ((rpoint @ E) & (D = E)) & (rcircle @ B) & (B = A) & ? [E:$i]: ((rpoint @ E) & (C = E)) & (ron @ C @ A)) => (? [E:$i]: (~ (E = D) & ~ (C = E) & (ron @ E @ A) & (rpoint @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[124])). 18.17/7.04 thf(62,axiom,((rpoint @ vd1409)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pred(406, 0)')). 18.17/7.04 thf(504,plain,((rpoint @ vd1409)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[62])). 18.17/7.04 thf(95,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((? [E:$i]: ((E != C) & (rS @ E @ C @ A) & (rpoint @ E))) <= ((C = D) & ~ (ron @ C @ A) & (rpoint @ D) & (B = A) & (rline @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(33), 0), imp(cond(axiom(33), 0)))')). 18.17/7.04 thf(802,plain,((! [A:$i,B:$i,C:$i,D:$i]: (? [E:$i]: (~ (E = C) & (rS @ E @ C @ A) & (rpoint @ E)) | ~ ((C = D) & ~ (ron @ C @ A) & (rpoint @ D) & (B = A) & (rline @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[95])). 18.17/7.04 thf(42,axiom,((! [A:$i,B:$i]: (((vf @ B @ A) = (vf @ A @ B)) <= (? [C:$i]: ((A = C) & (rpoint @ C)) & ? [C:$i]: ((C = B) & (rpoint @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(166), 0), imp(cond(axiom(166), 0)))')). 18.17/7.04 thf(344,plain,((! [A:$i,B:$i]: (((vf @ B @ A) = (vf @ A @ B)) | ~ (? [C:$i]: ((A = C) & (rpoint @ C)) & ? [C:$i]: ((C = B) & (rpoint @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[42])). 18.17/7.04 thf(15,axiom,((! [A:$i,B:$i,C:$i]: ((((vg @ A @ C @ B) = (vg @ A @ B @ C)) & ((vg @ A @ B @ C) = (vg @ C @ A @ B))) <= (? [D:$i]: ((B = D) & (rpoint @ D)) & ? [D:$i]: ((A = D) & (rpoint @ D)) & ? [D:$i]: ((D = C) & (rpoint @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(176), 0), imp(cond(axiom(176), 0)))')). 18.17/7.04 thf(196,plain,((! [A:$i,B:$i,C:$i]: ((((vg @ A @ C @ B) = (vg @ A @ B @ C)) & ((vg @ A @ B @ C) = (vg @ C @ A @ B))) | ~ (? [D:$i]: ((B = D) & (rpoint @ D)) & ? [D:$i]: ((A = D) & (rpoint @ D)) & ? [D:$i]: ((D = C) & (rpoint @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[15])). 18.17/7.04 thf(56,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i]: ((? [H:$i]: ((rpoint @ H) & (ron @ H @ A) & (ron @ H @ B) & ~ (rS @ H @ G @ C))) <= (~ (ron @ G @ C) & (ron @ E @ C) & (C = D) & ? [H:$i]: ((B = H) & (rcircle @ H)) & ? [H:$i]: ((A = H) & (rcircle @ H)) & (rline @ D) & (rintersect @ A @ B) & (rcenter @ E @ A) & (rcenter @ F @ B) & (ron @ F @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(71), 0), imp(cond(axiom(71), 0)))')). 18.17/7.04 thf(460,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i]: (? [H:$i]: ((rpoint @ H) & (ron @ H @ A) & (ron @ H @ B) & ~ (rS @ H @ G @ C)) | ~ (~ (ron @ G @ C) & (ron @ E @ C) & (C = D) & ? [H:$i]: ((B = H) & (rcircle @ H)) & ? [H:$i]: ((A = H) & (rcircle @ H)) & (rline @ D) & (rintersect @ A @ B) & (rcenter @ E @ A) & (rcenter @ F @ B) & (ron @ F @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[56])). 18.17/7.04 thf(127,axiom,((! [A:$i,B:$i]: (((B = A) & (rline @ B)) => (? [C:$i]: ((rpoint @ C) & (ron @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(15), 0), imp(cond(axiom(15), 0)))')). 18.17/7.04 thf(1087,plain,((! [A:$i,B:$i]: (((B = A) & (rline @ B)) => (? [C:$i]: ((rpoint @ C) & (ron @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[127])). 18.17/7.04 thf(31,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((rpoint @ (vskolem1052 @ A @ B @ C @ D)) <= ((rpoint @ D) & (A = B) & (rpoint @ B) & (C != A) & (C = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(206), 0), 2)')). 18.17/7.04 thf(289,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((rpoint @ (vskolem1052 @ A @ B @ C @ D)) | ~ ((rpoint @ D) & (A = B) & (rpoint @ B) & ~ (C = A) & (C = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[31])). 18.17/7.04 thf(19,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((vf @ A @ C) = (vf @ C @ (vskolem1052 @ A @ B @ C @ D))) <= ((rpoint @ D) & (A = B) & (rpoint @ B) & (C != A) & (C = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(206), 0), 1)')). 18.17/7.04 thf(216,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((vf @ A @ C) = (vf @ C @ (vskolem1052 @ A @ B @ C @ D))) | ~ ((rpoint @ D) & (A = B) & (rpoint @ B) & ~ (C = A) & (C = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[19])). 18.17/7.04 thf(13,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i]: (((vf @ E @ G) = (vf @ A @ (vskolem1120 @ A @ B @ C @ D @ E @ F @ G @ H))) <= ((A != C) & (H = G) & (F = E) & (rpoint @ F) & (D = C) & (rpoint @ B) & (B = A) & (rpoint @ D) & (rpoint @ H) & (G != E) & (rless @ (vf @ E @ G) @ (vf @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(238), 0), 0)')). 18.17/7.04 thf(179,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i]: (((vf @ E @ G) = (vf @ A @ (vskolem1120 @ A @ B @ C @ D @ E @ F @ G @ H))) | ~ (~ (A = C) & (H = G) & (F = E) & (rpoint @ F) & (D = C) & (rpoint @ B) & (B = A) & (rpoint @ D) & (rpoint @ H) & ~ (G = E) & (rless @ (vf @ E @ G) @ (vf @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[13])). 18.17/7.04 thf(122,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((rS @ A @ C @ D) | (rS @ B @ C @ D)) <= (~ (rS @ A @ B @ D) & ~ (ron @ A @ D) & ? [F:$i]: ((rpoint @ F) & (A = F)) & ? [F:$i]: ((rpoint @ F) & (B = F)) & ? [F:$i]: ((rpoint @ F) & (C = F)) & (rline @ E) & (D = E) & ~ (ron @ B @ D) & ~ (ron @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(103), 0), imp(cond(axiom(103), 0)))')). 18.17/7.04 thf(1040,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((rS @ A @ C @ D) | (rS @ B @ C @ D) | ~ (~ (rS @ A @ B @ D) & ~ (ron @ A @ D) & ? [F:$i]: ((rpoint @ F) & (A = F)) & ? [F:$i]: ((rpoint @ F) & (B = F)) & ? [F:$i]: ((rpoint @ F) & (C = F)) & (rline @ E) & (D = E) & ~ (ron @ B @ D) & ~ (ron @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[122])). 18.17/7.04 thf(129,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((? [E:$i]: ((rpoint @ E) & (ron @ E @ A) & (E != C))) <= ((ron @ C @ A) & (D = C) & (rpoint @ D) & (B = A) & (rcircle @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(43), 0), imp(cond(axiom(43), 0)))')). 18.17/7.04 thf(1109,plain,((! [A:$i,B:$i,C:$i,D:$i]: (? [E:$i]: ((rpoint @ E) & (ron @ E @ A) & ~ (E = C)) | ~ ((ron @ C @ A) & (D = C) & (rpoint @ D) & (B = A) & (rcircle @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[129])). 18.17/7.04 thf(18,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((vplus @ A @ C) = (vplus @ C @ A)) <= ((rreal @ D) & (rreal @ B) & (B = A) & (D = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(143), 0), imp(cond(axiom(143), 0)))')). 18.17/7.04 thf(211,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((vplus @ A @ C) = (vplus @ C @ A)) | ~ ((rreal @ D) & (rreal @ B) & (B = A) & (D = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[18])). 18.17/7.04 thf(59,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i]: (((rS @ E @ F @ C) & (ron @ E @ A) & ? [H:$i]: ((H = C) & (rline @ H)) & ? [H:$i]: ((rline @ H) & (A = H)) & ? [H:$i]: ((B = H) & (rline @ H)) & ? [H:$i]: ((rpoint @ H) & (D = H)) & ? [H:$i]: ((rpoint @ H) & (H = E)) & ? [H:$i]: ((rpoint @ H) & (H = F)) & ? [H:$i]: ((rpoint @ H) & (G = H)) & (ron @ D @ A) & (ron @ D @ B) & (ron @ D @ C) & (ron @ F @ C) & (ron @ G @ C) & (rS @ F @ G @ A)) => (~ (rS @ E @ G @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(113), 0), imp(cond(axiom(113), 0)))')). 18.17/7.04 thf(485,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i]: (((rS @ E @ F @ C) & (ron @ E @ A) & ? [H:$i]: ((H = C) & (rline @ H)) & ? [H:$i]: ((rline @ H) & (A = H)) & ? [H:$i]: ((B = H) & (rline @ H)) & ? [H:$i]: ((rpoint @ H) & (D = H)) & ? [H:$i]: ((rpoint @ H) & (H = E)) & ? [H:$i]: ((rpoint @ H) & (H = F)) & ? [H:$i]: ((rpoint @ H) & (G = H)) & (ron @ D @ A) & (ron @ D @ B) & (ron @ D @ C) & (ron @ F @ C) & (ron @ G @ C) & (rS @ F @ G @ A)) => (~ (rS @ E @ G @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[59])). 18.17/7.04 thf(110,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: ((~ (? [G:$i]: ((ron @ F @ G) & (ron @ E @ G) & (ron @ D @ G) & (rline @ G))) & ((vangle @ B @ A @ C) = (vangle @ E @ D @ F)) & ((vf @ D @ E) = (vf @ A @ B)) & ? [G:$i]: ((G = E) & (rpoint @ G)) & (C != B) & (C != A) & ? [G:$i]: ((G = B) & (rpoint @ G)) & ? [G:$i]: ((G = A) & (rpoint @ G)) & ? [G:$i]: ((C = G) & (rpoint @ G)) & (B != A) & ? [G:$i]: ((D = G) & (rpoint @ G)) & ? [G:$i]: ((F = G) & (rpoint @ G)) & ((vf @ D @ F) = (vf @ A @ C))) => ((vangle @ D @ E @ F) = (vangle @ A @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(264), 0), 1)')). 18.17/7.04 thf(937,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: ((~ (? [G:$i]: ((ron @ F @ G) & (ron @ E @ G) & (ron @ D @ G) & (rline @ G))) & ((vangle @ B @ A @ C) = (vangle @ E @ D @ F)) & ((vf @ D @ E) = (vf @ A @ B)) & ? [G:$i]: ((G = E) & (rpoint @ G)) & ~ (C = B) & ~ (C = A) & ? [G:$i]: ((G = B) & (rpoint @ G)) & ? [G:$i]: ((G = A) & (rpoint @ G)) & ? [G:$i]: ((C = G) & (rpoint @ G)) & ~ (B = A) & ? [G:$i]: ((D = G) & (rpoint @ G)) & ? [G:$i]: ((F = G) & (rpoint @ G)) & ((vf @ D @ F) = (vf @ A @ C))) => ((vangle @ D @ E @ F) = (vangle @ A @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[110])). 18.17/7.04 thf(43,axiom,((! [A:$i,B:$i]: ((? [C:$i]: ((A = C) & (rpoint @ C)) & ? [C:$i]: ((B = C) & (rpoint @ C))) => (v0 = (vg @ A @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(172), 0), imp(cond(axiom(172), 0)))')). 18.17/7.04 thf(348,plain,((! [A:$i,B:$i]: ((? [C:$i]: ((A = C) & (rpoint @ C)) & ? [C:$i]: ((B = C) & (rpoint @ C))) => (v0 = (vg @ A @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[43])). 