0.00/0.03 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.04 % Command : java -Xss128m -Xmx4g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar %s -t %d -p --atp cvc4=/export/starexec/sandbox/solver/bin/externals/cvc4 --atp e=/export/starexec/sandbox/solver/bin/externals/eprover --atp iprover=/export/starexec/sandbox/solver/bin/externals/iprover 0.03/0.24 % Computer : n185.star.cs.uiowa.edu 0.03/0.24 % Model : x86_64 x86_64 0.03/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz 0.03/0.24 % Memory : 32218.625MB 0.03/0.24 % OS : Linux 3.10.0-693.2.2.el7.x86_64 0.03/0.24 % CPULimit : 300 0.03/0.24 % DateTime : Sat Jul 14 04:45:25 CDT 2018 0.03/0.24 % CPUTime : 3.38/1.72 % [INFO] Running in sequential loop mode. 4.05/1.94 % [CONFIG] Using configuration: timeout(300) with strategy 4.32/2.03 % [INFO] iprover registered as external prover. 4.32/2.03 % [INFO] e registered as external prover. 4.32/2.03 % [INFO] cvc4 registered as external prover. 4.32/2.03 % [INFO] Parsing finished. Scanning for conjecture ... 4.70/2.10 % [INFO] Found a conjecture and 124 axioms. Running axiom selection ... 5.11/2.21 % [INFO] Axiom selection finished. Selected 124 axioms (removed 0 axioms). 6.28/2.60 % [INFO] Type checking passed. Searching for refutation ... 18.99/7.02 % [INFO] Killing All external provers ... 18.99/7.03 % Time passed: 6694ms 18.99/7.03 % Effective reasoning time: 5294ms 18.99/7.03 % Solved by strategy 18.99/7.03 % Axioms used in derivation (124): 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))), 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))), 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))), qu(cond(axiom(61), 0), imp(cond(axiom(61), 0))), and(pred(s2(plural(the(408))), 0), and(pred(s1(plural(the(408))), 0), pred(the(408), 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))) 18.99/7.03 % No. of inferences in proof: 252 18.99/7.03 % No. of processed clauses: 17 18.99/7.03 % No. of generated clauses: 11 18.99/7.03 % No. of forward subsumed clauses: 0 18.99/7.03 % No. of backward subsumed clauses: 0 18.99/7.03 % No. of ground rewrite rules in store: 11 18.99/7.03 % No. of non-ground rewrite rules in store: 0 18.99/7.03 % No. of positive (non-rewrite) units in store: 0 18.99/7.03 % No. of negative (non-rewrite) units in store: 5 18.99/7.03 % No. of choice functions detected: 0 18.99/7.03 % No. of choice instantiations: 0 18.99/7.04 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 6694 ms resp. 5294 ms w/o parsing 19.26/7.23 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p 19.26/7.23 thf(vd1416_type, type, vd1416: $i). 19.26/7.23 thf(rline_type, type, rline: ($i > $o)). 19.26/7.23 thf(vd1401_type, type, vd1401: $i). 19.26/7.23 thf(ron_type, type, ron: ($i > ($i > $o))). 19.26/7.23 thf(vd1399_type, type, vd1399: $i). 19.26/7.23 thf(vd684_type, type, vd684: $i). 19.26/7.23 thf(rreal_type, type, rreal: ($i > $o)). 19.26/7.23 thf(v0_type, type, v0: $i). 19.26/7.23 thf(vf_type, type, vf: ($i > ($i > $i))). 19.26/7.23 thf(rleq_type, type, rleq: ($i > ($i > $o))). 19.26/7.23 thf(rpoint_type, type, rpoint: ($i > $o)). 19.26/7.23 thf(vd1409_type, type, vd1409: $i). 19.26/7.23 thf(vskolem1052_type, type, vskolem1052: ($i > ($i > ($i > ($i > $i))))). 19.26/7.23 thf(vg_type, type, vg: ($i > ($i > ($i > $i)))). 19.26/7.23 thf(rR_type, type, rR: ($i > ($i > ($i > $o)))). 19.26/7.23 thf(vangle_type, type, vangle: ($i > ($i > ($i > $i)))). 19.26/7.23 thf(vskolem1078_type, type, vskolem1078: ($i > ($i > ($i > ($i > $i))))). 19.26/7.23 thf(rless_type, type, rless: ($i > ($i > $o))). 19.26/7.23 thf(vskolem1120_type, type, vskolem1120: ($i > ($i > ($i > ($i > ($i > ($i > ($i > ($i > $i))))))))). 19.26/7.23 thf(vplus_type, type, vplus: ($i > ($i > $i))). 19.26/7.23 thf(rcenter_type, type, rcenter: ($i > ($i > $o))). 19.26/7.23 thf(rcircle_type, type, rcircle: ($i > $o)). 19.26/7.23 thf(rgeq_type, type, rgeq: ($i > ($i > $o))). 19.26/7.23 thf(rinside_type, type, rinside: ($i > ($i > $o))). 19.26/7.23 thf(vd14_type, type, vd14: $i). 19.26/7.23 thf(rtriangle_type, type, rtriangle: ($i > $o)). 19.26/7.23 thf(vtriangle_type, type, vtriangle: ($i > ($i > ($i > $i)))). 19.26/7.23 thf(vperp_type, type, vperp: $i). 19.26/7.23 thf(rS_type, type, rS: ($i > ($i > ($i > $o)))). 19.26/7.23 thf(rintersect_type, type, rintersect: ($i > ($i > $o))). 19.26/7.23 thf(vd1406_type, type, vd1406: $i). 19.26/7.23 thf(vd1400_type, type, vd1400: $i). 19.26/7.23 thf(vd1407_type, type, vd1407: $i). 19.26/7.23 thf(77,axiom,((! [A:$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:$i]: ((((vf @ G @ H) = (vf @ I @ J)) & ((vangle @ K @ L @ M) = (vangle @ N @ O @ P))) <= ((R = Q) & ! [S:$i,T:$i,U:$i]: ((~ (rR @ D @ T @ E) & ((vf @ A @ C) = (vf @ S @ U)) & ((vangle @ C @ B @ A) = (vangle @ U @ T @ S)) & (S = D) & (rpoint @ U) & (rpoint @ T) & (rpoint @ S) & ((vangle @ B @ A @ C) = (vangle @ T @ S @ U)) & ((vangle @ S @ U @ T) = (vangle @ A @ C @ B)) & ((vf @ A @ B) = (vf @ S @ T)) & ((vf @ B @ C) = (vf @ T @ U)) & (ron @ T @ Q) & (rS @ U @ F @ Q)) => (((vangle @ K @ L @ M) = (vangle @ N @ O @ P)) & ((vf @ G @ H) = (vf @ I @ J)))) & (ron @ D @ Q) & ? [S:$i]: ((S = N) & (rpoint @ S)) & ? [S:$i]: ((L = S) & (rpoint @ S)) & ? [S:$i]: ((rpoint @ S) & (K = S)) & ? [S:$i]: ((S = I) & (rpoint @ S)) & ? [S:$i]: ((G = S) & (rpoint @ S)) & ? [S:$i]: ((rpoint @ S) & (D = S)) & (B != C) & (B != A) & ? [S:$i]: ((rpoint @ S) & (S = A)) & ? [S:$i]: ((B = S) & (rpoint @ S)) & ? [S:$i]: ((rpoint @ S) & (C = S)) & (A != C) & ? [S:$i]: ((rpoint @ S) & (S = E)) & ? [S:$i]: ((rpoint @ S) & (S = F)) & ? [S:$i]: ((H = S) & (rpoint @ S)) & ? [S:$i]: ((J = S) & (rpoint @ S)) & ? [S:$i]: ((M = S) & (rpoint @ S)) & ? [S:$i]: ((rpoint @ S) & (O = S)) & ? [S:$i]: ((S = P) & (rpoint @ S)) & (rline @ R) & (ron @ E @ Q) & ~ (ron @ F @ Q))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(204), 0), imp(cond(axiom(204), 0)))')). 19.26/7.23 thf(645,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]: ((((vf @ G @ H) = (vf @ I @ J)) & ((vangle @ K @ L @ M) = (vangle @ N @ O @ P))) | ~ ((R = Q) & ! [S:$i,T:$i,U:$i]: ((~ (rR @ D @ T @ E) & ((vf @ A @ C) = (vf @ S @ U)) & ((vangle @ C @ B @ A) = (vangle @ U @ T @ S)) & (S = D) & (rpoint @ U) & (rpoint @ T) & (rpoint @ S) & ((vangle @ B @ A @ C) = (vangle @ T @ S @ U)) & ((vangle @ S @ U @ T) = (vangle @ A @ C @ B)) & ((vf @ A @ B) = (vf @ S @ T)) & ((vf @ B @ C) = (vf @ T @ U)) & (ron @ T @ Q) & (rS @ U @ F @ Q)) => (((vangle @ K @ L @ M) = (vangle @ N @ O @ P)) & ((vf @ G @ H) = (vf @ I @ J)))) & (ron @ D @ Q) & ? [S:$i]: ((S = N) & (rpoint @ S)) & ? [S:$i]: ((L = S) & (rpoint @ S)) & ? [S:$i]: ((rpoint @ S) & (K = S)) & ? [S:$i]: ((S = I) & (rpoint @ S)) & ? [S:$i]: ((G = S) & (rpoint @ S)) & ? [S:$i]: ((rpoint @ S) & (D = S)) & ~ (B = C) & ~ (B = A) & ? [S:$i]: ((rpoint @ S) & (S = A)) & ? [S:$i]: ((B = S) & (rpoint @ S)) & ? [S:$i]: ((rpoint @ S) & (C = S)) & ~ (A = C) & ? [S:$i]: ((rpoint @ S) & (S = E)) & ? [S:$i]: ((rpoint @ S) & (S = F)) & ? [S:$i]: ((H = S) & (rpoint @ S)) & ? [S:$i]: ((J = S) & (rpoint @ S)) & ? [S:$i]: ((M = S) & (rpoint @ S)) & ? [S:$i]: ((rpoint @ S) & (O = S)) & ? [S:$i]: ((S = P) & (rpoint @ S)) & (rline @ R) & (ron @ E @ Q) & ~ (ron @ F @ Q))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[77])). 19.26/7.23 thf(92,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i]: (((ron @ B @ D) & (F = G) & (rline @ E) & ? [H:$i]: ((rpoint @ H) & (C = H)) & ? [H:$i]: ((B = H) & (rpoint @ H)) & ? [H:$i]: ((rpoint @ H) & (H = A)) & (D = E) & (rcircle @ G) & (ron @ A @ D) & (ron @ C @ D) & (rinside @ A @ F) & (ron @ B @ F) & (ron @ C @ F) & (B != C)) => (rR @ A @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(119), 0), imp(cond(axiom(119), 0)))')). 19.26/7.23 thf(809,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i]: (((ron @ B @ D) & (F = G) & (rline @ E) & ? [H:$i]: ((rpoint @ H) & (C = H)) & ? [H:$i]: ((B = H) & (rpoint @ H)) & ? [H:$i]: ((rpoint @ H) & (H = A)) & (D = E) & (rcircle @ G) & (ron @ A @ D) & (ron @ C @ D) & (rinside @ A @ F) & (ron @ B @ F) & (ron @ C @ F) & ~ (B = C)) => (rR @ A @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[92])). 19.26/7.23 thf(5,axiom,((rpoint @ vd1409)),file('/export/starexec/sandbox/benchmark/theBenchmark.p','pred(406, 0)')). 19.26/7.23 thf(138,plain,((rpoint @ vd1409)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])). 19.26/7.23 thf(58,axiom,((! [A:$i,B:$i]: ((? [C:$i]: ((C = B) & (rpoint @ C)) & ? [C:$i]: ((rpoint @ C) & (C = A)) & (A != B)) => (? [C:$i]: ((ron @ B @ C) & (rcenter @ A @ C) & (rcircle @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(53), 0), imp(cond(axiom(53), 0)))')). 