18.17/7.04 thf(58,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((rR @ A @ B @ C) | (rR @ C @ A @ B) | (rR @ B @ A @ C)) <= ((ron @ A @ D) & (A != C) & ? [F:$i]: ((B = F) & (rpoint @ F)) & ? [F:$i]: ((rpoint @ F) & (F = A)) & ? [F:$i]: ((rpoint @ F) & (C = F)) & (A != B) & (B != C) & (rline @ E) & (ron @ B @ D) & (ron @ C @ D) & (E = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(91), 0), imp(cond(axiom(91), 0)))')). 18.17/7.04 thf(480,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((rR @ A @ B @ C) | (rR @ C @ A @ B) | (rR @ B @ A @ C) | ~ ((ron @ A @ D) & ~ (A = C) & ? [F:$i]: ((B = F) & (rpoint @ F)) & ? [F:$i]: ((rpoint @ F) & (F = A)) & ? [F:$i]: ((rpoint @ F) & (C = F)) & ~ (A = B) & ~ (B = C) & (rline @ E) & (ron @ B @ D) & (ron @ C @ D) & (E = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[58])). 18.17/7.04 thf(81,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i]: (((rS @ F @ H @ C) & (rS @ G @ H @ B) & (rS @ F @ G @ A) & (ron @ G @ C) & (ron @ F @ B) & (ron @ E @ A) & ? [I:$i]: ((E = I) & (rpoint @ I)) & ? [I:$i]: ((rpoint @ I) & (D = I)) & ? [I:$i]: ((B = I) & (rline @ I)) & ? [I:$i]: ((rline @ I) & (I = A)) & ? [I:$i]: ((rline @ I) & (I = C)) & ? [I:$i]: ((F = I) & (rpoint @ I)) & ? [I:$i]: ((I = G) & (rpoint @ I)) & (ron @ D @ A) & (ron @ D @ B) & (ron @ D @ C) & (rS @ E @ F @ C)) => (rS @ F @ H @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(117), 0), imp(cond(axiom(117), 0)))')). 18.17/7.04 thf(687,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i]: (((rS @ F @ H @ C) & (rS @ G @ H @ B) & (rS @ F @ G @ A) & (ron @ G @ C) & (ron @ F @ B) & (ron @ E @ A) & ? [I:$i]: ((E = I) & (rpoint @ I)) & ? [I:$i]: ((rpoint @ I) & (D = I)) & ? [I:$i]: ((B = I) & (rline @ I)) & ? [I:$i]: ((rline @ I) & (I = A)) & ? [I:$i]: ((rline @ I) & (I = C)) & ? [I:$i]: ((F = I) & (rpoint @ I)) & ? [I:$i]: ((I = G) & (rpoint @ I)) & (ron @ D @ A) & (ron @ D @ B) & (ron @ D @ C) & (rS @ E @ F @ C)) => (rS @ F @ H @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[81])). 18.17/7.04 thf(32,axiom,((! [A:$i,B:$i,C:$i]: ((! [D:$i,E:$i,F:$i,G:$i]: (((vangle @ B @ C @ F) = (vangle @ C @ B @ D)) <= ((rpoint @ G) & (rpoint @ E) & (rR @ B @ A @ D) & (rR @ C @ A @ F) & (G = F) & (E = D)))) <= ((C != B) & (C != A) & (A != B) & ? [D:$i]: ((rpoint @ D) & (D = C)) & ? [D:$i]: ((A = D) & (rpoint @ D)) & ? [D:$i]: ((rpoint @ D) & (D = B)) & ((vf @ A @ C) = (vf @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(340), 0), 0)')). 18.17/7.04 thf(293,plain,((! [A:$i,B:$i,C:$i]: (! [D:$i,E:$i,F:$i,G:$i]: (((vangle @ B @ C @ F) = (vangle @ C @ B @ D)) | ~ ((rpoint @ G) & (rpoint @ E) & (rR @ B @ A @ D) & (rR @ C @ A @ F) & (G = F) & (E = D))) | ~ (~ (C = B) & ~ (C = A) & ~ (A = B) & ? [D:$i]: ((rpoint @ D) & (D = C)) & ? [D:$i]: ((A = D) & (rpoint @ D)) & ? [D:$i]: ((rpoint @ D) & (D = B)) & ((vf @ A @ C) = (vf @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[32])). 18.17/7.04 thf(102,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: (((vf @ B @ C) = (vf @ E @ F)) <= (? [G:$i]: ((G = F) & (rpoint @ G)) & ? [G:$i]: ((rpoint @ G) & (E = G)) & (C != B) & (B != A) & ? [G:$i]: ((rpoint @ G) & (G = C)) & ? [G:$i]: ((rpoint @ G) & (A = G)) & ? [G:$i]: ((G = B) & (rpoint @ G)) & (A != C) & ? [G:$i]: ((D = G) & (rpoint @ G)) & ((vf @ A @ B) = (vf @ D @ E)) & ((vf @ D @ F) = (vf @ A @ C)) & ((vangle @ B @ A @ C) = (vangle @ E @ D @ F)) & ~ (? [G:$i]: ((ron @ E @ G) & (rline @ G) & (ron @ D @ G) & (ron @ F @ G))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(264), 0), 2)')). 18.17/7.04 thf(866,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: (((vf @ B @ C) = (vf @ E @ F)) | ~ (? [G:$i]: ((G = F) & (rpoint @ G)) & ? [G:$i]: ((rpoint @ G) & (E = G)) & ~ (C = B) & ~ (B = A) & ? [G:$i]: ((rpoint @ G) & (G = C)) & ? [G:$i]: ((rpoint @ G) & (A = G)) & ? [G:$i]: ((G = B) & (rpoint @ G)) & ~ (A = C) & ? [G:$i]: ((D = G) & (rpoint @ G)) & ((vf @ A @ B) = (vf @ D @ E)) & ((vf @ D @ F) = (vf @ A @ C)) & ((vangle @ B @ A @ C) = (vangle @ E @ D @ F)) & ~ (? [G:$i]: ((ron @ E @ G) & (rline @ G) & (ron @ D @ G) & (ron @ F @ G))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[102])). 18.17/7.04 thf(25,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((D = C) <= ((rcenter @ D @ A) & (rcenter @ C @ A) & (B = A) & (rcircle @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(75), 0), imp(cond(axiom(75), 0)))')). 18.17/7.04 thf(248,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((D = C) | ~ ((rcenter @ D @ A) & (rcenter @ C @ A) & (B = A) & (rcircle @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[25])). 18.17/7.04 thf(20,axiom,((! [A:$i,B:$i]: ((? [C:$i]: ((rpoint @ C) & (C != A) & (B != C))) <= (? [C:$i]: ((C = B) & (rpoint @ C)) & ? [C:$i]: ((rpoint @ C) & (C = A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(9), 0), imp(cond(axiom(9), 0)))')). 18.17/7.04 thf(220,plain,((! [A:$i,B:$i]: (? [C:$i]: ((rpoint @ C) & ~ (C = A) & ~ (B = C)) | ~ (? [C:$i]: ((C = B) & (rpoint @ C)) & ? [C:$i]: ((rpoint @ C) & (C = A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[20])). 18.17/7.04 thf(66,axiom,((rS @ vd1401 @ vd1409 @ vd1406)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(conjunct1(406), 1410, 0)')). 18.17/7.04 thf(534,plain,((rS @ vd1401 @ vd1409 @ vd1406)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[66])). 18.17/7.04 thf(99,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: ((? [G:$i]: ((E != G) & (ron @ G @ A) & (rpoint @ G) & (C != G))) <= ((ron @ E @ A) & (ron @ C @ A) & (E = F) & (rpoint @ F) & (C = D) & (rline @ B) & (B = A) & (rpoint @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(19), 0), imp(cond(axiom(19), 0)))')). 18.17/7.04 thf(825,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: (? [G:$i]: (~ (E = G) & (ron @ G @ A) & (rpoint @ G) & ~ (C = G)) | ~ ((ron @ E @ A) & (ron @ C @ A) & (E = F) & (rpoint @ F) & (C = D) & (rline @ B) & (B = A) & (rpoint @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[99])). 18.17/7.04 thf(76,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i,I:$i,J:$i,K:$i,L:$i,M:$i,N:$i,O:$i,P:$i,Q:$i,R:$i]: (((rline @ R) & ? [S:$i]: ((S = P) & (rpoint @ S)) & ? [S:$i]: ((S = L) & (rpoint @ S)) & ? [S:$i]: ((K = S) & (rpoint @ S)) & ? [S:$i]: ((S = G) & (rpoint @ S)) & (A != C) & (B != A) & ? [S:$i]: ((rpoint @ S) & (S = C)) & ? [S:$i]: ((S = A) & (rpoint @ S)) & ? [S:$i]: ((B = S) & (rpoint @ S)) & (C != B) & ? [S:$i]: ((D = S) & (rpoint @ S)) & ? [S:$i]: ((S = E) & (rpoint @ S)) & ? [S:$i]: ((rpoint @ S) & (S = F)) & ? [S:$i]: ((S = H) & (rpoint @ S)) & ? [S:$i]: ((rpoint @ S) & (I = S)) & ? [S:$i]: ((S = J) & (rpoint @ S)) & ? [S:$i]: ((rpoint @ S) & (M = S)) & ? [S:$i]: ((S = N) & (rpoint @ S)) & ? [S:$i]: ((O = S) & (rpoint @ S)) & (ron @ D @ Q) & (ron @ E @ Q) & ~ (ron @ F @ Q) & ! [S:$i,T:$i,U:$i]: ((((vangle @ N @ O @ P) = (vangle @ K @ L @ M)) & ((vf @ G @ H) = (vf @ I @ J))) <= (((vf @ S @ T) = (vf @ A @ B)) & ((vangle @ A @ C @ B) = (vangle @ S @ U @ T)) & ((vangle @ U @ T @ S) = (vangle @ C @ B @ A)) & (D = S) & (rpoint @ U) & (rpoint @ S) & (rpoint @ T) & ((vangle @ B @ A @ C) = (vangle @ T @ S @ U)) & ((vf @ B @ C) = (vf @ T @ U)) & ((vf @ A @ C) = (vf @ S @ U)) & (ron @ T @ Q) & ~ (rR @ D @ T @ E) & (rS @ U @ F @ Q))) & (R = Q)) => (((vangle @ K @ L @ M) = (vangle @ N @ O @ P)) & ((vf @ G @ H) = (vf @ I @ J)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(204), 0), imp(cond(axiom(204), 0)))')). 18.17/7.04 thf(598,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i,I:$i,J:$i,K:$i,L:$i,M:$i,N:$i,O:$i,P:$i,Q:$i,R:$i]: (((rline @ R) & ? [S:$i]: ((S = P) & (rpoint @ S)) & ? [S:$i]: ((S = L) & (rpoint @ S)) & ? [S:$i]: ((K = S) & (rpoint @ S)) & ? [S:$i]: ((S = G) & (rpoint @ S)) & ~ (A = C) & ~ (B = A) & ? [S:$i]: ((rpoint @ S) & (S = C)) & ? [S:$i]: ((S = A) & (rpoint @ S)) & ? [S:$i]: ((B = S) & (rpoint @ S)) & ~ (C = B) & ? [S:$i]: ((D = S) & (rpoint @ S)) & ? [S:$i]: ((S = E) & (rpoint @ S)) & ? [S:$i]: ((rpoint @ S) & (S = F)) & ? [S:$i]: ((S = H) & (rpoint @ S)) & ? [S:$i]: ((rpoint @ S) & (I = S)) & ? [S:$i]: ((S = J) & (rpoint @ S)) & ? [S:$i]: ((rpoint @ S) & (M = S)) & ? [S:$i]: ((S = N) & (rpoint @ S)) & ? [S:$i]: ((O = S) & (rpoint @ S)) & (ron @ D @ Q) & (ron @ E @ Q) & ~ (ron @ F @ Q) & ! [S:$i,T:$i,U:$i]: ((((vangle @ N @ O @ P) = (vangle @ K @ L @ M)) & ((vf @ G @ H) = (vf @ I @ J))) | ~ (((vf @ S @ T) = (vf @ A @ B)) & ((vangle @ A @ C @ B) = (vangle @ S @ U @ T)) & ((vangle @ U @ T @ S) = (vangle @ C @ B @ A)) & (D = S) & (rpoint @ U) & (rpoint @ S) & (rpoint @ T) & ((vangle @ B @ A @ C) = (vangle @ T @ S @ U)) & ((vf @ B @ C) = (vf @ T @ U)) & ((vf @ A @ C) = (vf @ S @ U)) & (ron @ T @ Q) & ~ (rR @ D @ T @ E) & (rS @ U @ F @ Q))) & (R = Q)) => (((vangle @ K @ L @ M) = (vangle @ N @ O @ P)) & ((vf @ G @ H) = (vf @ I @ J)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[76])). 18.17/7.04 thf(4,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((rR @ D @ A @ B) & (rR @ B @ A @ C) & ? [E:$i]: ((D = E) & (rpoint @ E)) & ? [E:$i]: ((A = E) & (rpoint @ E)) & ? [E:$i]: ((rpoint @ E) & (E = B)) & ? [E:$i]: ((C = E) & (rpoint @ E))) => (rR @ D @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(87), 0), imp(cond(axiom(87), 0)))')). 18.17/7.04 thf(137,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((rR @ D @ A @ B) & (rR @ B @ A @ C) & ? [E:$i]: ((D = E) & (rpoint @ E)) & ? [E:$i]: ((A = E) & (rpoint @ E)) & ? [E:$i]: ((rpoint @ E) & (E = B)) & ? [E:$i]: ((C = E) & (rpoint @ E))) => (rR @ D @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])). 18.17/7.04 thf(10,axiom,((vd684 = v0)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pred(axiom(137), 2)')). 18.17/7.04 thf(165,plain,((vd684 = v0)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[10])). 18.17/7.04 thf(26,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((~ (rR @ B @ C @ D)) <= (? [E:$i]: ((B = E) & (rpoint @ E)) & ? [E:$i]: ((rpoint @ E) & (A = E)) & ? [E:$i]: ((rpoint @ E) & (E = C)) & ? [E:$i]: ((rpoint @ E) & (E = D)) & (rR @ B @ A @ C) & (rR @ B @ A @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(93), 0), imp(cond(axiom(93), 0)))')). 18.17/7.04 thf(252,plain,((! [A:$i,B:$i,C:$i,D:$i]: (~ (rR @ B @ C @ D) | ~ (? [E:$i]: ((B = E) & (rpoint @ E)) & ? [E:$i]: ((rpoint @ E) & (A = E)) & ? [E:$i]: ((rpoint @ E) & (E = C)) & ? [E:$i]: ((rpoint @ E) & (E = D)) & (rR @ B @ A @ C) & (rR @ B @ A @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[26])). 18.17/7.04 thf(103,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((? [E:$i]: ((ron @ E @ C) & (rpoint @ E) & (ron @ E @ A))) <= ((D = C) & (rline @ B) & (B = A) & (rline @ D) & (rintersect @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(55), 0), imp(cond(axiom(55), 0)))')). 18.17/7.04 thf(879,plain,((! [A:$i,B:$i,C:$i,D:$i]: (? [E:$i]: ((ron @ E @ C) & (rpoint @ E) & (ron @ E @ A)) | ~ ((D = C) & (rline @ B) & (B = A) & (rline @ D) & (rintersect @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[103])). 18.17/7.04 thf(101,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((ron @ C @ A) & ? [F:$i]: ((rpoint @ F) & (E = F)) & ? [F:$i]: ((C = F) & (rpoint @ F)) & (rline @ B) & (A = B) & ? [F:$i]: ((D = F) & (rpoint @ F)) & (ron @ D @ A) & (ron @ E @ A)) => (? [F:$i]: ((F != D) & (F != C) & (rpoint @ F) & (ron @ F @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(21), 0), imp(cond(axiom(21), 0)))')). 18.17/7.04 thf(852,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((ron @ C @ A) & ? [F:$i]: ((rpoint @ F) & (E = F)) & ? [F:$i]: ((C = F) & (rpoint @ F)) & (rline @ B) & (A = B) & ? [F:$i]: ((D = F) & (rpoint @ F)) & (ron @ D @ A) & (ron @ E @ A)) => (? [F:$i]: (~ (F = D) & ~ (F = C) & (rpoint @ F) & (ron @ F @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[101])). 18.17/7.04 thf(79,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: (((F = E) & (rR @ D @ C @ E) & (rpoint @ F) & (ron @ C @ A) & ? [G:$i]: ((rpoint @ G) & (G = D)) & (rline @ B) & (B = A) & ? [G:$i]: ((rpoint @ G) & (G = C)) & (ron @ D @ A)) => (? [G:$i]: ((E != G) & (rpoint @ G) & (rR @ D @ C @ G)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(31), 0), imp(cond(axiom(31), 0)))')). 18.17/7.04 thf(665,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: (((F = E) & (rR @ D @ C @ E) & (rpoint @ F) & (ron @ C @ A) & ? [G:$i]: ((rpoint @ G) & (G = D)) & (rline @ B) & (B = A) & ? [G:$i]: ((rpoint @ G) & (G = C)) & (ron @ D @ A)) => (? [G:$i]: (~ (E = G) & (rpoint @ G) & (rR @ D @ C @ G)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[79])). 18.17/7.04 thf(86,axiom,((! [A:$i,B:$i]: ((? [C:$i,D:$i]: ((ron @ D @ B) & (rpoint @ D) & (ron @ C @ B) & (ron @ C @ A) & (rpoint @ C) & (ron @ D @ A) & (C != D))) <= ((rintersect @ A @ B) & ? [C:$i]: ((C = A) & (rcircle @ C)) & ? [C:$i]: ((C = B) & (rcircle @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(67), 0), imp(cond(axiom(67), 0)))')). 18.17/7.04 thf(710,plain,((! [A:$i,B:$i]: (? [C:$i,D:$i]: ((ron @ D @ B) & (rpoint @ D) & (ron @ C @ B) & (ron @ C @ A) & (rpoint @ C) & (ron @ D @ A) & ~ (C = D)) | ~ ((rintersect @ A @ B) & ? [C:$i]: ((C = A) & (rcircle @ C)) & ? [C:$i]: ((C = B) & (rcircle @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[86])). 18.17/7.04 thf(39,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((rreal @ D) & (rreal @ B) & (A = B) & (C = D)) => (? [E:$i]: ((rreal @ E) & ((vplus @ A @ C) = E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(139), 0), imp(cond(axiom(139), 0)))')). 18.17/7.04 thf(324,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((rreal @ D) & (rreal @ B) & (A = B) & (C = D)) => (? [E:$i]: ((rreal @ E) & ((vplus @ A @ C) = E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[39])). 18.17/7.04 thf(120,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i]: ((? [I:$i]: ((rR @ I @ E @ G) & (rpoint @ I) & (ron @ I @ C) & (ron @ I @ A))) <= (~ (ron @ G @ A) & (H = G) & (rpoint @ H) & (ron @ E @ C) & (rinside @ E @ A) & (E = F) & (rpoint @ F) & (D = C) & (rline @ D) & (rcircle @ B) & (B = A) & ~ (rinside @ G @ A) & (ron @ G @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(61), 0), imp(cond(axiom(61), 0)))')). 18.17/7.04 thf(1012,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i]: (? [I:$i]: ((rR @ I @ E @ G) & (rpoint @ I) & (ron @ I @ C) & (ron @ I @ A)) | ~ (~ (ron @ G @ A) & (H = G) & (rpoint @ H) & (ron @ E @ C) & (rinside @ E @ A) & (E = F) & (rpoint @ F) & (D = C) & (rline @ D) & (rcircle @ B) & (B = A) & ~ (rinside @ G @ A) & (ron @ G @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[120])). 18.17/7.04 thf(38,axiom,((! [A:$i,B:$i]: ((? [C:$i]: ((C = (vf @ A @ B)) & (rreal @ C))) <= (? [C:$i]: ((C = A) & (rpoint @ C)) & ? [C:$i]: ((B = C) & (rpoint @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(160), 0), imp(cond(axiom(160), 0)))')). 18.17/7.04 thf(317,plain,((! [A:$i,B:$i]: (? [C:$i]: ((C = (vf @ A @ B)) & (rreal @ C)) | ~ (? [C:$i]: ((C = A) & (rpoint @ C)) & ? [C:$i]: ((B = C) & (rpoint @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[38])). 18.17/7.04 thf(5,axiom,((! [A:$i,B:$i,C:$i]: ((? [D:$i]: ((D = B) & (rpoint @ D)) & ? [D:$i]: ((A = D) & (rpoint @ D)) & ? [D:$i]: ((rpoint @ D) & (D = C)) & (A != B) & (C != A)) => ((vangle @ A @ B @ C) = (vangle @ C @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(168), 0), imp(cond(axiom(168), 0)))')). 18.17/7.04 thf(141,plain,((! [A:$i,B:$i,C:$i]: ((? [D:$i]: ((D = B) & (rpoint @ D)) & ? [D:$i]: ((A = D) & (rpoint @ D)) & ? [D:$i]: ((rpoint @ D) & (D = C)) & ~ (A = B) & ~ (C = A)) => ((vangle @ A @ B @ C) = (vangle @ C @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])). 18.17/7.04 thf(61,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((rS @ B @ A @ C) <= ((rS @ A @ B @ C) & (C = D) & (rline @ D) & ? [E:$i]: ((rpoint @ E) & (E = B)) & ? [E:$i]: ((E = A) & (rpoint @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(97), 0), imp(cond(axiom(97), 0)))')). 18.17/7.04 thf(499,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((rS @ B @ A @ C) | ~ ((rS @ A @ B @ C) & (C = D) & (rline @ D) & ? [E:$i]: ((rpoint @ E) & (E = B)) & ? [E:$i]: ((E = A) & (rpoint @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[61])). 18.17/7.04 thf(115,axiom,((! [A:$i]: (((ron @ vd1401 @ A) & (rline @ A) & (ron @ vd1399 @ A)) => (A = vskolem1416)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','replace(qu(theu(the(408), 1), imp(the(408))))')). 18.17/7.04 thf(989,plain,((! [A:$i]: (((ron @ vd1401 @ A) & (rline @ A) & (ron @ vd1399 @ A)) => (A = vskolem1416)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[115])). 18.17/7.04 thf(27,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((? [E:$i]: ((C != E) & (B != E) & (E != A) & (rpoint @ E) & (E != D))) <= (? [E:$i]: ((rpoint @ E) & (E = D)) & ? [E:$i]: ((rpoint @ E) & (E = B)) & ? [E:$i]: ((rpoint @ E) & (A = E)) & ? [E:$i]: ((C = E) & (rpoint @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(13), 0), imp(cond(axiom(13), 0)))')). 18.17/7.04 thf(256,plain,((! [A:$i,B:$i,C:$i,D:$i]: (? [E:$i]: (~ (C = E) & ~ (B = E) & ~ (E = A) & (rpoint @ E) & ~ (E = D)) | ~ (? [E:$i]: ((rpoint @ E) & (E = D)) & ? [E:$i]: ((rpoint @ E) & (E = B)) & ? [E:$i]: ((rpoint @ E) & (A = E)) & ? [E:$i]: ((C = E) & (rpoint @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[27])). 18.17/7.04 thf(41,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((~ (rless @ C @ A) | (C = A)) <= ((rless @ A @ C) & (B = A) & (rreal @ B) & (rreal @ D) & (C = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(147), 0), imp(cond(axiom(147), 0)))')). 18.17/7.04 thf(339,plain,((! [A:$i,B:$i,C:$i,D:$i]: (~ (rless @ C @ A) | (C = A) | ~ ((rless @ A @ C) & (B = A) & (rreal @ B) & (rreal @ D) & (C = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[41])). 18.17/7.04 thf(68,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((ron @ D @ A) & (ron @ C @ A) & ? [E:$i]: ((rpoint @ E) & (D = E)) & (B = A) & (rline @ B) & ? [E:$i]: ((E = C) & (rpoint @ E)) & (D != C)) => (? [E:$i]: ((rpoint @ E) & (rR @ E @ C @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(23), 0), imp(cond(axiom(23), 0)))')). 18.17/7.04 thf(537,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((ron @ D @ A) & (ron @ C @ A) & ? [E:$i]: ((rpoint @ E) & (D = E)) & (B = A) & (rline @ B) & ? [E:$i]: ((E = C) & (rpoint @ E)) & ~ (D = C)) => (? [E:$i]: ((rpoint @ E) & (rR @ E @ C @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[68])). 18.17/7.04 thf(60,axiom,((! [A:$i,B:$i]: ((? [C:$i]: ((ron @ A @ C) & (rline @ C) & (ron @ B @ C))) <= (? [C:$i]: ((B = C) & (rpoint @ C)) & ? [C:$i]: ((A = C) & (rpoint @ C)) & (A != B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(51), 0), imp(cond(axiom(51), 0)))')). 18.17/7.04 thf(489,plain,((! [A:$i,B:$i]: (? [C:$i]: ((ron @ A @ C) & (rline @ C) & (ron @ B @ C)) | ~ (? [C:$i]: ((B = C) & (rpoint @ C)) & ? [C:$i]: ((A = C) & (rpoint @ C)) & ~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[60])). 18.17/7.04 thf(85,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((ron @ B @ D) & (ron @ B @ C) & ? [E:$i]: ((rline @ E) & (E = D)) & (B != A) & ? [E:$i]: ((B = E) & (rpoint @ E)) & ? [E:$i]: ((rpoint @ E) & (E = A)) & ? [E:$i]: ((rline @ E) & (C = E)) & (ron @ A @ C) & (ron @ A @ D)) => (C = D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(73), 0), imp(cond(axiom(73), 0)))')). 18.17/7.04 thf(706,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((ron @ B @ D) & (ron @ B @ C) & ? [E:$i]: ((rline @ E) & (E = D)) & ~ (B = A) & ? [E:$i]: ((B = E) & (rpoint @ E)) & ? [E:$i]: ((rpoint @ E) & (E = A)) & ? [E:$i]: ((rline @ E) & (C = E)) & (ron @ A @ C) & (ron @ A @ D)) => (C = D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[85])). 