19.26/7.23 thf(479,plain,((! [A:$i,B:$i]: ((? [C:$i]: ((C = B) & (rpoint @ C)) & ? [C:$i]: ((rpoint @ C) & (C = A)) & ~ (A = B)) => (? [C:$i]: ((ron @ B @ C) & (rcenter @ A @ C) & (rcircle @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[58])). 19.26/7.23 thf(98,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: ((((vangle @ A @ C @ D) = vperp) <=> ((vangle @ D @ C @ B) = (vangle @ A @ C @ D))) <= ((E = F) & ? [G:$i]: ((D = G) & (rpoint @ G)) & ? [G:$i]: ((rpoint @ G) & (G = C)) & ? [G:$i]: ((rpoint @ G) & (A = G)) & ? [G:$i]: ((G = B) & (rpoint @ G)) & (rline @ F) & (rR @ C @ A @ B) & ~ (ron @ D @ E))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(192), 0), imp(cond(axiom(192), 0)))')). 19.26/7.23 thf(846,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: (((((vangle @ A @ C @ D) = vperp) => ((vangle @ D @ C @ B) = (vangle @ A @ C @ D))) & (((vangle @ D @ C @ B) = (vangle @ A @ C @ D)) => ((vangle @ A @ C @ D) = vperp))) | ~ ((E = F) & ? [G:$i]: ((D = G) & (rpoint @ G)) & ? [G:$i]: ((rpoint @ G) & (G = C)) & ? [G:$i]: ((rpoint @ G) & (A = G)) & ? [G:$i]: ((G = B) & (rpoint @ G)) & (rline @ F) & (rR @ C @ A @ B) & ~ (ron @ D @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[98])). 19.26/7.23 thf(26,axiom,((! [A:$i,B:$i]: ((rcenter @ A @ B) => (? [C:$i,D:$i]: ((D = B) & (rpoint @ C) & (A = C) & (rcircle @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(1), 0), imp(cond(axiom(1), 0)))')). 19.26/7.23 thf(249,plain,((! [A:$i,B:$i]: ((rcenter @ A @ B) => (? [C:$i,D:$i]: ((D = B) & (rpoint @ C) & (A = C) & (rcircle @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[26])). 19.26/7.23 thf(124,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((? [E:$i]: ((rpoint @ E) & (E = D)) & (rcircle @ B) & (B = A) & ? [E:$i]: ((C = E) & (rpoint @ E)) & (ron @ C @ A) & (ron @ D @ A)) => (? [E:$i]: ((E != D) & (C != E) & (rpoint @ E) & (ron @ E @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(45), 0), imp(cond(axiom(45), 0)))')). 19.26/7.23 thf(1083,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((? [E:$i]: ((rpoint @ E) & (E = D)) & (rcircle @ B) & (B = A) & ? [E:$i]: ((C = E) & (rpoint @ E)) & (ron @ C @ A) & (ron @ D @ A)) => (? [E:$i]: (~ (E = D) & ~ (C = E) & (rpoint @ E) & (ron @ E @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[124])). 19.26/7.23 thf(50,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((rless @ C @ A) | (C = A) | (rless @ A @ C)) <= ((C = D) & (B = A) & (rreal @ B) & (rreal @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(145), 0), imp(cond(axiom(145), 0)))')). 19.26/7.23 thf(408,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((rless @ C @ A) | (C = A) | (rless @ A @ C) | ~ ((C = D) & (B = A) & (rreal @ B) & (rreal @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[50])). 19.26/7.23 thf(37,axiom,((! [A:$i,B:$i]: (((vf @ A @ B) = (vf @ B @ A)) <= (? [C:$i]: ((rpoint @ C) & (B = C)) & ? [C:$i]: ((A = C) & (rpoint @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(166), 0), imp(cond(axiom(166), 0)))')). 19.26/7.23 thf(308,plain,((! [A:$i,B:$i]: (((vf @ A @ B) = (vf @ B @ A)) | ~ (? [C:$i]: ((rpoint @ C) & (B = C)) & ? [C:$i]: ((A = C) & (rpoint @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[37])). 19.26/7.23 thf(123,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((rS @ A @ C @ D) & ? [F:$i]: ((F = A) & (rpoint @ F)) & ? [F:$i]: ((B = F) & (rpoint @ F)) & ? [F:$i]: ((C = F) & (rpoint @ F)) & (rline @ E) & (D = E) & (rS @ A @ B @ D)) => (rS @ B @ C @ D)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(101), 0), imp(cond(axiom(101), 0)))')). 19.26/7.23 thf(1078,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((rS @ A @ C @ D) & ? [F:$i]: ((F = A) & (rpoint @ F)) & ? [F:$i]: ((B = F) & (rpoint @ F)) & ? [F:$i]: ((C = F) & (rpoint @ F)) & (rline @ E) & (D = E) & (rS @ A @ B @ D)) => (rS @ B @ C @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[123])). 19.26/7.23 thf(93,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: ((~ (? [G:$i]: ((rline @ G) & (ron @ D @ G) & (ron @ E @ G) & (ron @ F @ G))) & ((vf @ D @ F) = (vf @ A @ C)) & ? [G:$i]: ((G = F) & (rpoint @ G)) & ? [G:$i]: ((rpoint @ G) & (G = D)) & (B != A) & ? [G:$i]: ((rpoint @ G) & (C = G)) & ? [G:$i]: ((G = A) & (rpoint @ G)) & ? [G:$i]: ((G = B) & (rpoint @ G)) & (C != A) & (B != C) & ? [G:$i]: ((G = E) & (rpoint @ G)) & ((vf @ A @ B) = (vf @ D @ E)) & ((vangle @ E @ D @ F) = (vangle @ B @ A @ C))) => ((vf @ E @ F) = (vf @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(264), 0), 2)')). 19.26/7.23 thf(814,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: ((~ (? [G:$i]: ((rline @ G) & (ron @ D @ G) & (ron @ E @ G) & (ron @ F @ G))) & ((vf @ D @ F) = (vf @ A @ C)) & ? [G:$i]: ((G = F) & (rpoint @ G)) & ? [G:$i]: ((rpoint @ G) & (G = D)) & ~ (B = A) & ? [G:$i]: ((rpoint @ G) & (C = G)) & ? [G:$i]: ((G = A) & (rpoint @ G)) & ? [G:$i]: ((G = B) & (rpoint @ G)) & ~ (C = A) & ~ (B = C) & ? [G:$i]: ((G = E) & (rpoint @ G)) & ((vf @ A @ B) = (vf @ D @ E)) & ((vangle @ E @ D @ F) = (vangle @ B @ A @ C))) => ((vf @ E @ F) = (vf @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[93])). 19.26/7.23 thf(87,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((? [E:$i]: ((rS @ E @ C @ A) & (rpoint @ E) & (C != E))) <= ((C = D) & ~ (ron @ C @ A) & (rpoint @ D) & (rline @ B) & (B = A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(33), 0), imp(cond(axiom(33), 0)))')). 19.26/7.23 thf(747,plain,((! [A:$i,B:$i,C:$i,D:$i]: (? [E:$i]: ((rS @ E @ C @ A) & (rpoint @ E) & ~ (C = E)) | ~ ((C = D) & ~ (ron @ C @ A) & (rpoint @ D) & (rline @ B) & (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[87])). 19.26/7.23 thf(114,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i]: ((? [I:$i]: ((rR @ E @ I @ G) & (ron @ I @ A) & (rpoint @ I) & (ron @ I @ C))) <= ((E != G) & (ron @ G @ C) & (H = G) & (rpoint @ H) & (ron @ E @ C) & (C = D) & (B = A) & (rcircle @ B) & (rline @ D) & (rpoint @ F) & (F = E) & (rinside @ E @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(63), 0), imp(cond(axiom(63), 0)))')). 19.26/7.23 thf(1001,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i]: (? [I:$i]: ((rR @ E @ I @ G) & (ron @ I @ A) & (rpoint @ I) & (ron @ I @ C)) | ~ (~ (E = G) & (ron @ G @ C) & (H = G) & (rpoint @ H) & (ron @ E @ C) & (C = D) & (B = A) & (rcircle @ B) & (rline @ D) & (rpoint @ F) & (F = E) & (rinside @ E @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[114])). 19.26/7.23 thf(97,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((ron @ C @ D) & (ron @ A @ D) & (rline @ E) & ? [F:$i]: ((rpoint @ F) & (C = F)) & ? [F:$i]: ((rpoint @ F) & (A = F)) & ? [F:$i]: ((rpoint @ F) & (F = B)) & (rR @ B @ A @ C) & (D = E)) => (ron @ B @ D)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(85), 0), imp(cond(axiom(85), 0)))')). 19.26/7.23 thf(841,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((ron @ C @ D) & (ron @ A @ D) & (rline @ E) & ? [F:$i]: ((rpoint @ F) & (C = F)) & ? [F:$i]: ((rpoint @ F) & (A = F)) & ? [F:$i]: ((rpoint @ F) & (F = B)) & (rR @ B @ A @ C) & (D = E)) => (ron @ B @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[97])). 19.26/7.23 thf(120,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((~ (ron @ B @ D) & ~ (ron @ B @ D)) <= ((rR @ C @ A @ B) & (D = E) & ? [F:$i]: ((rpoint @ F) & (F = C)) & ? [F:$i]: ((F = B) & (rpoint @ F)) & ? [F:$i]: ((F = A) & (rpoint @ F)) & (rcircle @ E) & ((ron @ A @ D) | (rinside @ A @ D)) & ~ (rinside @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(123), 0), imp(cond(axiom(123), 0)))')). 19.26/7.23 thf(1046,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (~ (ron @ B @ D) | ~ ((rR @ C @ A @ B) & (D = E) & ? [F:$i]: ((rpoint @ F) & (F = C)) & ? [F:$i]: ((F = B) & (rpoint @ F)) & ? [F:$i]: ((F = A) & (rpoint @ F)) & (rcircle @ E) & ((ron @ A @ D) | (rinside @ A @ D)) & ~ (rinside @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[120])). 19.26/7.23 thf(40,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((rtriangle @ D) & (D = (vtriangle @ A @ B @ C))) => (? [E:$i]: ((rpoint @ E) & (E = A)) & ? [E:$i]: ((E = B) & (rpoint @ E)) & ? [E:$i]: ((C = E) & (rpoint @ E)) & (A != B) & (A != C) & (C != B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(3), 0), imp(cond(axiom(3), 0)))')). 19.26/7.23 thf(320,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((rtriangle @ D) & (D = (vtriangle @ A @ B @ C))) => (? [E:$i]: ((rpoint @ E) & (E = A)) & ? [E:$i]: ((E = B) & (rpoint @ E)) & ? [E:$i]: ((C = E) & (rpoint @ E)) & ~ (A = B) & ~ (A = C) & ~ (C = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[40])). 