18.17/7.04 thf(117,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((C = D) & ~ (ron @ C @ A) & (B = A) & (rline @ B) & (rpoint @ D)) => (? [E:$i]: ((rpoint @ E) & ~ (rS @ E @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(39), 0), imp(cond(axiom(39), 0)))')). 18.17/7.04 thf(997,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((C = D) & ~ (ron @ C @ A) & (B = A) & (rline @ B) & (rpoint @ D)) => (? [E:$i]: ((rpoint @ E) & ~ (rS @ E @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[117])). 18.17/7.04 thf(84,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((~ (ron @ A @ C)) <= ((C = D) & (rline @ D) & ? [E:$i]: ((rpoint @ E) & (B = E)) & ? [E:$i]: ((rpoint @ E) & (E = A)) & (rS @ A @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(99), 0), imp(cond(axiom(99), 0)))')). 18.17/7.04 thf(701,plain,((! [A:$i,B:$i,C:$i,D:$i]: (~ (ron @ A @ C) | ~ ((C = D) & (rline @ D) & ? [E:$i]: ((rpoint @ E) & (B = E)) & ? [E:$i]: ((rpoint @ E) & (E = A)) & (rS @ A @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[84])). 18.17/7.04 thf(24,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((rR @ B @ A @ D) <= ((rR @ B @ A @ C) & ? [E:$i]: ((A = E) & (rpoint @ E)) & ? [E:$i]: ((rpoint @ E) & (E = B)) & ? [E:$i]: ((C = E) & (rpoint @ E)) & ? [E:$i]: ((E = D) & (rpoint @ E)) & (rR @ C @ B @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(89), 0), imp(cond(axiom(89), 0)))')). 18.17/7.04 thf(244,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((rR @ B @ A @ D) | ~ ((rR @ B @ A @ C) & ? [E:$i]: ((A = E) & (rpoint @ E)) & ? [E:$i]: ((rpoint @ E) & (E = B)) & ? [E:$i]: ((C = E) & (rpoint @ E)) & ? [E:$i]: ((E = D) & (rpoint @ E)) & (rR @ C @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[24])). 18.17/7.04 thf(94,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((ron @ D @ A) & (ron @ C @ A) & ? [F:$i]: ((rpoint @ F) & (F = E)) & ? [F:$i]: ((C = F) & (rpoint @ F)) & (B = A) & (rline @ B) & ? [F:$i]: ((rpoint @ F) & (F = D)) & (rR @ E @ C @ D)) => (? [F:$i]: ((rR @ F @ C @ D) & (rpoint @ F) & (F != E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(25), 0), imp(cond(axiom(25), 0)))')). 18.17/7.04 thf(792,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((ron @ D @ A) & (ron @ C @ A) & ? [F:$i]: ((rpoint @ F) & (F = E)) & ? [F:$i]: ((C = F) & (rpoint @ F)) & (B = A) & (rline @ B) & ? [F:$i]: ((rpoint @ F) & (F = D)) & (rR @ E @ C @ D)) => (? [F:$i]: ((rR @ F @ C @ D) & (rpoint @ F) & ~ (F = E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[94])). 18.17/7.04 thf(108,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: (((rR @ C @ A @ B) & (rline @ F) & ? [G:$i]: ((rpoint @ G) & (A = G)) & ? [G:$i]: ((G = B) & (rpoint @ G)) & ? [G:$i]: ((rpoint @ G) & (G = C)) & ? [G:$i]: ((D = G) & (rpoint @ G)) & (E = F) & ~ (ron @ D @ E)) => (((vangle @ D @ C @ B) = (vangle @ A @ C @ D)) <=> (vperp = (vangle @ A @ C @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(192), 0), imp(cond(axiom(192), 0)))')). 18.17/7.04 thf(921,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: (((rR @ C @ A @ B) & (rline @ F) & ? [G:$i]: ((rpoint @ G) & (A = G)) & ? [G:$i]: ((G = B) & (rpoint @ G)) & ? [G:$i]: ((rpoint @ G) & (G = C)) & ? [G:$i]: ((D = G) & (rpoint @ G)) & (E = F) & ~ (ron @ D @ E)) => ((((vangle @ D @ C @ B) = (vangle @ A @ C @ D)) => (vperp = (vangle @ A @ C @ D))) & ((vperp = (vangle @ A @ C @ D)) => ((vangle @ D @ C @ B) = (vangle @ A @ C @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[108])). 18.17/7.04 thf(121,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i]: ((rinside @ C @ F) <= ((rR @ C @ A @ B) & (F = G) & (rcircle @ G) & (E = D) & ? [H:$i]: ((rpoint @ H) & (H = B)) & ? [H:$i]: ((A = H) & (rpoint @ H)) & ? [H:$i]: ((C = H) & (rpoint @ H)) & (rline @ E) & ((ron @ A @ F) | (rinside @ A @ F)) & ((ron @ B @ F) | (rinside @ B @ F)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(121), 0), imp(cond(axiom(121), 0)))')). 18.17/7.04 thf(1026,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i]: ((rinside @ C @ F) | ~ ((rR @ C @ A @ B) & (F = G) & (rcircle @ G) & (E = D) & ? [H:$i]: ((rpoint @ H) & (H = B)) & ? [H:$i]: ((A = H) & (rpoint @ H)) & ? [H:$i]: ((C = H) & (rpoint @ H)) & (rline @ E) & ((ron @ A @ F) | (rinside @ A @ F)) & ((ron @ B @ F) | (rinside @ B @ F)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[121])). 18.17/7.04 thf(33,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: (((rreal @ F) & (C = D) & (rreal @ D) & (rreal @ B) & (A = B) & (E = F) & ((vplus @ C @ E) = (vplus @ A @ E))) => (C = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(156, 0), 0)')). 18.17/7.04 thf(298,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: (((rreal @ F) & (C = D) & (rreal @ D) & (rreal @ B) & (A = B) & (E = F) & ((vplus @ C @ E) = (vplus @ A @ E))) => (C = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[33])). 18.17/7.04 thf(9,axiom,((! [A:$i,B:$i]: ((? [C:$i]: ((rpoint @ C) & (A = C)) & ? [C:$i]: ((C = B) & (rpoint @ C)) & (A != B)) => (! [C:$i,D:$i]: ((rpoint @ (vskolem1078 @ C @ D @ A @ B)) <= ((rpoint @ D) & (A != C) & (C != B) & (C = D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(219), 0), 1)')). 18.17/7.04 thf(161,plain,((! [A:$i,B:$i]: ((? [C:$i]: ((rpoint @ C) & (A = C)) & ? [C:$i]: ((C = B) & (rpoint @ C)) & ~ (A = B)) => (! [C:$i,D:$i]: ((rpoint @ (vskolem1078 @ C @ D @ A @ B)) | ~ ((rpoint @ D) & ~ (A = C) & ~ (C = B) & (C = D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[9])). 18.17/7.04 thf(7,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i]: ((rR @ (vskolem1120 @ A @ B @ C @ D @ E @ F @ G @ H) @ A @ C) <= ((G != E) & (rpoint @ H) & (rpoint @ F) & (C = D) & (rpoint @ D) & (rpoint @ B) & (B = A) & (F = E) & (H = G) & (A != C) & (rless @ (vf @ E @ G) @ (vf @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(238), 0), 1)')). 18.17/7.04 thf(149,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i]: ((rR @ (vskolem1120 @ A @ B @ C @ D @ E @ F @ G @ H) @ A @ C) | ~ (~ (G = E) & (rpoint @ H) & (rpoint @ F) & (C = D) & (rpoint @ D) & (rpoint @ B) & (B = A) & (F = E) & (H = G) & ~ (A = C) & (rless @ (vf @ E @ G) @ (vf @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])). 18.17/7.04 thf(75,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i]: (((G != E) & (ron @ G @ C) & (rpoint @ F) & (C = D) & (rline @ D) & (rcircle @ B) & (A = B) & (E = F) & (rinside @ E @ A) & (ron @ E @ C) & (rpoint @ H) & (G = H)) => (? [I:$i]: ((rR @ E @ I @ G) & (ron @ I @ C) & (rpoint @ I) & (ron @ I @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(63), 0), imp(cond(axiom(63), 0)))')). 18.17/7.04 thf(584,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i]: ((~ (G = E) & (ron @ G @ C) & (rpoint @ F) & (C = D) & (rline @ D) & (rcircle @ B) & (A = B) & (E = F) & (rinside @ E @ A) & (ron @ E @ C) & (rpoint @ H) & (G = H)) => (? [I:$i]: ((rR @ E @ I @ G) & (ron @ I @ C) & (rpoint @ I) & (ron @ I @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[75])). 18.17/7.04 thf(87,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: (((A = B) & (rpoint @ B) & (rcenter @ C @ D) & (rpoint @ F) & (F = E) & (ron @ E @ D)) => (((vf @ C @ A) = (vf @ C @ E)) <=> (ron @ A @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(184), 0), imp(cond(axiom(184), 0)))')). 18.17/7.04 thf(732,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: (((A = B) & (rpoint @ B) & (rcenter @ C @ D) & (rpoint @ F) & (F = E) & (ron @ E @ D)) => ((((vf @ C @ A) = (vf @ C @ E)) => (ron @ A @ D)) & ((ron @ A @ D) => ((vf @ C @ A) = (vf @ C @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[87])). 18.17/7.04 thf(106,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i]: ((? [H:$i]: ((rS @ H @ G @ C) & (rpoint @ H) & (ron @ H @ A) & (ron @ H @ B))) <= (~ (ron @ G @ C) & (ron @ E @ C) & (rcenter @ F @ B) & (rcenter @ E @ A) & (rintersect @ A @ B) & ? [H:$i]: ((B = H) & (rcircle @ H)) & ? [H:$i]: ((rcircle @ H) & (A = H)) & (rline @ D) & (C = D) & (ron @ F @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(69), 0), imp(cond(axiom(69), 0)))')). 18.17/7.04 thf(900,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i]: (? [H:$i]: ((rS @ H @ G @ C) & (rpoint @ H) & (ron @ H @ A) & (ron @ H @ B)) | ~ (~ (ron @ G @ C) & (ron @ E @ C) & (rcenter @ F @ B) & (rcenter @ E @ A) & (rintersect @ A @ B) & ? [H:$i]: ((B = H) & (rcircle @ H)) & ? [H:$i]: ((rcircle @ H) & (A = H)) & (rline @ D) & (C = D) & (ron @ F @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[106])). 18.17/7.04 thf(93,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((~ (ron @ B @ D) & ~ (ron @ B @ D)) <= ((rR @ C @ A @ B) & ? [F:$i]: ((rpoint @ F) & (C = F)) & ? [F:$i]: ((rpoint @ F) & (B = F)) & ? [F:$i]: ((A = F) & (rpoint @ F)) & (rcircle @ E) & (D = E) & ((rinside @ A @ D) | (ron @ A @ D)) & ~ (rinside @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(123), 0), imp(cond(axiom(123), 0)))')). 18.17/7.04 thf(784,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (~ (ron @ B @ D) | ~ ((rR @ C @ A @ B) & ? [F:$i]: ((rpoint @ F) & (C = F)) & ? [F:$i]: ((rpoint @ F) & (B = F)) & ? [F:$i]: ((A = F) & (rpoint @ F)) & (rcircle @ E) & (D = E) & ((rinside @ A @ D) | (ron @ A @ D)) & ~ (rinside @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[93])). 18.17/7.04 thf(21,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: ((rless @ (vplus @ A @ E) @ (vplus @ C @ E)) <= ((rless @ A @ C) & (E = F) & (rreal @ F) & (rreal @ B) & (B = A) & (rreal @ D) & (D = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(153), 0), imp(cond(axiom(153), 0)))')). 18.17/7.04 thf(230,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: ((rless @ (vplus @ A @ E) @ (vplus @ C @ E)) | ~ ((rless @ A @ C) & (E = F) & (rreal @ F) & (rreal @ B) & (B = A) & (rreal @ D) & (D = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[21])). 18.17/7.04 thf(72,axiom,(((ron @ vd1409 @ vd1419) & (ron @ vd1401 @ vd1419) & (rline @ vd1419))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','and(pred(s2(plural(the(409))), 0), and(pred(s1(plural(the(409))), 0), pred(the(409), 0)))')). 18.17/7.04 thf(567,plain,(((ron @ vd1409 @ vd1419) & (ron @ vd1401 @ vd1419) & (rline @ vd1419))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[72])). 18.17/7.04 thf(34,axiom,((! [A:$i,B:$i,C:$i]: ((? [D:$i]: ((A = D) & (rpoint @ D)) & ? [D:$i]: ((rpoint @ D) & (B = D)) & ? [D:$i]: ((D = C) & (rpoint @ D))) => (? [D:$i]: ((rreal @ D) & (D = (vg @ A @ B @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(198), 0), imp(cond(axiom(198), 0)))')). 18.17/7.04 thf(303,plain,((! [A:$i,B:$i,C:$i]: ((? [D:$i]: ((A = D) & (rpoint @ D)) & ? [D:$i]: ((rpoint @ D) & (B = D)) & ? [D:$i]: ((D = C) & (rpoint @ D))) => (? [D:$i]: ((rreal @ D) & (D = (vg @ A @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[34])). 18.17/7.04 thf(104,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((rS @ A @ A @ C) <= ((rline @ D) & (rpoint @ B) & (A = B) & (D = C) & ~ (ron @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(95), 0), imp(cond(axiom(95), 0)))')). 18.17/7.04 thf(890,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((rS @ A @ A @ C) | ~ ((rline @ D) & (rpoint @ B) & (A = B) & (D = C) & ~ (ron @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[104])). 18.17/7.04 thf(67,axiom,(((vf @ vd1400 @ vd1401) = (vf @ vd1400 @ vd1409))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(conjunct1(conjunct2(conjunct2(406))), 1412, 0)')). 18.17/7.04 thf(535,plain,(((vf @ vd1400 @ vd1401) = (vf @ vd1400 @ vd1409))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[67])). 18.17/7.04 thf(105,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i]: ((rR @ A @ B @ C) <= ((C != B) & (rinside @ A @ F) & (ron @ B @ D) & (G = F) & (rcircle @ G) & (E = D) & (rline @ E) & ? [H:$i]: ((rpoint @ H) & (H = C)) & ? [H:$i]: ((H = A) & (rpoint @ H)) & ? [H:$i]: ((B = H) & (rpoint @ H)) & (ron @ A @ D) & (ron @ C @ D) & (ron @ B @ F) & (ron @ C @ F))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(119), 0), imp(cond(axiom(119), 0)))')). 18.17/7.04 thf(895,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i]: ((rR @ A @ B @ C) | ~ (~ (C = B) & (rinside @ A @ F) & (ron @ B @ D) & (G = F) & (rcircle @ G) & (E = D) & (rline @ E) & ? [H:$i]: ((rpoint @ H) & (H = C)) & ? [H:$i]: ((H = A) & (rpoint @ H)) & ? [H:$i]: ((B = H) & (rpoint @ H)) & (ron @ A @ D) & (ron @ C @ D) & (ron @ B @ F) & (ron @ C @ F))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[105])). 18.17/7.04 thf(1,conjecture,((! [A:$i]: (((ron @ vd1409 @ A) & (ron @ vd1401 @ A) & (rline @ A)) => (A = vd1419)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(theu(the(409), 1), imp(the(409)))')). 18.17/7.04 thf(2,negated_conjecture,((~ (! [A:$i]: (((ron @ vd1409 @ A) & (ron @ vd1401 @ A) & (rline @ A)) => (A = vd1419))))),inference(neg_conjecture,[status(cth)],[1])). 18.17/7.04 thf(130,plain,((~ (! [A:$i]: (((ron @ vd1409 @ A) & (ron @ vd1401 @ A) & (rline @ A)) => (A = vd1419))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])). 18.17/7.04 thf(49,axiom,((! [A:$i,B:$i]: (((B = A) & (rreal @ B)) => (~ (rless @ A @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(149), 0), imp(cond(axiom(149), 0)))')). 18.17/7.04 thf(399,plain,((! [A:$i,B:$i]: (((B = A) & (rreal @ B)) => (~ (rless @ A @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[49])). 18.17/7.04 thf(55,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: (((D = C) & (ron @ B @ E) & (ron @ A @ E) & ~ (rS @ A @ B @ C) & (rline @ D) & ? [G:$i]: ((rpoint @ G) & (A = G)) & ? [G:$i]: ((rpoint @ G) & (B = G)) & (rline @ F) & (E = F)) => (rintersect @ C @ E)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(127), 0), imp(cond(axiom(127), 0)))')). 18.17/7.04 thf(455,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: (((D = C) & (ron @ B @ E) & (ron @ A @ E) & ~ (rS @ A @ B @ C) & (rline @ D) & ? [G:$i]: ((rpoint @ G) & (A = G)) & ? [G:$i]: ((rpoint @ G) & (B = G)) & (rline @ F) & (E = F)) => (rintersect @ C @ E)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[55])). 18.17/7.04 thf(63,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i]: ((rS @ E @ F @ C) <= (~ (ron @ G @ B) & (ron @ F @ B) & (ron @ D @ B) & (ron @ D @ A) & ? [H:$i]: ((G = H) & (rpoint @ H)) & ? [H:$i]: ((rline @ H) & (C = H)) & ? [H:$i]: ((H = A) & (rline @ H)) & ? [H:$i]: ((B = H) & (rline @ H)) & ? [H:$i]: ((H = D) & (rpoint @ H)) & ? [H:$i]: ((rpoint @ H) & (H = E)) & ? [H:$i]: ((rpoint @ H) & (H = F)) & (ron @ D @ C) & (ron @ E @ A) & (ron @ G @ C) & (rS @ F @ G @ A) & ~ (rS @ E @ G @ B) & (E != D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(115), 0), imp(cond(axiom(115), 0)))')). 18.17/7.04 thf(505,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i]: ((rS @ E @ F @ C) | ~ (~ (ron @ G @ B) & (ron @ F @ B) & (ron @ D @ B) & (ron @ D @ A) & ? [H:$i]: ((G = H) & (rpoint @ H)) & ? [H:$i]: ((rline @ H) & (C = H)) & ? [H:$i]: ((H = A) & (rline @ H)) & ? [H:$i]: ((B = H) & (rline @ H)) & ? [H:$i]: ((H = D) & (rpoint @ H)) & ? [H:$i]: ((rpoint @ H) & (H = E)) & ? [H:$i]: ((rpoint @ H) & (H = F)) & (ron @ D @ C) & (ron @ E @ A) & (ron @ G @ C) & (rS @ F @ G @ A) & ~ (rS @ E @ G @ B) & ~ (E = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[63])). 18.17/7.04 thf(11,axiom,((! [A:$i,B:$i]: ((? [C:$i]: ((rpoint @ C) & (C != A))) <= ((B = A) & (rpoint @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(7), 0), imp(cond(axiom(7), 0)))')). 18.17/7.04 thf(167,plain,((! [A:$i,B:$i]: (? [C:$i]: ((rpoint @ C) & ~ (C = A)) | ~ ((B = A) & (rpoint @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[11])). 18.17/7.04 thf(57,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((C != D) & (B = A) & (rline @ B) & ? [E:$i]: ((C = E) & (rpoint @ E)) & ? [E:$i]: ((E = D) & (rpoint @ E)) & (ron @ C @ A) & (ron @ D @ A)) => (? [E:$i]: ((rR @ D @ C @ E) & (rpoint @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(29), 0), imp(cond(axiom(29), 0)))')). 18.17/7.04 thf(473,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((~ (C = D) & (B = A) & (rline @ B) & ? [E:$i]: ((C = E) & (rpoint @ E)) & ? [E:$i]: ((E = D) & (rpoint @ E)) & (ron @ C @ A) & (ron @ D @ A)) => (? [E:$i]: ((rR @ D @ C @ E) & (rpoint @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[57])). 18.17/7.04 thf(126,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((? [E:$i]: ((ron @ E @ A) & (rpoint @ E) & (ron @ E @ C))) <= ((C = D) & (rcircle @ D) & (B = A) & (rcircle @ B) & (rintersect @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(65), 0), imp(cond(axiom(65), 0)))')). 18.17/7.04 thf(1076,plain,((! [A:$i,B:$i,C:$i,D:$i]: (? [E:$i]: ((ron @ E @ A) & (rpoint @ E) & (ron @ E @ C)) | ~ ((C = D) & (rcircle @ D) & (B = A) & (rcircle @ B) & (rintersect @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[126])). 18.17/7.04 thf(77,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((rinside @ A @ D) <=> (rless @ (vf @ C @ A) @ (vf @ C @ B))) <= ((ron @ B @ D) & (rcenter @ C @ D) & ? [E:$i]: ((rpoint @ E) & (E = A)) & ? [E:$i]: ((rpoint @ E) & (E = B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(186), 0), imp(cond(axiom(186), 0)))')). 18.17/7.04 thf(648,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((((rinside @ A @ D) => (rless @ (vf @ C @ A) @ (vf @ C @ B))) & ((rless @ (vf @ C @ A) @ (vf @ C @ B)) => (rinside @ A @ D))) | ~ ((ron @ B @ D) & (rcenter @ C @ D) & ? [E:$i]: ((rpoint @ E) & (E = A)) & ? [E:$i]: ((rpoint @ E) & (E = B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[77])). 18.17/7.04 thf(90,axiom,((! [A:$i,B:$i]: (((A = B) & (rcircle @ B)) => (? [C:$i]: ((rpoint @ C) & ~ (rinside @ C @ A) & ~ (ron @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(49), 0), imp(cond(axiom(49), 0)))')). 18.17/7.04 thf(749,plain,((! [A:$i,B:$i]: (((A = B) & (rcircle @ B)) => (? [C:$i]: ((rpoint @ C) & ~ (rinside @ C @ A) & ~ (ron @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[90])). 18.17/7.04 thf(71,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: (((D = C) & (rS @ E @ C @ A) & ~ (ron @ C @ A) & (B = A) & (rline @ B) & (rpoint @ D) & (rpoint @ F) & (E = F)) => (? [G:$i]: ((C != G) & (rS @ G @ C @ A) & (rpoint @ G) & (E != G)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(35), 0), imp(cond(axiom(35), 0)))')). 18.17/7.04 thf(553,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: (((D = C) & (rS @ E @ C @ A) & ~ (ron @ C @ A) & (B = A) & (rline @ B) & (rpoint @ D) & (rpoint @ F) & (E = F)) => (? [G:$i]: (~ (C = G) & (rS @ G @ C @ A) & (rpoint @ G) & ~ (E = G)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[71])). 18.17/7.04 thf(114,axiom,(((vd1406 = vd1407) & (ron @ vd1400 @ vd1406) & (rline @ vd1407) & (vd1399 != vd1401) & ? [A:$i]: ((vd1401 = A) & (rpoint @ A)) & ? [A:$i]: ((rpoint @ A) & (A = vd1399)) & ? [A:$i]: ((A = vd1400) & (rpoint @ A)) & (vd1399 != vd1400) & (vd1401 != vd1400) & (ron @ vd1399 @ vd1406))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','and(pred(conjunct2(405), 5), and(pred(s2(plural(conjunct2(405))), 0), and(pred(s1(plural(conjunct2(405))), 0), and(pred(conjunct2(405), 1), and(pred(conjunct1(405), 9), and(pred(conjunct1(405), 8), and(pred(conjunct1(405), 7), and(qe(s3(plural(405))), and(qe(s2(plural(405))), qe(s1(plural(405))))))))))))')). 