19.26/7.23 thf(16,axiom,((! [A:$i,B:$i]: ((! [C:$i,D:$i]: (((vf @ C @ (vskolem1078 @ C @ D @ A @ B)) = (vf @ A @ B)) <= ((C = D) & (C != B) & (rpoint @ D) & (A != C)))) <= (? [C:$i]: ((rpoint @ C) & (C = B)) & ? [C:$i]: ((rpoint @ C) & (C = A)) & (A != B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(219), 0), 0)')). 19.26/7.23 thf(184,plain,((! [A:$i,B:$i]: (! [C:$i,D:$i]: (((vf @ C @ (vskolem1078 @ C @ D @ A @ B)) = (vf @ A @ B)) | ~ ((C = D) & ~ (C = B) & (rpoint @ D) & ~ (A = C))) | ~ (? [C:$i]: ((rpoint @ C) & (C = B)) & ? [C:$i]: ((rpoint @ C) & (C = A)) & ~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[16])). 19.26/7.23 thf(76,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((? [E:$i]: ((rR @ E @ C @ D) & (rpoint @ E))) <= (? [E:$i]: ((rpoint @ E) & (E = D)) & ? [E:$i]: ((C = E) & (rpoint @ E)) & (rline @ B) & (B = A) & (ron @ C @ A) & (ron @ D @ A) & (C != D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(23), 0), imp(cond(axiom(23), 0)))')). 19.26/7.23 thf(638,plain,((! [A:$i,B:$i,C:$i,D:$i]: (? [E:$i]: ((rR @ E @ C @ D) & (rpoint @ E)) | ~ (? [E:$i]: ((rpoint @ E) & (E = D)) & ? [E:$i]: ((C = E) & (rpoint @ E)) & (rline @ B) & (B = A) & (ron @ C @ A) & (ron @ D @ A) & ~ (C = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[76])). 19.26/7.23 thf(72,axiom,(((vf @ vd1399 @ vd1409) = (vf @ vd1399 @ vd1401))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conjunct1(conjunct2(406)), 1411, 0)')). 19.26/7.23 thf(606,plain,(((vf @ vd1399 @ vd1409) = (vf @ vd1399 @ vd1401))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[72])). 19.26/7.23 thf(9,axiom,((! [A:$i,B:$i]: ((v0 = (vg @ A @ A @ B)) <= (? [C:$i]: ((rpoint @ C) & (C = A)) & ? [C:$i]: ((rpoint @ C) & (B = C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(172), 0), imp(cond(axiom(172), 0)))')). 19.26/7.23 thf(152,plain,((! [A:$i,B:$i]: ((v0 = (vg @ A @ A @ B)) | ~ (? [C:$i]: ((rpoint @ C) & (C = A)) & ? [C:$i]: ((rpoint @ C) & (B = C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[9])). 19.26/7.23 thf(39,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((rR @ D @ A @ C) <= (? [E:$i]: ((rpoint @ E) & (E = B)) & ? [E:$i]: ((E = A) & (rpoint @ E)) & ? [E:$i]: ((E = C) & (rpoint @ E)) & ? [E:$i]: ((D = E) & (rpoint @ E)) & (rR @ B @ A @ C) & (rR @ D @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(87), 0), imp(cond(axiom(87), 0)))')). 19.26/7.23 thf(316,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((rR @ D @ A @ C) | ~ (? [E:$i]: ((rpoint @ E) & (E = B)) & ? [E:$i]: ((E = A) & (rpoint @ E)) & ? [E:$i]: ((E = C) & (rpoint @ E)) & ? [E:$i]: ((D = E) & (rpoint @ E)) & (rR @ B @ A @ C) & (rR @ D @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[39])). 19.26/7.23 thf(55,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((rintersect @ C @ A) & (D = C) & (B = A) & (rcircle @ B) & (rline @ D)) => (? [E:$i]: ((rpoint @ E) & (ron @ E @ C) & (ron @ E @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(57), 0), imp(cond(axiom(57), 0)))')). 19.26/7.23 thf(443,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((rintersect @ C @ A) & (D = C) & (B = A) & (rcircle @ B) & (rline @ D)) => (? [E:$i]: ((rpoint @ E) & (ron @ E @ C) & (ron @ E @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[55])). 19.26/7.23 thf(46,axiom,((! [A:$i,B:$i,C:$i]: (((rleq @ v0 @ (vangle @ A @ B @ C)) & (rleq @ (vangle @ A @ B @ C) @ (vplus @ vperp @ vperp))) <= (? [D:$i]: ((rpoint @ D) & (B = D)) & ? [D:$i]: ((D = A) & (rpoint @ D)) & ? [D:$i]: ((D = C) & (rpoint @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(170), 0), imp(cond(axiom(170), 0)))')). 19.26/7.23 thf(376,plain,((! [A:$i,B:$i,C:$i]: (((rleq @ v0 @ (vangle @ A @ B @ C)) & (rleq @ (vangle @ A @ B @ C) @ (vplus @ vperp @ vperp))) | ~ (? [D:$i]: ((rpoint @ D) & (B = D)) & ? [D:$i]: ((D = A) & (rpoint @ D)) & ? [D:$i]: ((D = C) & (rpoint @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[46])). 19.26/7.23 thf(68,axiom,(((vf @ vd1400 @ vd1401) = (vf @ vd1400 @ vd1409))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conjunct1(conjunct2(conjunct2(406))), 1412, 0)')). 19.26/7.23 thf(574,plain,(((vf @ vd1400 @ vd1401) = (vf @ vd1400 @ vd1409))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[68])). 19.26/7.23 thf(3,axiom,((rreal @ vd684)),file('/export/starexec/sandbox/benchmark/theBenchmark.p','pred(axiom(137), 1)')). 19.26/7.23 thf(133,plain,((rreal @ vd684)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])). 19.26/7.23 thf(29,axiom,((! [A:$i,B:$i]: ((? [C:$i]: ((rinside @ C @ A) & (rpoint @ C))) <= ((A = B) & (rcircle @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(47), 0), imp(cond(axiom(47), 0)))')). 19.26/7.23 thf(265,plain,((! [A:$i,B:$i]: (? [C:$i]: ((rinside @ C @ A) & (rpoint @ C)) | ~ ((A = B) & (rcircle @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[29])). 19.26/7.23 thf(61,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: ((((vangle @ B @ A @ C) = (vangle @ E @ D @ F)) & ((vf @ A @ C) = (vf @ D @ F)) & ? [G:$i]: ((G = E) & (rpoint @ G)) & (C != B) & (A != C) & ? [G:$i]: ((rpoint @ G) & (G = C)) & ? [G:$i]: ((rpoint @ G) & (G = A)) & ? [G:$i]: ((G = B) & (rpoint @ G)) & (B != A) & ? [G:$i]: ((rpoint @ G) & (G = D)) & ? [G:$i]: ((rpoint @ G) & (G = F)) & ((vf @ D @ E) = (vf @ A @ B)) & ~ (? [G:$i]: ((ron @ E @ G) & (rline @ G) & (ron @ D @ G) & (ron @ F @ G)))) => ((vangle @ D @ F @ E) = (vangle @ A @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(264), 0), 0)')). 19.26/7.23 thf(507,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: ((((vangle @ B @ A @ C) = (vangle @ E @ D @ F)) & ((vf @ A @ C) = (vf @ D @ F)) & ? [G:$i]: ((G = E) & (rpoint @ G)) & ~ (C = B) & ~ (A = C) & ? [G:$i]: ((rpoint @ G) & (G = C)) & ? [G:$i]: ((rpoint @ G) & (G = A)) & ? [G:$i]: ((G = B) & (rpoint @ G)) & ~ (B = A) & ? [G:$i]: ((rpoint @ G) & (G = D)) & ? [G:$i]: ((rpoint @ G) & (G = F)) & ((vf @ D @ E) = (vf @ A @ B)) & ~ (? [G:$i]: ((ron @ E @ G) & (rline @ G) & (ron @ D @ G) & (ron @ F @ G)))) => ((vangle @ D @ F @ E) = (vangle @ A @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[61])). 19.26/7.23 thf(38,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((D = C) <= ((rcenter @ D @ A) & (rcenter @ C @ A) & (A = B) & (rcircle @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(75), 0), imp(cond(axiom(75), 0)))')). 19.26/7.23 thf(312,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((D = C) | ~ ((rcenter @ D @ A) & (rcenter @ C @ A) & (A = B) & (rcircle @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[38])). 19.26/7.23 thf(36,axiom,((rpoint @ vd14)),file('/export/starexec/sandbox/benchmark/theBenchmark.p','pred(axiom(5), 0)')). 19.26/7.23 thf(307,plain,((rpoint @ vd14)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[36])). 19.26/7.23 thf(109,axiom,((! [A:$i,B:$i]: ((? [C:$i]: (~ (ron @ C @ A) & ~ (rinside @ C @ A) & (rpoint @ C))) <= ((rcircle @ B) & (B = A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(49), 0), imp(cond(axiom(49), 0)))')). 19.26/7.23 thf(942,plain,((! [A:$i,B:$i]: (? [C:$i]: (~ (ron @ C @ A) & ~ (rinside @ C @ A) & (rpoint @ C)) | ~ ((rcircle @ B) & (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[109])). 19.26/7.23 thf(54,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((ron @ B @ D) & (rinside @ B @ C) & ? [E:$i]: ((E = A) & (rpoint @ E)) & ? [E:$i]: ((rpoint @ E) & (E = B)) & (ron @ A @ C) & (rinside @ A @ D)) => (rintersect @ C @ D)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(135), 0), imp(cond(axiom(135), 0)))')). 19.26/7.23 thf(439,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((ron @ B @ D) & (rinside @ B @ C) & ? [E:$i]: ((E = A) & (rpoint @ E)) & ? [E:$i]: ((rpoint @ E) & (E = B)) & (ron @ A @ C) & (rinside @ A @ D)) => (rintersect @ C @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[54])). 19.26/7.23 thf(119,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((ron @ A @ D) & (ron @ A @ C) & ? [E:$i]: ((rline @ E) & (E = D)) & ? [E:$i]: ((rline @ E) & (C = E)) & ? [E:$i]: ((rpoint @ E) & (A = E)) & ? [E:$i]: ((rpoint @ E) & (B = E)) & (A != B) & (ron @ B @ C) & (ron @ B @ D)) => (D = C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(73), 0), imp(cond(axiom(73), 0)))')). 19.26/7.23 thf(1042,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((ron @ A @ D) & (ron @ A @ C) & ? [E:$i]: ((rline @ E) & (E = D)) & ? [E:$i]: ((rline @ E) & (C = E)) & ? [E:$i]: ((rpoint @ E) & (A = E)) & ? [E:$i]: ((rpoint @ E) & (B = E)) & ~ (A = B) & (ron @ B @ C) & (ron @ B @ D)) => (D = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[119])). 