18.17/7.04 thf(968,plain,(((vd1406 = vd1407) & (ron @ vd1400 @ vd1406) & (rline @ vd1407) & ~ (vd1399 = vd1401) & ? [A:$i]: ((vd1401 = A) & (rpoint @ A)) & ? [A:$i]: ((rpoint @ A) & (A = vd1399)) & ? [A:$i]: ((A = vd1400) & (rpoint @ A)) & ~ (vd1399 = vd1400) & ~ (vd1401 = vd1400) & (ron @ vd1399 @ vd1406))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[114])). 18.17/7.04 thf(98,axiom,(((vf @ vd1399 @ vd1401) = (vf @ vd1399 @ vd1409))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(conjunct1(conjunct2(406)), 1411, 0)')). 18.17/7.04 thf(823,plain,(((vf @ vd1399 @ vd1401) = (vf @ vd1399 @ vd1409))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[98])). 18.17/7.04 thf(6,axiom,((! [A:$i,B:$i]: ((? [C:$i]: ((B = C) & (rpoint @ C)) & ? [C:$i]: ((rpoint @ C) & (C = A))) => (rleq @ v0 @ (vf @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(164), 0), imp(cond(axiom(164), 0)))')). 18.17/7.04 thf(145,plain,((! [A:$i,B:$i]: ((? [C:$i]: ((B = C) & (rpoint @ C)) & ? [C:$i]: ((rpoint @ C) & (C = A))) => (rleq @ v0 @ (vf @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])). 18.17/7.04 thf(30,axiom,((! [A:$i,B:$i]: ((rcenter @ A @ B) => (? [C:$i,D:$i]: ((rcircle @ D) & (C = A) & (rpoint @ C) & (D = B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(1), 0), imp(cond(axiom(1), 0)))')). 18.17/7.04 thf(282,plain,((! [A:$i,B:$i]: ((rcenter @ A @ B) => (? [C:$i,D:$i]: ((rcircle @ D) & (C = A) & (rpoint @ C) & (D = B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[30])). 18.17/7.04 thf(51,axiom,((! [A:$i,B:$i,C:$i]: ((? [D:$i]: ((C = D) & (rpoint @ D)) & ? [D:$i]: ((rpoint @ D) & (B = D)) & ? [D:$i]: ((A = D) & (rpoint @ D))) => (? [D:$i]: ((D != A) & (rpoint @ D) & (B != D) & (D != C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(11), 0), imp(cond(axiom(11), 0)))')). 18.17/7.04 thf(409,plain,((! [A:$i,B:$i,C:$i]: ((? [D:$i]: ((C = D) & (rpoint @ D)) & ? [D:$i]: ((rpoint @ D) & (B = D)) & ? [D:$i]: ((A = D) & (rpoint @ D))) => (? [D:$i]: (~ (D = A) & (rpoint @ D) & ~ (B = D) & ~ (D = C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[51])). 18.17/7.04 thf(35,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((C = D) & (rpoint @ D) & (A = B) & (rpoint @ B) & (A != C)) => ((vf @ (vskolem1052 @ A @ B @ C @ D) @ A) = (vf @ C @ (vskolem1052 @ A @ B @ C @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(206), 0), 0)')). 18.17/7.04 thf(310,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((C = D) & (rpoint @ D) & (A = B) & (rpoint @ B) & ~ (A = C)) => ((vf @ (vskolem1052 @ A @ B @ C @ D) @ A) = (vf @ C @ (vskolem1052 @ A @ B @ C @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[35])). 18.17/7.04 thf(48,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((B != C) & (C != A) & ? [E:$i]: ((B = E) & (rpoint @ E)) & ? [E:$i]: ((E = A) & (rpoint @ E)) & ? [E:$i]: ((rpoint @ E) & (C = E)) & (B != A)) <= ((rtriangle @ D) & (D = (vtriangle @ A @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(3), 0), imp(cond(axiom(3), 0)))')). 18.17/7.04 thf(370,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((~ (B = C) & ~ (C = A) & ? [E:$i]: ((B = E) & (rpoint @ E)) & ? [E:$i]: ((E = A) & (rpoint @ E)) & ? [E:$i]: ((rpoint @ E) & (C = E)) & ~ (B = A)) | ~ ((rtriangle @ D) & (D = (vtriangle @ A @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[48])). 18.17/7.04 thf(69,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i]: (((vangle @ D @ A @ E) = (vangle @ B @ A @ C)) <= (~ (rR @ A @ C @ E) & (A != E) & (A != D) & (A != C) & (ron @ C @ G) & (ron @ B @ F) & ? [H:$i]: ((rline @ H) & (H = G)) & ? [H:$i]: ((H = F) & (rline @ H)) & ? [H:$i]: ((rpoint @ H) & (E = H)) & ? [H:$i]: ((rpoint @ H) & (H = C)) & ? [H:$i]: ((rpoint @ H) & (H = A)) & ? [H:$i]: ((rpoint @ H) & (H = B)) & ? [H:$i]: ((H = D) & (rpoint @ H)) & (ron @ A @ F) & (ron @ D @ F) & (ron @ E @ G) & (A != B) & ~ (rR @ A @ B @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(194), 0), imp(cond(axiom(194), 0)))')). 18.17/7.04 thf(544,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i]: (((vangle @ D @ A @ E) = (vangle @ B @ A @ C)) | ~ (~ (rR @ A @ C @ E) & ~ (A = E) & ~ (A = D) & ~ (A = C) & (ron @ C @ G) & (ron @ B @ F) & ? [H:$i]: ((rline @ H) & (H = G)) & ? [H:$i]: ((H = F) & (rline @ H)) & ? [H:$i]: ((rpoint @ H) & (E = H)) & ? [H:$i]: ((rpoint @ H) & (H = C)) & ? [H:$i]: ((rpoint @ H) & (H = A)) & ? [H:$i]: ((rpoint @ H) & (H = B)) & ? [H:$i]: ((H = D) & (rpoint @ H)) & (ron @ A @ F) & (ron @ D @ F) & (ron @ E @ G) & ~ (A = B) & ~ (rR @ A @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[69])). 18.17/7.04 thf(89,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((~ (ron @ A @ C)) <= ((C = D) & (rcircle @ D) & (A = B) & (rpoint @ B) & (rinside @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(79), 0), imp(cond(axiom(79), 0)))')). 18.17/7.04 thf(744,plain,((! [A:$i,B:$i,C:$i,D:$i]: (~ (ron @ A @ C) | ~ ((C = D) & (rcircle @ D) & (A = B) & (rpoint @ B) & (rinside @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[89])). 18.17/7.04 thf(12,axiom,((! [A:$i,B:$i]: ((? [C:$i]: ((rpoint @ C) & (B = C)) & ? [C:$i]: ((rpoint @ C) & (C = A)) & (B != A)) => (! [C:$i,D:$i]: (((C = D) & (B != C) & (rpoint @ D) & (C != A)) => ((vf @ C @ (vskolem1078 @ C @ D @ A @ B)) = (vf @ A @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(219), 0), 0)')). 18.17/7.04 thf(175,plain,((! [A:$i,B:$i]: ((? [C:$i]: ((rpoint @ C) & (B = C)) & ? [C:$i]: ((rpoint @ C) & (C = A)) & ~ (B = A)) => (! [C:$i,D:$i]: (((C = D) & ~ (B = C) & (rpoint @ D) & ~ (C = A)) => ((vf @ C @ (vskolem1078 @ C @ D @ A @ B)) = (vf @ A @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[12])). 18.17/7.04 thf(119,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((E = D) <= (((vf @ C @ A) = (vf @ C @ B)) & (rcenter @ C @ E) & (rcenter @ C @ D) & ? [F:$i]: ((B = F) & (rpoint @ F)) & ? [F:$i]: ((F = A) & (rpoint @ F)) & (ron @ A @ D) & (ron @ B @ E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(182), 0), imp(cond(axiom(182), 0)))')). 18.17/7.04 thf(1008,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((E = D) | ~ (((vf @ C @ A) = (vf @ C @ B)) & (rcenter @ C @ E) & (rcenter @ C @ D) & ? [F:$i]: ((B = F) & (rpoint @ F)) & ? [F:$i]: ((F = A) & (rpoint @ F)) & (ron @ A @ D) & (ron @ B @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[119])). 18.17/7.04 thf(36,axiom,((rpoint @ vd14)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pred(axiom(5), 0)')). 18.17/7.04 thf(314,plain,((rpoint @ vd14)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[36])). 18.17/7.04 thf(73,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((C = D) & (rpoint @ D) & (B = A) & (rline @ B) & (ron @ C @ A)) => (? [E:$i]: ((rpoint @ E) & (ron @ E @ A) & (C != E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(17), 0), imp(cond(axiom(17), 0)))')). 18.17/7.04 thf(571,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((C = D) & (rpoint @ D) & (B = A) & (rline @ B) & (ron @ C @ A)) => (? [E:$i]: ((rpoint @ E) & (ron @ E @ A) & ~ (C = E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[73])). 18.17/7.04 thf(47,axiom,((! [A:$i,B:$i]: ((((vf @ A @ B) = v0) <=> (A = B)) <= (? [C:$i]: ((rpoint @ C) & (A = C)) & ? [C:$i]: ((B = C) & (rpoint @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(162), 0), imp(cond(axiom(162), 0)))')). 18.17/7.04 thf(363,plain,((! [A:$i,B:$i]: (((((vf @ A @ B) = v0) => (A = B)) & ((A = B) => ((vf @ A @ B) = v0))) | ~ (? [C:$i]: ((rpoint @ C) & (A = C)) & ? [C:$i]: ((B = C) & (rpoint @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[47])). 18.17/7.04 thf(16,axiom,((! [A:$i,B:$i,C:$i]: (((vf @ A @ C) = (vplus @ (vf @ A @ B) @ (vf @ B @ C))) <= ((rR @ B @ A @ C) & ? [D:$i]: ((rpoint @ D) & (D = B)) & ? [D:$i]: ((D = A) & (rpoint @ D)) & ? [D:$i]: ((rpoint @ D) & (D = C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(180), 0), imp(cond(axiom(180), 0)))')). 18.17/7.04 thf(203,plain,((! [A:$i,B:$i,C:$i]: (((vf @ A @ C) = (vplus @ (vf @ A @ B) @ (vf @ B @ C))) | ~ ((rR @ B @ A @ C) & ? [D:$i]: ((rpoint @ D) & (D = B)) & ? [D:$i]: ((D = A) & (rpoint @ D)) & ? [D:$i]: ((rpoint @ D) & (D = C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[16])). 18.17/7.04 thf(96,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((D = E) & (rR @ B @ A @ C) & ? [F:$i]: ((rpoint @ F) & (A = F)) & ? [F:$i]: ((rpoint @ F) & (F = B)) & ? [F:$i]: ((F = C) & (rpoint @ F)) & (rline @ E) & (ron @ A @ D) & (ron @ B @ D)) => (ron @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(83), 0), imp(cond(axiom(83), 0)))')). 18.17/7.04 thf(813,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((D = E) & (rR @ B @ A @ C) & ? [F:$i]: ((rpoint @ F) & (A = F)) & ? [F:$i]: ((rpoint @ F) & (F = B)) & ? [F:$i]: ((F = C) & (rpoint @ F)) & (rline @ E) & (ron @ A @ D) & (ron @ B @ D)) => (ron @ C @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[96])). 18.17/7.04 thf(113,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((rS @ B @ C @ D) <= ((rS @ A @ C @ D) & (rS @ A @ B @ D) & (E = D) & (rline @ E) & ? [F:$i]: ((rpoint @ F) & (F = C)) & ? [F:$i]: ((rpoint @ F) & (B = F)) & ? [F:$i]: ((A = F) & (rpoint @ F)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(101), 0), imp(cond(axiom(101), 0)))')). 18.17/7.04 thf(963,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((rS @ B @ C @ D) | ~ ((rS @ A @ C @ D) & (rS @ A @ B @ D) & (E = D) & (rline @ E) & ? [F:$i]: ((rpoint @ F) & (F = C)) & ? [F:$i]: ((rpoint @ F) & (B = F)) & ? [F:$i]: ((A = F) & (rpoint @ F)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[113])). 18.17/7.04 thf(22,axiom,((! [A:$i,B:$i,C:$i]: ((? [D:$i]: ((D = C) & (rpoint @ D)) & ? [D:$i]: ((A = D) & (rpoint @ D)) & ? [D:$i]: ((rpoint @ D) & (D = B)) & (A != B) & (A != C) & (C != B) & ((vangle @ A @ C @ B) = (vangle @ A @ B @ C))) => ((vf @ A @ B) = (vf @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(382), 0), 0)')). 18.17/7.04 thf(235,plain,((! [A:$i,B:$i,C:$i]: ((? [D:$i]: ((D = C) & (rpoint @ D)) & ? [D:$i]: ((A = D) & (rpoint @ D)) & ? [D:$i]: ((rpoint @ D) & (D = B)) & ~ (A = B) & ~ (A = C) & ~ (C = B) & ((vangle @ A @ C @ B) = (vangle @ A @ B @ C))) => ((vf @ A @ B) = (vf @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[22])). 18.17/7.04 thf(64,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: ((? [G:$i]: ((G != F) & (rpoint @ G) & (rR @ G @ C @ D) & (E != G))) <= ((rR @ F @ C @ D) & (rR @ E @ C @ D) & (ron @ E @ A) & ? [G:$i]: ((rpoint @ G) & (G = F)) & ? [G:$i]: ((G = D) & (rpoint @ G)) & ? [G:$i]: ((C = G) & (rpoint @ G)) & (rline @ B) & (A = B) & ? [G:$i]: ((rpoint @ G) & (G = E)) & (ron @ C @ A) & (ron @ D @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(27), 0), imp(cond(axiom(27), 0)))')). 18.17/7.04 thf(510,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: (? [G:$i]: (~ (G = F) & (rpoint @ G) & (rR @ G @ C @ D) & ~ (E = G)) | ~ ((rR @ F @ C @ D) & (rR @ E @ C @ D) & (ron @ E @ A) & ? [G:$i]: ((rpoint @ G) & (G = F)) & ? [G:$i]: ((G = D) & (rpoint @ G)) & ? [G:$i]: ((C = G) & (rpoint @ G)) & (rline @ B) & (A = B) & ? [G:$i]: ((rpoint @ G) & (G = E)) & (ron @ C @ A) & (ron @ D @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[64])). 18.17/7.04 thf(17,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i]: (((G != E) & (G = H) & (E = F) & (C = D) & (rpoint @ D) & (rpoint @ B) & (B = A) & (rpoint @ F) & (rpoint @ H) & (C != A) & (rless @ (vf @ E @ G) @ (vf @ A @ C))) => (rpoint @ (vskolem1120 @ A @ B @ C @ D @ E @ F @ G @ H))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(238), 0), 2)')). 18.17/7.04 thf(207,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i]: ((~ (G = E) & (G = H) & (E = F) & (C = D) & (rpoint @ D) & (rpoint @ B) & (B = A) & (rpoint @ F) & (rpoint @ H) & ~ (C = A) & (rless @ (vf @ E @ G) @ (vf @ A @ C))) => (rpoint @ (vskolem1120 @ A @ B @ C @ D @ E @ F @ G @ H))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[17])). 18.17/7.04 thf(109,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i]: ((((rS @ E @ A @ G) <= ((ron @ E @ G) & (ron @ E @ F))) & (rintersect @ F @ G)) <= ((ron @ C @ H) & (ron @ C @ G) & (ron @ B @ G) & ? [I:$i]: ((I = F) & (rline @ I)) & ? [I:$i]: ((rpoint @ I) & (I = E)) & ? [I:$i]: ((rpoint @ I) & (I = D)) & ? [I:$i]: ((B = I) & (rpoint @ I)) & ? [I:$i]: ((I = A) & (rpoint @ I)) & ? [I:$i]: ((rpoint @ I) & (I = C)) & ? [I:$i]: ((rline @ I) & (G = I)) & ? [I:$i]: ((rline @ I) & (H = I)) & (ron @ A @ F) & (ron @ B @ F) & (ron @ D @ H) & (B != C) & (rS @ A @ D @ G) & (rless @ (vplus @ (vangle @ A @ B @ C) @ (vangle @ B @ C @ D)) @ (vplus @ vperp @ vperp)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(196), 0), imp(cond(axiom(196), 0)))')). 18.17/7.04 thf(929,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i]: ((((rS @ E @ A @ G) | ~ ((ron @ E @ G) & (ron @ E @ F))) & (rintersect @ F @ G)) | ~ ((ron @ C @ H) & (ron @ C @ G) & (ron @ B @ G) & ? [I:$i]: ((I = F) & (rline @ I)) & ? [I:$i]: ((rpoint @ I) & (I = E)) & ? [I:$i]: ((rpoint @ I) & (I = D)) & ? [I:$i]: ((B = I) & (rpoint @ I)) & ? [I:$i]: ((I = A) & (rpoint @ I)) & ? [I:$i]: ((rpoint @ I) & (I = C)) & ? [I:$i]: ((rline @ I) & (G = I)) & ? [I:$i]: ((rline @ I) & (H = I)) & (ron @ A @ F) & (ron @ B @ F) & (ron @ D @ H) & ~ (B = C) & (rS @ A @ D @ G) & (rless @ (vplus @ (vangle @ A @ B @ C) @ (vangle @ B @ C @ D)) @ (vplus @ vperp @ vperp)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[109])). 18.17/7.04 thf(28,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((A = B) & (rreal @ B) & (rreal @ D) & (D = C)) => ((A = C) | (rless @ C @ A) | (rless @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(145), 0), imp(cond(axiom(145), 0)))')). 18.17/7.04 thf(272,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((A = B) & (rreal @ B) & (rreal @ D) & (D = C)) => ((A = C) | (rless @ C @ A) | (rless @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[28])). 18.17/7.04 thf(70,axiom,(((rline @ vskolem1416) & (ron @ vd1401 @ vskolem1416) & (ron @ vd1399 @ vskolem1416))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','replace(replace(and(pred(s2(plural(the(408))), 0), and(pred(s1(plural(the(408))), 0), pred(the(408), 0)))))')). 18.17/7.04 thf(549,plain,(((rline @ vskolem1416) & (ron @ vd1401 @ vskolem1416) & (ron @ vd1399 @ vskolem1416))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[70])). 18.17/7.04 thf(123,axiom,((! [A:$i,B:$i]: ((? [C:$i]: ((rpoint @ C) & (C = A)) & ? [C:$i]: ((rpoint @ C) & (B = C)) & (B != A)) => (? [C:$i]: ((rcircle @ C) & (rcenter @ A @ C) & (ron @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(53), 0), imp(cond(axiom(53), 0)))')). 18.17/7.04 thf(1045,plain,((! [A:$i,B:$i]: ((? [C:$i]: ((rpoint @ C) & (C = A)) & ? [C:$i]: ((rpoint @ C) & (B = C)) & ~ (B = A)) => (? [C:$i]: ((rcircle @ C) & (rcenter @ A @ C) & (ron @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[123])). 18.17/7.04 thf(37,axiom,((! [A:$i,B:$i]: ((rinside @ A @ B) <= (rcenter @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(77), 0), imp(cond(axiom(77), 0)))')). 18.17/7.04 thf(315,plain,((! [A:$i,B:$i]: ((rinside @ A @ B) | ~ (rcenter @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[37])). 18.17/7.04 thf(54,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((? [E:$i,F:$i]: ((rpoint @ F) & (ron @ E @ A) & (rpoint @ E) & (ron @ E @ C) & (ron @ F @ C) & (ron @ F @ A) & (F != E))) <= ((rline @ D) & (A = B) & (rcircle @ B) & (D = C) & (rintersect @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(59), 0), imp(cond(axiom(59), 0)))')). 18.17/7.04 thf(432,plain,((! [A:$i,B:$i,C:$i,D:$i]: (? [E:$i,F:$i]: ((rpoint @ F) & (ron @ E @ A) & (rpoint @ E) & (ron @ E @ C) & (ron @ F @ C) & (ron @ F @ A) & ~ (F = E)) | ~ ((rline @ D) & (A = B) & (rcircle @ B) & (D = C) & (rintersect @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[54])). 18.17/7.04 thf(111,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((ron @ B @ D) & (rline @ E) & ? [F:$i]: ((rpoint @ F) & (B = F)) & ? [F:$i]: ((F = A) & (rpoint @ F)) & ? [F:$i]: ((C = F) & (rpoint @ F)) & (D = E) & (rR @ B @ A @ C)) => (~ (rS @ A @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(109), 0), imp(cond(axiom(109), 0)))')). 18.17/7.04 thf(950,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((ron @ B @ D) & (rline @ E) & ? [F:$i]: ((rpoint @ F) & (B = F)) & ? [F:$i]: ((F = A) & (rpoint @ F)) & ? [F:$i]: ((C = F) & (rpoint @ F)) & (D = E) & (rR @ B @ A @ C)) => (~ (rS @ A @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[111])). 18.17/7.04 thf(97,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((~ (rS @ A @ C @ D) & (ron @ C @ E) & (D != E) & ? [F:$i]: ((F = A) & (rpoint @ F)) & ? [F:$i]: ((F = B) & (rpoint @ F)) & ? [F:$i]: ((rpoint @ F) & (F = C)) & (B != A) & (C != A) & (B != C) & ? [F:$i]: ((F = D) & (rline @ F)) & ? [F:$i]: ((F = E) & (rline @ F)) & (ron @ A @ E) & (ron @ B @ E) & (ron @ B @ D)) => (rR @ B @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(111), 0), imp(cond(axiom(111), 0)))')). 18.17/7.04 thf(818,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((~ (rS @ A @ C @ D) & (ron @ C @ E) & ~ (D = E) & ? [F:$i]: ((F = A) & (rpoint @ F)) & ? [F:$i]: ((F = B) & (rpoint @ F)) & ? [F:$i]: ((rpoint @ F) & (F = C)) & ~ (B = A) & ~ (C = A) & ~ (B = C) & ? [F:$i]: ((F = D) & (rline @ F)) & ? [F:$i]: ((F = E) & (rline @ F)) & (ron @ A @ E) & (ron @ B @ E) & (ron @ B @ D)) => (rR @ B @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[97])). 18.17/7.04 thf(14,axiom,((! [A:$i,B:$i,C:$i]: ((? [D:$i]: ((rpoint @ D) & (B = D)) & ? [D:$i]: ((D = A) & (rpoint @ D)) & ? [D:$i]: ((C = D) & (rpoint @ D)) & (rR @ B @ A @ C)) => (~ (rR @ A @ B @ C) & (A != C) & (A != B) & (rR @ B @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(81), 0), imp(cond(axiom(81), 0)))')). 18.17/7.04 thf(183,plain,((! [A:$i,B:$i,C:$i]: ((? [D:$i]: ((rpoint @ D) & (B = D)) & ? [D:$i]: ((D = A) & (rpoint @ D)) & ? [D:$i]: ((C = D) & (rpoint @ D)) & (rR @ B @ A @ C)) => (~ (rR @ A @ B @ C) & ~ (A = C) & ~ (A = B) & (rR @ B @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[14])). 18.17/7.04 thf(52,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((rS @ B @ C @ D) <= ((rR @ B @ A @ C) & (D = E) & ? [F:$i]: ((rpoint @ F) & (F = B)) & ? [F:$i]: ((A = F) & (rpoint @ F)) & ? [F:$i]: ((C = F) & (rpoint @ F)) & (rline @ E) & (ron @ A @ D) & ~ (ron @ B @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(107), 0), imp(cond(axiom(107), 0)))')). 18.17/7.04 thf(422,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((rS @ B @ C @ D) | ~ ((rR @ B @ A @ C) & (D = E) & ? [F:$i]: ((rpoint @ F) & (F = B)) & ? [F:$i]: ((A = F) & (rpoint @ F)) & ? [F:$i]: ((C = F) & (rpoint @ F)) & (rline @ E) & (ron @ A @ D) & ~ (ron @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[52])). 18.17/7.04 thf(23,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: ((rless @ A @ E) <= ((rreal @ D) & (rreal @ B) & (B = A) & (C = D) & (rreal @ F) & (F = E) & (rless @ A @ C) & (rless @ C @ E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(151), 0), imp(cond(axiom(151), 0)))')). 18.17/7.04 thf(239,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: ((rless @ A @ E) | ~ ((rreal @ D) & (rreal @ B) & (B = A) & (C = D) & (rreal @ F) & (F = E) & (rless @ A @ C) & (rless @ C @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[23])). 18.17/7.04 thf(3,axiom,((rreal @ vd684)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pred(axiom(137), 1)')). 18.17/7.04 thf(136,plain,((rreal @ vd684)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])). 