19.26/7.23 thf(28,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: (((F = E) & (rpoint @ F) & (D = C) & (rpoint @ D) & (rpoint @ B) & (B = A)) => (rgeq @ (vg @ A @ C @ E) @ v0)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(174), 0), imp(cond(axiom(174), 0)))')). 19.26/7.23 thf(260,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: (((F = E) & (rpoint @ F) & (D = C) & (rpoint @ D) & (rpoint @ B) & (B = A)) => (rgeq @ (vg @ A @ C @ E) @ v0)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[28])). 19.26/7.23 thf(41,axiom,((! [A:$i,B:$i]: ((rinside @ A @ B) <= (rcenter @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(77), 0), imp(cond(axiom(77), 0)))')). 19.26/7.23 thf(349,plain,((! [A:$i,B:$i]: ((rinside @ A @ B) | ~ (rcenter @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[41])). 19.26/7.23 thf(71,axiom,((! [A:$i,B:$i]: ((? [C:$i]: ((ron @ C @ A) & (rpoint @ C))) <= ((rline @ B) & (B = A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(15), 0), imp(cond(axiom(15), 0)))')). 19.26/7.23 thf(598,plain,((! [A:$i,B:$i]: (? [C:$i]: ((ron @ C @ A) & (rpoint @ C)) | ~ ((rline @ B) & (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[71])). 19.26/7.23 thf(49,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((? [E:$i]: ((E != D) & (C != E) & (E != B) & (rpoint @ E) & (E != A))) <= (? [E:$i]: ((rpoint @ E) & (E = D)) & ? [E:$i]: ((C = E) & (rpoint @ E)) & ? [E:$i]: ((B = E) & (rpoint @ E)) & ? [E:$i]: ((A = E) & (rpoint @ E)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(13), 0), imp(cond(axiom(13), 0)))')). 19.26/7.23 thf(392,plain,((! [A:$i,B:$i,C:$i,D:$i]: (? [E:$i]: (~ (E = D) & ~ (C = E) & ~ (E = B) & (rpoint @ E) & ~ (E = A)) | ~ (? [E:$i]: ((rpoint @ E) & (E = D)) & ? [E:$i]: ((C = E) & (rpoint @ E)) & ? [E:$i]: ((B = E) & (rpoint @ E)) & ? [E:$i]: ((A = E) & (rpoint @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[49])). 19.26/7.23 thf(78,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((ron @ B @ D) & ? [E:$i]: ((rpoint @ E) & (E = A)) & ? [E:$i]: ((rpoint @ E) & (B = E)) & (rcenter @ C @ D)) => ((rless @ (vf @ C @ A) @ (vf @ C @ B)) <=> (rinside @ A @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(186), 0), imp(cond(axiom(186), 0)))')). 19.26/7.23 thf(693,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((ron @ B @ D) & ? [E:$i]: ((rpoint @ E) & (E = A)) & ? [E:$i]: ((rpoint @ E) & (B = E)) & (rcenter @ C @ D)) => (((rless @ (vf @ C @ A) @ (vf @ C @ B)) => (rinside @ A @ D)) & ((rinside @ A @ D) => (rless @ (vf @ C @ A) @ (vf @ C @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[78])). 19.26/7.23 thf(75,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: (((rR @ C @ A @ B) <=> ((vplus @ (vg @ A @ C @ D) @ (vg @ D @ C @ B)) = (vg @ A @ D @ B))) <= (~ (ron @ D @ E) & (rline @ F) & (C != D) & (C != A) & (B != A) & ? [G:$i]: ((G = D) & (rpoint @ G)) & ? [G:$i]: ((C = G) & (rpoint @ G)) & ? [G:$i]: ((G = B) & (rpoint @ G)) & ? [G:$i]: ((A = G) & (rpoint @ G)) & (D != A) & (C != B) & (D != B) & (F = E))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(202), 0), imp(cond(axiom(202), 0)))')). 19.26/7.23 thf(630,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: ((((rR @ C @ A @ B) => ((vplus @ (vg @ A @ C @ D) @ (vg @ D @ C @ B)) = (vg @ A @ D @ B))) & (((vplus @ (vg @ A @ C @ D) @ (vg @ D @ C @ B)) = (vg @ A @ D @ B)) => (rR @ C @ A @ B))) | ~ (~ (ron @ D @ E) & (rline @ F) & ~ (C = D) & ~ (C = A) & ~ (B = A) & ? [G:$i]: ((G = D) & (rpoint @ G)) & ? [G:$i]: ((C = G) & (rpoint @ G)) & ? [G:$i]: ((G = B) & (rpoint @ G)) & ? [G:$i]: ((A = G) & (rpoint @ G)) & ~ (D = A) & ~ (C = B) & ~ (D = B) & (F = E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[75])). 19.26/7.23 thf(12,axiom,((! [A:$i,B:$i,C:$i]: (((vangle @ A @ B @ C) = (vangle @ C @ B @ A)) <= ((B != A) & ? [D:$i]: ((A = D) & (rpoint @ D)) & ? [D:$i]: ((D = B) & (rpoint @ D)) & ? [D:$i]: ((rpoint @ D) & (D = C)) & (C != A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(168), 0), imp(cond(axiom(168), 0)))')). 19.26/7.23 thf(165,plain,((! [A:$i,B:$i,C:$i]: (((vangle @ A @ B @ C) = (vangle @ C @ B @ A)) | ~ (~ (B = A) & ? [D:$i]: ((A = D) & (rpoint @ D)) & ? [D:$i]: ((D = B) & (rpoint @ D)) & ? [D:$i]: ((rpoint @ D) & (D = C)) & ~ (C = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[12])). 19.26/7.23 thf(81,axiom,(((vangle @ vd1399 @ vd1409 @ vd1401) = (vangle @ vd1399 @ vd1401 @ vd1409))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(407, 1414, 0)')). 19.26/7.23 thf(710,plain,(((vangle @ vd1399 @ vd1409 @ vd1401) = (vangle @ vd1399 @ vd1401 @ vd1409))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[81])). 19.26/7.23 thf(10,axiom,((! [A:$i,B:$i,C:$i]: ((((vf @ A @ C) = (vf @ A @ B)) & (B != C) & ? [D:$i]: ((rpoint @ D) & (C = D)) & ? [D:$i]: ((A = D) & (rpoint @ D)) & ? [D:$i]: ((B = D) & (rpoint @ D)) & (A != B) & (A != C)) => (! [D:$i,E:$i,F:$i,G:$i]: (((F = G) & (rR @ C @ A @ F) & (rR @ B @ A @ D) & (rpoint @ E) & (rpoint @ G) & (D = E)) => ((vangle @ B @ C @ F) = (vangle @ C @ B @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(340), 0), 0)')). 19.26/7.23 thf(156,plain,((! [A:$i,B:$i,C:$i]: ((((vf @ A @ C) = (vf @ A @ B)) & ~ (B = C) & ? [D:$i]: ((rpoint @ D) & (C = D)) & ? [D:$i]: ((A = D) & (rpoint @ D)) & ? [D:$i]: ((B = D) & (rpoint @ D)) & ~ (A = B) & ~ (A = C)) => (! [D:$i,E:$i,F:$i,G:$i]: (((F = G) & (rR @ C @ A @ F) & (rR @ B @ A @ D) & (rpoint @ E) & (rpoint @ G) & (D = E)) => ((vangle @ B @ C @ F) = (vangle @ C @ B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[10])). 19.26/7.23 thf(122,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((~ (? [E:$i]: (rS @ A @ B @ E)) & ((rinside @ B @ C) | (ron @ B @ C)) & ((ron @ A @ C) | (rinside @ A @ C)) & ? [E:$i]: ((rpoint @ E) & (A = E)) & ? [E:$i]: ((E = B) & (rpoint @ E)) & ? [E:$i]: ((E = C) & (rcircle @ E)) & ? [E:$i]: ((rcircle @ E) & (E = D))) => (? [E:$i]: (rintersect @ E @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(129), 0), imp(cond(axiom(129), 0)))')). 19.26/7.23 thf(1064,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((~ (? [E:$i]: (rS @ A @ B @ E)) & ((rinside @ B @ C) | (ron @ B @ C)) & ((ron @ A @ C) | (rinside @ A @ C)) & ? [E:$i]: ((rpoint @ E) & (A = E)) & ? [E:$i]: ((E = B) & (rpoint @ E)) & ? [E:$i]: ((E = C) & (rcircle @ E)) & ? [E:$i]: ((rcircle @ E) & (E = D))) => (? [E:$i]: (rintersect @ E @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[122])). 19.26/7.23 thf(125,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((~ (ron @ B @ D) & (E = D) & ? [F:$i]: ((C = F) & (rpoint @ F)) & ? [F:$i]: ((rpoint @ F) & (F = B)) & ? [F:$i]: ((rpoint @ F) & (A = F)) & (rline @ E) & (rR @ B @ A @ C) & (ron @ A @ D)) => (rS @ B @ C @ D)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(107), 0), imp(cond(axiom(107), 0)))')). 19.26/7.23 thf(1096,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((~ (ron @ B @ D) & (E = D) & ? [F:$i]: ((C = F) & (rpoint @ F)) & ? [F:$i]: ((rpoint @ F) & (F = B)) & ? [F:$i]: ((rpoint @ F) & (A = F)) & (rline @ E) & (rR @ B @ A @ C) & (ron @ A @ D)) => (rS @ B @ C @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[125])). 19.26/7.23 thf(17,axiom,((! [A:$i,B:$i,C:$i]: ((! [D:$i,E:$i,F:$i,G:$i]: (((E = D) & (F = G) & (rR @ B @ A @ D) & (rpoint @ E) & (rpoint @ G) & (rR @ C @ A @ F)) => ((vangle @ A @ C @ B) = (vangle @ A @ B @ C)))) <= (((vf @ A @ C) = (vf @ A @ B)) & (C != A) & (A != B) & ? [D:$i]: ((rpoint @ D) & (C = D)) & ? [D:$i]: ((rpoint @ D) & (B = D)) & ? [D:$i]: ((rpoint @ D) & (D = A)) & (C != B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(340), 0), 1)')). 19.26/7.23 thf(188,plain,((! [A:$i,B:$i,C:$i]: (! [D:$i,E:$i,F:$i,G:$i]: (((E = D) & (F = G) & (rR @ B @ A @ D) & (rpoint @ E) & (rpoint @ G) & (rR @ C @ A @ F)) => ((vangle @ A @ C @ B) = (vangle @ A @ B @ C))) | ~ (((vf @ A @ C) = (vf @ A @ B)) & ~ (C = A) & ~ (A = B) & ? [D:$i]: ((rpoint @ D) & (C = D)) & ? [D:$i]: ((rpoint @ D) & (B = D)) & ? [D:$i]: ((rpoint @ D) & (D = A)) & ~ (C = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[17])). 19.26/7.23 thf(48,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((vf @ C @ (vskolem1052 @ A @ B @ C @ D)) = (vf @ (vskolem1052 @ A @ B @ C @ D) @ A)) <= ((C = D) & (A != C) & (B = A) & (rpoint @ B) & (rpoint @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(206), 0), 0)')). 19.26/7.23 thf(388,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((vf @ C @ (vskolem1052 @ A @ B @ C @ D)) = (vf @ (vskolem1052 @ A @ B @ C @ D) @ A)) | ~ ((C = D) & ~ (A = C) & (B = A) & (rpoint @ B) & (rpoint @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[48])). 19.26/7.23 thf(13,axiom,((! [A:$i,B:$i]: ((! [C:$i,D:$i]: (((C = D) & (B != C) & (C != A) & (rpoint @ D)) => (rpoint @ (vskolem1078 @ C @ D @ A @ B)))) <= ((A != B) & ? [C:$i]: ((rpoint @ C) & (B = C)) & ? [C:$i]: ((C = A) & (rpoint @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(219), 0), 1)')). 19.26/7.23 thf(169,plain,((! [A:$i,B:$i]: (! [C:$i,D:$i]: (((C = D) & ~ (B = C) & ~ (C = A) & (rpoint @ D)) => (rpoint @ (vskolem1078 @ C @ D @ A @ B))) | ~ (~ (A = B) & ? [C:$i]: ((rpoint @ C) & (B = C)) & ? [C:$i]: ((C = A) & (rpoint @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[13])). 19.26/7.23 thf(27,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((rR @ B @ A @ D) <= ((rR @ C @ B @ D) & ? [E:$i]: ((D = E) & (rpoint @ E)) & ? [E:$i]: ((E = C) & (rpoint @ E)) & ? [E:$i]: ((rpoint @ E) & (E = A)) & ? [E:$i]: ((rpoint @ E) & (E = B)) & (rR @ B @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(89), 0), imp(cond(axiom(89), 0)))')). 19.26/7.23 thf(256,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((rR @ B @ A @ D) | ~ ((rR @ C @ B @ D) & ? [E:$i]: ((D = E) & (rpoint @ E)) & ? [E:$i]: ((E = C) & (rpoint @ E)) & ? [E:$i]: ((rpoint @ E) & (E = A)) & ? [E:$i]: ((rpoint @ E) & (E = B)) & (rR @ B @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[27])). 19.26/7.23 thf(18,axiom,((! [A:$i,B:$i]: ((? [C:$i]: ((rpoint @ C) & (C != A) & (C != B))) <= (? [C:$i]: ((A = C) & (rpoint @ C)) & ? [C:$i]: ((rpoint @ C) & (B = C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(9), 0), imp(cond(axiom(9), 0)))')). 19.26/7.23 thf(193,plain,((! [A:$i,B:$i]: (? [C:$i]: ((rpoint @ C) & ~ (C = A) & ~ (C = B)) | ~ (? [C:$i]: ((A = C) & (rpoint @ C)) & ? [C:$i]: ((rpoint @ C) & (B = C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[18])). 19.26/7.23 thf(59,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i]: ((? [H:$i]: ((ron @ H @ B) & (ron @ H @ A) & (rpoint @ H) & ~ (rS @ H @ G @ C))) <= (~ (ron @ G @ C) & (rcenter @ E @ A) & (rintersect @ A @ B) & (C = D) & (rline @ D) & ? [H:$i]: ((rcircle @ H) & (H = A)) & ? [H:$i]: ((rcircle @ H) & (H = B)) & (rcenter @ F @ B) & (ron @ E @ C) & (ron @ F @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(71), 0), imp(cond(axiom(71), 0)))')). 19.26/7.23 thf(489,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i]: (? [H:$i]: ((ron @ H @ B) & (ron @ H @ A) & (rpoint @ H) & ~ (rS @ H @ G @ C)) | ~ (~ (ron @ G @ C) & (rcenter @ E @ A) & (rintersect @ A @ B) & (C = D) & (rline @ D) & ? [H:$i]: ((rcircle @ H) & (H = A)) & ? [H:$i]: ((rcircle @ H) & (H = B)) & (rcenter @ F @ B) & (ron @ E @ C) & (ron @ F @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[59])). 19.26/7.23 thf(70,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((? [E:$i]: (~ (rS @ E @ C @ A) & (rpoint @ E))) <= (~ (ron @ C @ A) & (A = B) & (rline @ B) & (rpoint @ D) & (D = C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(39), 0), imp(cond(axiom(39), 0)))')). 19.26/7.23 thf(590,plain,((! [A:$i,B:$i,C:$i,D:$i]: (? [E:$i]: (~ (rS @ E @ C @ A) & (rpoint @ E)) | ~ (~ (ron @ C @ A) & (A = B) & (rline @ B) & (rpoint @ D) & (D = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[70])). 19.26/7.23 thf(96,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((D = E) <= (((vf @ C @ A) = (vf @ C @ B)) & (ron @ A @ D) & (rcenter @ C @ D) & ? [F:$i]: ((rpoint @ F) & (F = A)) & ? [F:$i]: ((B = F) & (rpoint @ F)) & (rcenter @ C @ E) & (ron @ B @ E))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(182), 0), imp(cond(axiom(182), 0)))')). 19.26/7.23 thf(837,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((D = E) | ~ (((vf @ C @ A) = (vf @ C @ B)) & (ron @ A @ D) & (rcenter @ C @ D) & ? [F:$i]: ((rpoint @ F) & (F = A)) & ? [F:$i]: ((B = F) & (rpoint @ F)) & (rcenter @ C @ E) & (ron @ B @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[96])). 19.26/7.23 thf(112,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((? [E:$i]: ((C != E) & (ron @ E @ A) & (rpoint @ E))) <= ((ron @ C @ A) & (B = A) & (rline @ B) & (rpoint @ D) & (D = C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(17), 0), imp(cond(axiom(17), 0)))')). 19.26/7.23 thf(985,plain,((! [A:$i,B:$i,C:$i,D:$i]: (? [E:$i]: (~ (C = E) & (ron @ E @ A) & (rpoint @ E)) | ~ ((ron @ C @ A) & (B = A) & (rline @ B) & (rpoint @ D) & (D = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[112])). 19.26/7.23 thf(14,axiom,((! [A:$i,B:$i]: ((((vf @ A @ B) = v0) <=> (A = B)) <= (? [C:$i]: ((rpoint @ C) & (C = A)) & ? [C:$i]: ((rpoint @ C) & (C = B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(162), 0), imp(cond(axiom(162), 0)))')). 19.26/7.23 thf(173,plain,((! [A:$i,B:$i]: (((((vf @ A @ B) = v0) => (A = B)) & ((A = B) => ((vf @ A @ B) = v0))) | ~ (? [C:$i]: ((rpoint @ C) & (C = A)) & ? [C:$i]: ((rpoint @ C) & (C = B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[14])). 19.26/7.23 thf(67,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((ron @ C @ D) <= ((E = D) & (rline @ E) & ? [F:$i]: ((rpoint @ F) & (C = F)) & ? [F:$i]: ((B = F) & (rpoint @ F)) & ? [F:$i]: ((rpoint @ F) & (A = F)) & (rR @ B @ A @ C) & (ron @ A @ D) & (ron @ B @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(83), 0), imp(cond(axiom(83), 0)))')). 19.26/7.23 thf(569,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((ron @ C @ D) | ~ ((E = D) & (rline @ E) & ? [F:$i]: ((rpoint @ F) & (C = F)) & ? [F:$i]: ((B = F) & (rpoint @ F)) & ? [F:$i]: ((rpoint @ F) & (A = F)) & (rR @ B @ A @ C) & (ron @ A @ D) & (ron @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[67])). 19.26/7.23 thf(4,axiom,((! [A:$i,B:$i]: ((rleq @ v0 @ (vf @ A @ B)) <= (? [C:$i]: ((A = C) & (rpoint @ C)) & ? [C:$i]: ((C = B) & (rpoint @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(164), 0), imp(cond(axiom(164), 0)))')). 19.26/7.23 thf(134,plain,((! [A:$i,B:$i]: ((rleq @ v0 @ (vf @ A @ B)) | ~ (? [C:$i]: ((A = C) & (rpoint @ C)) & ? [C:$i]: ((C = B) & (rpoint @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])). 19.26/7.23 thf(108,axiom,(((ron @ vd1399 @ vd1416) & (ron @ vd1401 @ vd1416) & (rline @ vd1416))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','and(pred(s2(plural(the(408))), 0), and(pred(s1(plural(the(408))), 0), pred(the(408), 0)))')). 19.26/7.23 thf(938,plain,(((ron @ vd1399 @ vd1416) & (ron @ vd1401 @ vd1416) & (rline @ vd1416))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[108])). 19.26/7.23 thf(105,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: ((rintersect @ C @ E) <= ((E = F) & (ron @ A @ E) & (rline @ F) & ~ (rS @ A @ B @ C) & ? [G:$i]: ((G = A) & (rpoint @ G)) & ? [G:$i]: ((B = G) & (rpoint @ G)) & (rline @ D) & (ron @ B @ E) & (D = C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(127), 0), imp(cond(axiom(127), 0)))')). 19.26/7.23 thf(921,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: ((rintersect @ C @ E) | ~ ((E = F) & (ron @ A @ E) & (rline @ F) & ~ (rS @ A @ B @ C) & ? [G:$i]: ((G = A) & (rpoint @ G)) & ? [G:$i]: ((B = G) & (rpoint @ G)) & (rline @ D) & (ron @ B @ E) & (D = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[105])). 19.26/7.23 thf(121,axiom,((! [A:$i,B:$i]: ((? [C:$i]: ((ron @ B @ C) & (ron @ A @ C) & (rline @ C))) <= ((B != A) & ? [C:$i]: ((rpoint @ C) & (C = A)) & ? [C:$i]: ((rpoint @ C) & (B = C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(51), 0), imp(cond(axiom(51), 0)))')). 19.26/7.23 thf(1054,plain,((! [A:$i,B:$i]: (? [C:$i]: ((ron @ B @ C) & (ron @ A @ C) & (rline @ C)) | ~ (~ (B = A) & ? [C:$i]: ((rpoint @ C) & (C = A)) & ? [C:$i]: ((rpoint @ C) & (B = C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[121])). 19.26/7.23 thf(63,axiom,((rS @ vd1401 @ vd1409 @ vd1406)),file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conjunct1(406), 1410, 0)')). 19.26/7.23 thf(530,plain,((rS @ vd1401 @ vd1409 @ vd1406)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[63])). 19.26/7.23 thf(110,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((rR @ E @ C @ D) & (ron @ D @ A) & (ron @ C @ A) & ? [F:$i]: ((C = F) & (rpoint @ F)) & (B = A) & (rline @ B) & ? [F:$i]: ((rpoint @ F) & (F = D)) & ? [F:$i]: ((E = F) & (rpoint @ F))) => (? [F:$i]: ((E != F) & (rR @ F @ C @ D) & (rpoint @ F)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(25), 0), imp(cond(axiom(25), 0)))')). 19.26/7.23 thf(953,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((rR @ E @ C @ D) & (ron @ D @ A) & (ron @ C @ A) & ? [F:$i]: ((C = F) & (rpoint @ F)) & (B = A) & (rline @ B) & ? [F:$i]: ((rpoint @ F) & (F = D)) & ? [F:$i]: ((E = F) & (rpoint @ F))) => (? [F:$i]: (~ (E = F) & (rR @ F @ C @ D) & (rpoint @ F)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[110])). 