18.17/7.04 thf(46,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: (((D = C) & (rpoint @ B) & (A = B) & (rpoint @ D) & (rpoint @ F) & (E = F)) => (rgeq @ (vg @ A @ C @ E) @ v0)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(174), 0), imp(cond(axiom(174), 0)))')). 18.17/7.04 thf(358,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: (((D = C) & (rpoint @ B) & (A = B) & (rpoint @ D) & (rpoint @ F) & (E = F)) => (rgeq @ (vg @ A @ C @ E) @ v0)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[46])). 18.17/7.04 thf(83,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: (((F = E) & (C = D) & (rpoint @ B) & (A = B) & (rcircle @ D) & (rline @ F) & (rinside @ A @ C) & (ron @ A @ E)) => (rintersect @ E @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(131), 0), imp(cond(axiom(131), 0)))')). 18.17/7.04 thf(696,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: (((F = E) & (C = D) & (rpoint @ B) & (A = B) & (rcircle @ D) & (rline @ F) & (rinside @ A @ C) & (ron @ A @ E)) => (rintersect @ E @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[83])). 18.17/7.04 thf(112,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((ron @ C @ D) <=> (v0 = (vg @ A @ B @ C))) <= ((ron @ A @ D) & (B != A) & ? [F:$i]: ((A = F) & (rpoint @ F)) & ? [F:$i]: ((F = B) & (rpoint @ F)) & ? [F:$i]: ((rpoint @ F) & (C = F)) & (rline @ E) & (E = D) & (ron @ B @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(200), 0), imp(cond(axiom(200), 0)))')). 18.17/7.04 thf(955,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((((ron @ C @ D) => (v0 = (vg @ A @ B @ C))) & ((v0 = (vg @ A @ B @ C)) => (ron @ C @ D))) | ~ ((ron @ A @ D) & ~ (B = A) & ? [F:$i]: ((A = F) & (rpoint @ F)) & ? [F:$i]: ((F = B) & (rpoint @ F)) & ? [F:$i]: ((rpoint @ F) & (C = F)) & (rline @ E) & (E = D) & (ron @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[112])). 18.17/7.04 thf(100,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: ((~ (? [G:$i]: ((rline @ G) & (ron @ D @ G) & (ron @ E @ G) & (ron @ F @ G))) & ? [G:$i]: ((D = G) & (rpoint @ G)) & (B != A) & ? [G:$i]: ((rpoint @ G) & (G = A)) & ? [G:$i]: ((rpoint @ G) & (G = B)) & ? [G:$i]: ((rpoint @ G) & (G = C)) & (C != A) & (C != B) & ? [G:$i]: ((E = G) & (rpoint @ G)) & ? [G:$i]: ((rpoint @ G) & (G = F)) & ((vf @ D @ E) = (vf @ A @ B)) & ((vf @ D @ F) = (vf @ A @ C)) & ((vangle @ E @ D @ F) = (vangle @ B @ A @ C))) => ((vangle @ A @ C @ B) = (vangle @ D @ F @ E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(264), 0), 0)')). 18.17/7.04 thf(839,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: ((~ (? [G:$i]: ((rline @ G) & (ron @ D @ G) & (ron @ E @ G) & (ron @ F @ G))) & ? [G:$i]: ((D = G) & (rpoint @ G)) & ~ (B = A) & ? [G:$i]: ((rpoint @ G) & (G = A)) & ? [G:$i]: ((rpoint @ G) & (G = B)) & ? [G:$i]: ((rpoint @ G) & (G = C)) & ~ (C = A) & ~ (C = B) & ? [G:$i]: ((E = G) & (rpoint @ G)) & ? [G:$i]: ((rpoint @ G) & (G = F)) & ((vf @ D @ E) = (vf @ A @ B)) & ((vf @ D @ F) = (vf @ A @ C)) & ((vangle @ E @ D @ F) = (vangle @ B @ A @ C))) => ((vangle @ A @ C @ B) = (vangle @ D @ F @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[100])). 18.17/7.04 thf(88,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((rintersect @ C @ D) <= ((rinside @ A @ D) & (rinside @ B @ C) & ? [E:$i]: ((rpoint @ E) & (E = A)) & ? [E:$i]: ((rpoint @ E) & (B = E)) & (ron @ A @ C) & (ron @ B @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(135), 0), imp(cond(axiom(135), 0)))')). 18.17/7.04 thf(740,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((rintersect @ C @ D) | ~ ((rinside @ A @ D) & (rinside @ B @ C) & ? [E:$i]: ((rpoint @ E) & (E = A)) & ? [E:$i]: ((rpoint @ E) & (B = E)) & (ron @ A @ C) & (ron @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[88])). 18.17/7.04 thf(40,axiom,((! [A:$i,B:$i,C:$i]: (((rleq @ v0 @ (vangle @ A @ B @ C)) & (rleq @ (vangle @ A @ B @ C) @ (vplus @ vperp @ vperp))) <= (? [D:$i]: ((rpoint @ D) & (D = C)) & ? [D:$i]: ((rpoint @ D) & (B = D)) & ? [D:$i]: ((rpoint @ D) & (D = A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(170), 0), imp(cond(axiom(170), 0)))')). 18.17/7.04 thf(332,plain,((! [A:$i,B:$i,C:$i]: (((rleq @ v0 @ (vangle @ A @ B @ C)) & (rleq @ (vangle @ A @ B @ C) @ (vplus @ vperp @ vperp))) | ~ (? [D:$i]: ((rpoint @ D) & (D = C)) & ? [D:$i]: ((rpoint @ D) & (B = D)) & ? [D:$i]: ((rpoint @ D) & (D = A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[40])). 18.17/7.04 thf(53,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((D = E) & (ron @ A @ D) & ? [F:$i]: ((B = F) & (rpoint @ F)) & ? [F:$i]: ((A = F) & (rpoint @ F)) & ? [F:$i]: ((F = C) & (rpoint @ F)) & (rline @ E) & (rR @ B @ A @ C) & (ron @ C @ D)) => (ron @ B @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(85), 0), imp(cond(axiom(85), 0)))')). 18.17/7.04 thf(427,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((D = E) & (ron @ A @ D) & ? [F:$i]: ((B = F) & (rpoint @ F)) & ? [F:$i]: ((A = F) & (rpoint @ F)) & ? [F:$i]: ((F = C) & (rpoint @ F)) & (rline @ E) & (rR @ B @ A @ C) & (ron @ C @ D)) => (ron @ B @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[53])). 18.17/7.04 thf(116,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i]: (((G = H) & (rline @ H) & (rcenter @ F @ B) & (ron @ D @ A) & (ron @ C @ B) & (ron @ C @ A) & (rintersect @ A @ B) & ? [I:$i]: ((rcircle @ I) & (I = B)) & ? [I:$i]: ((I = A) & (rcircle @ I)) & (A != B) & ? [I:$i]: ((C = I) & (rpoint @ I)) & ? [I:$i]: ((D = I) & (rpoint @ I)) & (ron @ D @ B) & (C != D) & (rcenter @ E @ A) & (ron @ E @ G) & (ron @ F @ G)) => (~ (rS @ C @ D @ G))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(125), 0), imp(cond(axiom(125), 0)))')). 18.17/7.04 thf(992,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i]: (((G = H) & (rline @ H) & (rcenter @ F @ B) & (ron @ D @ A) & (ron @ C @ B) & (ron @ C @ A) & (rintersect @ A @ B) & ? [I:$i]: ((rcircle @ I) & (I = B)) & ? [I:$i]: ((I = A) & (rcircle @ I)) & ~ (A = B) & ? [I:$i]: ((C = I) & (rpoint @ I)) & ? [I:$i]: ((D = I) & (rpoint @ I)) & (ron @ D @ B) & ~ (C = D) & (rcenter @ E @ A) & (ron @ E @ G) & (ron @ F @ G)) => (~ (rS @ C @ D @ G))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[116])). 18.17/7.04 thf(29,axiom,((! [A:$i,B:$i]: (((A = B) & (rreal @ B)) => ((vplus @ A @ v0) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(141), 0), imp(cond(axiom(141), 0)))')). 18.17/7.04 thf(277,plain,((! [A:$i,B:$i]: (((A = B) & (rreal @ B)) => ((vplus @ A @ v0) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[29])). 18.17/7.04 thf(82,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((rS @ A @ C @ D) & (E = D) & (rline @ E) & ? [F:$i]: ((A = F) & (rpoint @ F)) & ? [F:$i]: ((F = B) & (rpoint @ F)) & ? [F:$i]: ((rpoint @ F) & (C = F)) & (rR @ B @ A @ C)) => (rS @ A @ B @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(105), 0), imp(cond(axiom(105), 0)))')). 18.17/7.04 thf(691,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((rS @ A @ C @ D) & (E = D) & (rline @ E) & ? [F:$i]: ((A = F) & (rpoint @ F)) & ? [F:$i]: ((F = B) & (rpoint @ F)) & ? [F:$i]: ((rpoint @ F) & (C = F)) & (rR @ B @ A @ C)) => (rS @ A @ B @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[82])). 18.17/7.04 thf(45,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: ((((vf @ A @ B) = (vf @ D @ E)) & ? [G:$i]: ((G = D) & (rpoint @ G)) & ? [G:$i]: ((rpoint @ G) & (C = G)) & ? [G:$i]: ((rpoint @ G) & (G = B)) & ? [G:$i]: ((A = G) & (rpoint @ G)) & ? [G:$i]: ((rpoint @ G) & (G = E)) & ? [G:$i]: ((rpoint @ G) & (G = F)) & ((vf @ E @ F) = (vf @ B @ C)) & ((vf @ F @ D) = (vf @ C @ A)) & ((vangle @ A @ B @ C) = (vangle @ D @ E @ F)) & ((vangle @ E @ F @ D) = (vangle @ B @ C @ A)) & ((vangle @ C @ A @ B) = (vangle @ F @ D @ E))) => ((vg @ D @ E @ F) = (vg @ A @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(178), 0), imp(cond(axiom(178), 0)))')). 18.17/7.04 thf(354,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: ((((vf @ A @ B) = (vf @ D @ E)) & ? [G:$i]: ((G = D) & (rpoint @ G)) & ? [G:$i]: ((rpoint @ G) & (C = G)) & ? [G:$i]: ((rpoint @ G) & (G = B)) & ? [G:$i]: ((A = G) & (rpoint @ G)) & ? [G:$i]: ((rpoint @ G) & (G = E)) & ? [G:$i]: ((rpoint @ G) & (G = F)) & ((vf @ E @ F) = (vf @ B @ C)) & ((vf @ F @ D) = (vf @ C @ A)) & ((vangle @ A @ B @ C) = (vangle @ D @ E @ F)) & ((vangle @ E @ F @ D) = (vangle @ B @ C @ A)) & ((vangle @ C @ A @ B) = (vangle @ F @ D @ E))) => ((vg @ D @ E @ F) = (vg @ A @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[45])). 18.17/7.04 thf(80,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((rintersect @ C @ A) & (C = D) & (rline @ D) & (rcircle @ B) & (A = B)) => (? [E:$i]: ((ron @ E @ A) & (ron @ E @ C) & (rpoint @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(57), 0), imp(cond(axiom(57), 0)))')). 18.17/7.04 thf(676,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((rintersect @ C @ A) & (C = D) & (rline @ D) & (rcircle @ B) & (A = B)) => (? [E:$i]: ((ron @ E @ A) & (ron @ E @ C) & (rpoint @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[80])). 18.17/7.04 thf(1140,plain,($false),inference(cvc4,[status(thm)],[760,777,352,523,582,1005,1068,655,913,153,1095,404,1055,504,802,344,196,460,1087,289,216,179,1040,1109,211,485,937,348,480,687,293,866,248,220,534,825,598,137,165,252,879,852,665,710,324,1012,317,141,499,989,256,339,537,489,706,997,701,244,792,921,1026,298,161,149,584,732,900,784,230,567,303,890,535,895,130,399,455,505,167,473,1076,648,749,553,968,823,145,282,409,310,370,544,744,175,1008,314,571,363,203,813,963,235,510,207,929,272,549,1045,315,432,950,818,183,422,239,136,358,696,955,839,740,332,427,992,277,691,354,676])). 18.17/7.04 % SZS output end CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 18.17/7.04 % [INFO] Killing All external provers ... 18.30/7.11 EOF