19.26/7.23 thf(106,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((rline @ E) & ? [F:$i]: ((rpoint @ F) & (F = C)) & ? [F:$i]: ((F = B) & (rpoint @ F)) & ? [F:$i]: ((F = A) & (rpoint @ F)) & (E = D) & (rR @ B @ A @ C) & (rS @ A @ C @ D)) => (rS @ A @ B @ D)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(105), 0), imp(cond(axiom(105), 0)))')). 19.26/7.23 thf(926,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((rline @ E) & ? [F:$i]: ((rpoint @ F) & (F = C)) & ? [F:$i]: ((F = B) & (rpoint @ F)) & ? [F:$i]: ((F = A) & (rpoint @ F)) & (E = D) & (rR @ B @ A @ C) & (rS @ A @ C @ D)) => (rS @ A @ B @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[106])). 19.26/7.23 thf(11,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((A = B) & (rpoint @ B) & (rpoint @ D) & (A != C) & (D = C)) => (rpoint @ (vskolem1052 @ A @ B @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(206), 0), 2)')). 19.26/7.23 thf(161,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((A = B) & (rpoint @ B) & (rpoint @ D) & ~ (A = C) & (D = C)) => (rpoint @ (vskolem1052 @ A @ B @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[11])). 19.26/7.23 thf(15,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: ((((vangle @ C @ A @ B) = (vangle @ F @ D @ E)) & ((vf @ B @ C) = (vf @ E @ F)) & ? [G:$i]: ((rpoint @ G) & (F = G)) & ? [G:$i]: ((rpoint @ G) & (G = E)) & ? [G:$i]: ((rpoint @ G) & (C = G)) & ? [G:$i]: ((rpoint @ G) & (A = G)) & ? [G:$i]: ((rpoint @ G) & (G = B)) & ? [G:$i]: ((G = D) & (rpoint @ G)) & ((vf @ A @ B) = (vf @ D @ E)) & ((vf @ F @ D) = (vf @ C @ A)) & ((vangle @ A @ B @ C) = (vangle @ D @ E @ F)) & ((vangle @ B @ C @ A) = (vangle @ E @ F @ D))) => ((vg @ A @ B @ C) = (vg @ D @ E @ F))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(178), 0), imp(cond(axiom(178), 0)))')). 19.26/7.23 thf(180,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: ((((vangle @ C @ A @ B) = (vangle @ F @ D @ E)) & ((vf @ B @ C) = (vf @ E @ F)) & ? [G:$i]: ((rpoint @ G) & (F = G)) & ? [G:$i]: ((rpoint @ G) & (G = E)) & ? [G:$i]: ((rpoint @ G) & (C = G)) & ? [G:$i]: ((rpoint @ G) & (A = G)) & ? [G:$i]: ((rpoint @ G) & (G = B)) & ? [G:$i]: ((G = D) & (rpoint @ G)) & ((vf @ A @ B) = (vf @ D @ E)) & ((vf @ F @ D) = (vf @ C @ A)) & ((vangle @ A @ B @ C) = (vangle @ D @ E @ F)) & ((vangle @ B @ C @ A) = (vangle @ E @ F @ D))) => ((vg @ A @ B @ C) = (vg @ D @ E @ F))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[15])). 19.26/7.23 thf(33,axiom,((! [A:$i,B:$i,C:$i]: ((? [D:$i]: ((D = C) & (rpoint @ D)) & ? [D:$i]: ((rpoint @ D) & (D = B)) & ? [D:$i]: ((A = D) & (rpoint @ D)) & (rR @ B @ A @ C)) => ((vf @ A @ C) = (vplus @ (vf @ A @ B) @ (vf @ B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(180), 0), imp(cond(axiom(180), 0)))')). 19.26/7.23 thf(291,plain,((! [A:$i,B:$i,C:$i]: ((? [D:$i]: ((D = C) & (rpoint @ D)) & ? [D:$i]: ((rpoint @ D) & (D = B)) & ? [D:$i]: ((A = D) & (rpoint @ D)) & (rR @ B @ A @ C)) => ((vf @ A @ C) = (vplus @ (vf @ A @ B) @ (vf @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[33])). 19.26/7.23 thf(65,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((? [E:$i]: ((rpoint @ E) & (ron @ E @ A) & (E != C))) <= ((C = D) & (rpoint @ D) & (B = A) & (rcircle @ B) & (ron @ C @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(43), 0), imp(cond(axiom(43), 0)))')). 19.26/7.23 thf(545,plain,((! [A:$i,B:$i,C:$i,D:$i]: (? [E:$i]: ((rpoint @ E) & (ron @ E @ A) & ~ (E = C)) | ~ ((C = D) & (rpoint @ D) & (B = A) & (rcircle @ B) & (ron @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[65])). 19.26/7.23 thf(51,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((vplus @ A @ C) = (vplus @ C @ A)) <= ((C = D) & (rreal @ B) & (A = B) & (rreal @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(143), 0), imp(cond(axiom(143), 0)))')). 19.26/7.23 thf(413,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((vplus @ A @ C) = (vplus @ C @ A)) | ~ ((C = D) & (rreal @ B) & (A = B) & (rreal @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[51])). 19.26/7.23 thf(24,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: ((((vplus @ C @ E) = (vplus @ A @ E)) & (E = F) & (rreal @ F) & (C = D) & (rreal @ D) & (rreal @ B) & (B = A)) => (C = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(156, 0), 0)')). 19.26/7.23 thf(236,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: ((((vplus @ C @ E) = (vplus @ A @ E)) & (E = F) & (rreal @ F) & (C = D) & (rreal @ D) & (rreal @ B) & (B = A)) => (C = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[24])). 19.26/7.23 thf(90,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((D = C) & (B = A) & (rcircle @ B) & (rcircle @ D) & (rintersect @ A @ C)) => (? [E:$i]: ((ron @ E @ C) & (rpoint @ E) & (ron @ E @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(65), 0), imp(cond(axiom(65), 0)))')). 19.26/7.23 thf(784,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((D = C) & (B = A) & (rcircle @ B) & (rcircle @ D) & (rintersect @ A @ C)) => (? [E:$i]: ((ron @ E @ C) & (rpoint @ E) & (ron @ E @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[90])). 19.26/7.23 thf(86,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((? [E:$i]: ((ron @ E @ C) & (ron @ E @ A) & (rpoint @ E))) <= ((C = D) & (B = A) & (rline @ B) & (rline @ D) & (rintersect @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(55), 0), imp(cond(axiom(55), 0)))')). 19.26/7.23 thf(736,plain,((! [A:$i,B:$i,C:$i,D:$i]: (? [E:$i]: ((ron @ E @ C) & (ron @ E @ A) & (rpoint @ E)) | ~ ((C = D) & (B = A) & (rline @ B) & (rline @ D) & (rintersect @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[86])). 19.26/7.23 thf(113,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i]: (((ron @ F @ G) & (ron @ E @ G) & (G = H) & (rline @ H) & (rcenter @ F @ B) & (ron @ D @ A) & (ron @ C @ B) & ? [I:$i]: ((C = I) & (rpoint @ I)) & (rintersect @ A @ B) & ? [I:$i]: ((rcircle @ I) & (I = B)) & ? [I:$i]: ((rcircle @ I) & (I = A)) & (A != B) & ? [I:$i]: ((D = I) & (rpoint @ I)) & (ron @ C @ A) & (ron @ D @ B) & (D != C) & (rcenter @ E @ A)) => (~ (rS @ C @ D @ G))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(125), 0), imp(cond(axiom(125), 0)))')). 19.26/7.23 thf(996,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i]: (((ron @ F @ G) & (ron @ E @ G) & (G = H) & (rline @ H) & (rcenter @ F @ B) & (ron @ D @ A) & (ron @ C @ B) & ? [I:$i]: ((C = I) & (rpoint @ I)) & (rintersect @ A @ B) & ? [I:$i]: ((rcircle @ I) & (I = B)) & ? [I:$i]: ((rcircle @ I) & (I = A)) & ~ (A = B) & ? [I:$i]: ((D = I) & (rpoint @ I)) & (ron @ C @ A) & (ron @ D @ B) & ~ (D = C) & (rcenter @ E @ A)) => (~ (rS @ C @ D @ G))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[113])). 19.26/7.23 thf(88,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((rS @ B @ C @ D) | (rS @ A @ C @ D)) <= (~ (rS @ A @ B @ D) & (D = E) & (rline @ E) & ? [F:$i]: ((A = F) & (rpoint @ F)) & ? [F:$i]: ((rpoint @ F) & (F = B)) & ? [F:$i]: ((C = F) & (rpoint @ F)) & ~ (ron @ A @ D) & ~ (ron @ B @ D) & ~ (ron @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(103), 0), imp(cond(axiom(103), 0)))')). 19.26/7.23 thf(758,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((rS @ B @ C @ D) | (rS @ A @ C @ D) | ~ (~ (rS @ A @ B @ D) & (D = E) & (rline @ E) & ? [F:$i]: ((A = F) & (rpoint @ F)) & ? [F:$i]: ((rpoint @ F) & (F = B)) & ? [F:$i]: ((C = F) & (rpoint @ F)) & ~ (ron @ A @ D) & ~ (ron @ B @ D) & ~ (ron @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[88])). 19.26/7.23 thf(79,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((ron @ B @ D) & (ron @ B @ E) & ~ (rS @ A @ C @ D) & (ron @ C @ E) & (ron @ A @ E) & ? [F:$i]: ((rline @ F) & (F = E)) & ? [F:$i]: ((F = D) & (rline @ F)) & (B != C) & ? [F:$i]: ((C = F) & (rpoint @ F)) & ? [F:$i]: ((rpoint @ F) & (F = B)) & ? [F:$i]: ((rpoint @ F) & (F = A)) & (B != A) & (A != C) & (D != E)) => (rR @ B @ A @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(111), 0), imp(cond(axiom(111), 0)))')). 19.26/7.23 thf(700,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((ron @ B @ D) & (ron @ B @ E) & ~ (rS @ A @ C @ D) & (ron @ C @ E) & (ron @ A @ E) & ? [F:$i]: ((rline @ F) & (F = E)) & ? [F:$i]: ((F = D) & (rline @ F)) & ~ (B = C) & ? [F:$i]: ((C = F) & (rpoint @ F)) & ? [F:$i]: ((rpoint @ F) & (F = B)) & ? [F:$i]: ((rpoint @ F) & (F = A)) & ~ (B = A) & ~ (A = C) & ~ (D = E)) => (rR @ B @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[79])). 19.26/7.23 thf(62,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: (((F != E) & ~ (ron @ D @ E) & (C != A) & (B != A) & (ron @ B @ E) & (ron @ A @ E) & ? [G:$i]: ((B = G) & (rpoint @ G)) & ? [G:$i]: ((rpoint @ G) & (A = G)) & ? [G:$i]: ((rpoint @ G) & (G = C)) & ? [G:$i]: ((rpoint @ G) & (D = G)) & ? [G:$i]: ((rline @ G) & (E = G)) & ? [G:$i]: ((rline @ G) & (G = F)) & (ron @ A @ F) & (ron @ C @ F) & ~ (ron @ D @ F)) => (((rS @ B @ D @ F) & (rS @ C @ D @ E)) <=> ((vplus @ (vangle @ B @ A @ D) @ (vangle @ D @ A @ C)) = (vangle @ B @ A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(190), 0), imp(cond(axiom(190), 0)))')). 19.26/7.23 thf(520,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: ((~ (F = E) & ~ (ron @ D @ E) & ~ (C = A) & ~ (B = A) & (ron @ B @ E) & (ron @ A @ E) & ? [G:$i]: ((B = G) & (rpoint @ G)) & ? [G:$i]: ((rpoint @ G) & (A = G)) & ? [G:$i]: ((rpoint @ G) & (G = C)) & ? [G:$i]: ((rpoint @ G) & (D = G)) & ? [G:$i]: ((rline @ G) & (E = G)) & ? [G:$i]: ((rline @ G) & (G = F)) & (ron @ A @ F) & (ron @ C @ F) & ~ (ron @ D @ F)) => ((((rS @ B @ D @ F) & (rS @ C @ D @ E)) => ((vplus @ (vangle @ B @ A @ D) @ (vangle @ D @ A @ C)) = (vangle @ B @ A @ C))) & (((vplus @ (vangle @ B @ A @ D) @ (vangle @ D @ A @ C)) = (vangle @ B @ A @ C)) => ((rS @ B @ D @ F) & (rS @ C @ D @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[62])). 19.26/7.23 thf(103,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: (((rR @ F @ C @ D) & (ron @ C @ A) & ? [G:$i]: ((rpoint @ G) & (F = G)) & ? [G:$i]: ((rpoint @ G) & (G = D)) & (rline @ B) & (B = A) & ? [G:$i]: ((C = G) & (rpoint @ G)) & ? [G:$i]: ((G = E) & (rpoint @ G)) & (ron @ D @ A) & (ron @ E @ A) & (rR @ E @ C @ D)) => (? [G:$i]: ((rpoint @ G) & (rR @ G @ C @ D) & (E != G) & (F != G)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(27), 0), imp(cond(axiom(27), 0)))')). 19.26/7.23 thf(895,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: (((rR @ F @ C @ D) & (ron @ C @ A) & ? [G:$i]: ((rpoint @ G) & (F = G)) & ? [G:$i]: ((rpoint @ G) & (G = D)) & (rline @ B) & (B = A) & ? [G:$i]: ((C = G) & (rpoint @ G)) & ? [G:$i]: ((G = E) & (rpoint @ G)) & (ron @ D @ A) & (ron @ E @ A) & (rR @ E @ C @ D)) => (? [G:$i]: ((rpoint @ G) & (rR @ G @ C @ D) & ~ (E = G) & ~ (F = G)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[103])). 19.26/7.23 thf(94,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((rR @ B @ A @ C) & (E = D) & ? [F:$i]: ((rpoint @ F) & (C = F)) & ? [F:$i]: ((rpoint @ F) & (A = F)) & ? [F:$i]: ((B = F) & (rpoint @ F)) & (rline @ E) & (ron @ B @ D)) => (~ (rS @ A @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(109), 0), imp(cond(axiom(109), 0)))')). 19.26/7.23 thf(827,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((rR @ B @ A @ C) & (E = D) & ? [F:$i]: ((rpoint @ F) & (C = F)) & ? [F:$i]: ((rpoint @ F) & (A = F)) & ? [F:$i]: ((B = F) & (rpoint @ F)) & (rline @ E) & (ron @ B @ D)) => (~ (rS @ A @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[94])). 19.26/7.23 thf(31,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: ((rless @ (vplus @ A @ E) @ (vplus @ C @ E)) <= ((D = C) & (rreal @ D) & (A = B) & (rreal @ B) & (rreal @ F) & (F = E) & (rless @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(153), 0), imp(cond(axiom(153), 0)))')). 19.26/7.23 thf(278,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: ((rless @ (vplus @ A @ E) @ (vplus @ C @ E)) | ~ ((D = C) & (rreal @ D) & (A = B) & (rreal @ B) & (rreal @ F) & (F = E) & (rless @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[31])). 19.26/7.23 thf(115,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i]: (((rS @ F @ H @ C) & (rS @ G @ H @ B) & (ron @ G @ C) & (ron @ F @ B) & (ron @ E @ A) & (ron @ D @ C) & (ron @ D @ B) & ? [I:$i]: ((rpoint @ I) & (I = G)) & ? [I:$i]: ((rpoint @ I) & (F = I)) & ? [I:$i]: ((rline @ I) & (C = I)) & ? [I:$i]: ((rline @ I) & (A = I)) & ? [I:$i]: ((rline @ I) & (I = B)) & ? [I:$i]: ((rpoint @ I) & (D = I)) & ? [I:$i]: ((E = I) & (rpoint @ I)) & (ron @ D @ A) & (rS @ F @ G @ A) & (rS @ E @ F @ C)) => (rS @ F @ H @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(117), 0), imp(cond(axiom(117), 0)))')). 19.26/7.23 thf(1015,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) & (ron @ G @ C) & (ron @ F @ B) & (ron @ E @ A) & (ron @ D @ C) & (ron @ D @ B) & ? [I:$i]: ((rpoint @ I) & (I = G)) & ? [I:$i]: ((rpoint @ I) & (F = I)) & ? [I:$i]: ((rline @ I) & (C = I)) & ? [I:$i]: ((rline @ I) & (A = I)) & ? [I:$i]: ((rline @ I) & (I = B)) & ? [I:$i]: ((rpoint @ I) & (D = I)) & ? [I:$i]: ((E = I) & (rpoint @ I)) & (ron @ D @ A) & (rS @ F @ G @ A) & (rS @ E @ F @ C)) => (rS @ F @ H @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[115])). 19.26/7.23 thf(21,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i]: (((rless @ (vf @ E @ G) @ (vf @ A @ C)) & (H = G) & (rpoint @ H) & (E = F) & (rpoint @ F) & (C = D) & (rpoint @ D) & (rpoint @ B) & (A = B) & (C != A) & (E != G)) => ((vf @ E @ G) = (vf @ A @ (vskolem1120 @ A @ B @ C @ D @ E @ F @ G @ H)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(238), 0), 0)')). 19.26/7.23 thf(223,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i]: (((rless @ (vf @ E @ G) @ (vf @ A @ C)) & (H = G) & (rpoint @ H) & (E = F) & (rpoint @ F) & (C = D) & (rpoint @ D) & (rpoint @ B) & (A = B) & ~ (C = A) & ~ (E = G)) => ((vf @ E @ G) = (vf @ A @ (vskolem1120 @ A @ B @ C @ D @ E @ F @ G @ H)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[21])). 19.26/7.23 thf(73,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((rR @ A @ B @ C) | (rR @ C @ A @ B) | (rR @ B @ A @ C)) <= ((E = D) & (ron @ C @ D) & (ron @ B @ D) & (rline @ E) & ? [F:$i]: ((C = F) & (rpoint @ F)) & ? [F:$i]: ((F = B) & (rpoint @ F)) & ? [F:$i]: ((A = F) & (rpoint @ F)) & (A != B) & (C != A) & (C != B) & (ron @ A @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(91), 0), imp(cond(axiom(91), 0)))')). 19.26/7.23 thf(608,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((rR @ A @ B @ C) | (rR @ C @ A @ B) | (rR @ B @ A @ C) | ~ ((E = D) & (ron @ C @ D) & (ron @ B @ D) & (rline @ E) & ? [F:$i]: ((C = F) & (rpoint @ F)) & ? [F:$i]: ((F = B) & (rpoint @ F)) & ? [F:$i]: ((A = F) & (rpoint @ F)) & ~ (A = B) & ~ (C = A) & ~ (C = B) & (ron @ A @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[73])). 19.26/7.23 thf(25,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((? [E:$i]: ((E = (vplus @ A @ C)) & (rreal @ E))) <= ((D = C) & (rreal @ D) & (rreal @ B) & (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(139), 0), imp(cond(axiom(139), 0)))')). 19.26/7.23 thf(241,plain,((! [A:$i,B:$i,C:$i,D:$i]: (? [E:$i]: ((E = (vplus @ A @ C)) & (rreal @ E)) | ~ ((D = C) & (rreal @ D) & (rreal @ B) & (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[25])). 19.26/7.23 thf(118,axiom,((! [A:$i,B:$i]: (((B = A) & (rcircle @ B)) => (? [C:$i]: ((rpoint @ C) & (ron @ C @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(41), 0), imp(cond(axiom(41), 0)))')). 19.26/7.23 thf(1034,plain,((! [A:$i,B:$i]: (((B = A) & (rcircle @ B)) => (? [C:$i]: ((rpoint @ C) & (ron @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[118])). 19.26/7.23 thf(64,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i]: (((ron @ G @ C) & ~ (ron @ G @ A) & (rpoint @ H) & (ron @ E @ C) & (rinside @ E @ A) & (E = F) & (rpoint @ F) & (B = A) & (rcircle @ B) & (rline @ D) & (C = D) & (H = G) & ~ (rinside @ G @ A)) => (? [I:$i]: ((ron @ I @ A) & (rpoint @ I) & (ron @ I @ C) & (rR @ I @ E @ G)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(61), 0), imp(cond(axiom(61), 0)))')). 19.26/7.23 thf(531,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i]: (((ron @ G @ C) & ~ (ron @ G @ A) & (rpoint @ H) & (ron @ E @ C) & (rinside @ E @ A) & (E = F) & (rpoint @ F) & (B = A) & (rcircle @ B) & (rline @ D) & (C = D) & (H = G) & ~ (rinside @ G @ A)) => (? [I:$i]: ((ron @ I @ A) & (rpoint @ I) & (ron @ I @ C) & (rR @ I @ E @ G)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[64])). 19.26/7.23 thf(91,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((? [F:$i]: ((rpoint @ F) & (F = E)) & ? [F:$i]: ((C = F) & (rpoint @ F)) & (A = B) & (rline @ B) & ? [F:$i]: ((D = F) & (rpoint @ F)) & (ron @ C @ A) & (ron @ D @ A) & (ron @ E @ A)) => (? [F:$i]: ((D != F) & (C != F) & (rpoint @ F) & (ron @ F @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(21), 0), imp(cond(axiom(21), 0)))')). 19.26/7.23 thf(795,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((? [F:$i]: ((rpoint @ F) & (F = E)) & ? [F:$i]: ((C = F) & (rpoint @ F)) & (A = B) & (rline @ B) & ? [F:$i]: ((D = F) & (rpoint @ F)) & (ron @ C @ A) & (ron @ D @ A) & (ron @ E @ A)) => (? [F:$i]: (~ (D = F) & ~ (C = F) & (rpoint @ F) & (ron @ F @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[91])). 19.26/7.23 thf(43,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i]: (((rless @ (vf @ E @ G) @ (vf @ A @ C)) & (G != E) & (A != C) & (rpoint @ H) & (E = F) & (D = C) & (rpoint @ D) & (rpoint @ B) & (A = B) & (rpoint @ F) & (H = G)) => (rR @ (vskolem1120 @ A @ B @ C @ D @ E @ F @ G @ H) @ A @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(238), 0), 1)')). 19.26/7.23 thf(355,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i]: (((rless @ (vf @ E @ G) @ (vf @ A @ C)) & ~ (G = E) & ~ (A = C) & (rpoint @ H) & (E = F) & (D = C) & (rpoint @ D) & (rpoint @ B) & (A = B) & (rpoint @ F) & (H = G)) => (rR @ (vskolem1120 @ A @ B @ C @ D @ E @ F @ G @ H) @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[43])). 19.26/7.23 thf(82,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i]: (((D != A) & (ron @ E @ G) & (ron @ D @ F) & ? [H:$i]: ((rline @ H) & (G = H)) & ? [H:$i]: ((rpoint @ H) & (H = D)) & ? [H:$i]: ((A = H) & (rpoint @ H)) & ? [H:$i]: ((rpoint @ H) & (H = B)) & ? [H:$i]: ((rpoint @ H) & (C = H)) & ? [H:$i]: ((rpoint @ H) & (H = E)) & ? [H:$i]: ((rline @ H) & (F = H)) & (ron @ A @ F) & (ron @ B @ F) & (ron @ C @ G) & (A != B) & (A != C) & (E != A) & ~ (rR @ A @ B @ D) & ~ (rR @ A @ C @ E)) => ((vangle @ D @ A @ E) = (vangle @ B @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(194), 0), imp(cond(axiom(194), 0)))')). 19.26/7.23 thf(712,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i]: ((~ (D = A) & (ron @ E @ G) & (ron @ D @ F) & ? [H:$i]: ((rline @ H) & (G = H)) & ? [H:$i]: ((rpoint @ H) & (H = D)) & ? [H:$i]: ((A = H) & (rpoint @ H)) & ? [H:$i]: ((rpoint @ H) & (H = B)) & ? [H:$i]: ((rpoint @ H) & (C = H)) & ? [H:$i]: ((rpoint @ H) & (H = E)) & ? [H:$i]: ((rline @ H) & (F = H)) & (ron @ A @ F) & (ron @ B @ F) & (ron @ C @ G) & ~ (A = B) & ~ (A = C) & ~ (E = A) & ~ (rR @ A @ B @ D) & ~ (rR @ A @ C @ E)) => ((vangle @ D @ A @ E) = (vangle @ B @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[82])). 19.26/7.23 thf(34,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((rreal @ B) & (B = A) & (rreal @ D) & (C = D) & (rless @ A @ C)) => ((C = A) | ~ (rless @ C @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(147), 0), imp(cond(axiom(147), 0)))')). 19.26/7.23 thf(295,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((rreal @ B) & (B = A) & (rreal @ D) & (C = D) & (rless @ A @ C)) => ((C = A) | ~ (rless @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[34])). 19.26/7.23 thf(80,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((~ (ron @ A @ C)) <= ((C = D) & (rcircle @ D) & (B = A) & (rpoint @ B) & (rinside @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(79), 0), imp(cond(axiom(79), 0)))')). 19.26/7.23 thf(705,plain,((! [A:$i,B:$i,C:$i,D:$i]: (~ (ron @ A @ C) | ~ ((C = D) & (rcircle @ D) & (B = A) & (rpoint @ B) & (rinside @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[80])). 19.26/7.23 thf(8,axiom,((vd684 = v0)),file('/export/starexec/sandbox/benchmark/theBenchmark.p','pred(axiom(137), 2)')). 19.26/7.23 thf(150,plain,((vd684 = v0)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8])). 19.26/7.23 thf(102,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((ron @ B @ D) & (A != B) & (D = E) & (rline @ E) & ? [F:$i]: ((rpoint @ F) & (F = C)) & ? [F:$i]: ((A = F) & (rpoint @ F)) & ? [F:$i]: ((rpoint @ F) & (F = B)) & (ron @ A @ D)) => ((v0 = (vg @ A @ B @ C)) <=> (ron @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(200), 0), imp(cond(axiom(200), 0)))')). 19.26/7.23 thf(887,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((ron @ B @ D) & ~ (A = B) & (D = E) & (rline @ E) & ? [F:$i]: ((rpoint @ F) & (F = C)) & ? [F:$i]: ((A = F) & (rpoint @ F)) & ? [F:$i]: ((rpoint @ F) & (F = B)) & (ron @ A @ D)) => (((v0 = (vg @ A @ B @ C)) => (ron @ C @ D)) & ((ron @ C @ D) => (v0 = (vg @ A @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[102])). 19.26/7.23 thf(83,axiom,((vd1409 != vd1401)),file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conjunct2(conjunct2(conjunct2(406))), 1413, 0)')). 19.26/7.23 thf(717,plain,((~ (vd1409 = vd1401))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[83])). 19.26/7.23 thf(60,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((rS @ B @ A @ C) <= ((rline @ D) & ? [E:$i]: ((rpoint @ E) & (A = E)) & ? [E:$i]: ((E = B) & (rpoint @ E)) & (C = D) & (rS @ A @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(97), 0), imp(cond(axiom(97), 0)))')). 19.26/7.23 thf(502,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((rS @ B @ A @ C) | ~ ((rline @ D) & ? [E:$i]: ((rpoint @ E) & (A = E)) & ? [E:$i]: ((E = B) & (rpoint @ E)) & (C = D) & (rS @ A @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[60])). 19.26/7.23 thf(1,conjecture,((! [A:$i]: ((vd1416 = A) <= ((rline @ A) & (ron @ vd1401 @ A) & (ron @ vd1399 @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(theu(the(408), 1), imp(the(408)))')). 19.26/7.23 thf(2,negated_conjecture,((~ (! [A:$i]: ((vd1416 = A) <= ((rline @ A) & (ron @ vd1401 @ A) & (ron @ vd1399 @ A)))))),inference(neg_conjecture,[status(cth)],[1])). 19.26/7.23 thf(127,plain,((~ (! [A:$i]: ((vd1416 = A) | ~ ((rline @ A) & (ron @ vd1401 @ A) & (ron @ vd1399 @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])). 19.26/7.23 thf(69,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i]: ((rinside @ C @ F) <= ((F = G) & (E = D) & ? [H:$i]: ((B = H) & (rpoint @ H)) & ? [H:$i]: ((A = H) & (rpoint @ H)) & ? [H:$i]: ((rpoint @ H) & (H = C)) & (rline @ E) & (rcircle @ G) & ((ron @ A @ F) | (rinside @ A @ F)) & ((rinside @ B @ F) | (ron @ B @ F)) & (rR @ C @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(121), 0), imp(cond(axiom(121), 0)))')). 19.26/7.23 thf(576,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i]: ((rinside @ C @ F) | ~ ((F = G) & (E = D) & ? [H:$i]: ((B = H) & (rpoint @ H)) & ? [H:$i]: ((A = H) & (rpoint @ H)) & ? [H:$i]: ((rpoint @ H) & (H = C)) & (rline @ E) & (rcircle @ G) & ((ron @ A @ F) | (rinside @ A @ F)) & ((rinside @ B @ F) | (ron @ B @ F)) & (rR @ C @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[69])). 19.26/7.23 thf(44,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i]: (((rless @ (vf @ E @ G) @ (vf @ A @ C)) & (H = G) & (rpoint @ H) & (rpoint @ B) & (A = B) & (rpoint @ D) & (C = D) & (rpoint @ F) & (E = F) & (A != C) & (E != G)) => (rpoint @ (vskolem1120 @ A @ B @ C @ D @ E @ F @ G @ H))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(238), 0), 2)')). 19.26/7.23 thf(359,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i]: (((rless @ (vf @ E @ G) @ (vf @ A @ C)) & (H = G) & (rpoint @ H) & (rpoint @ B) & (A = B) & (rpoint @ D) & (C = D) & (rpoint @ F) & (E = F) & ~ (A = C) & ~ (E = G)) => (rpoint @ (vskolem1120 @ A @ B @ C @ D @ E @ F @ G @ H))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[44])). 19.26/7.23 thf(74,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i]: (((G = H) & (rS @ G @ C @ A) & (rS @ E @ C @ A) & (rpoint @ F) & ~ (ron @ C @ A) & (rpoint @ D) & (A = B) & (rline @ B) & (rpoint @ H) & (E = F) & (C = D)) => (? [I:$i]: ((I != G) & (C != I) & (rpoint @ I) & (rS @ I @ C @ A) & (E != I)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(37), 0), imp(cond(axiom(37), 0)))')). 19.26/7.23 thf(613,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i]: (((G = H) & (rS @ G @ C @ A) & (rS @ E @ C @ A) & (rpoint @ F) & ~ (ron @ C @ A) & (rpoint @ D) & (A = B) & (rline @ B) & (rpoint @ H) & (E = F) & (C = D)) => (? [I:$i]: (~ (I = G) & ~ (C = I) & (rpoint @ I) & (rS @ I @ C @ A) & ~ (E = I)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[74])). 19.26/7.23 thf(100,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((? [E:$i,F:$i]: ((ron @ F @ C) & (rpoint @ F) & (rpoint @ E) & (ron @ E @ C) & (ron @ E @ A) & (ron @ F @ A) & (E != F))) <= ((rintersect @ C @ A) & (rline @ D) & (A = B) & (rcircle @ B) & (C = D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(59), 0), imp(cond(axiom(59), 0)))')). 19.26/7.23 thf(859,plain,((! [A:$i,B:$i,C:$i,D:$i]: (? [E:$i,F:$i]: ((ron @ F @ C) & (rpoint @ F) & (rpoint @ E) & (ron @ E @ C) & (ron @ E @ A) & (ron @ F @ A) & ~ (E = F)) | ~ ((rintersect @ C @ A) & (rline @ D) & (A = B) & (rcircle @ B) & (C = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[100])). 19.26/7.23 thf(57,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: (((ron @ E @ A) & (C = D) & (rpoint @ D) & (A = B) & (rline @ B) & (rpoint @ F) & (F = E) & (ron @ C @ A)) => (? [G:$i]: ((E != G) & (ron @ G @ A) & (rpoint @ G) & (C != G)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(19), 0), imp(cond(axiom(19), 0)))')). 19.26/7.24 thf(465,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: (((ron @ E @ A) & (C = D) & (rpoint @ D) & (A = B) & (rline @ B) & (rpoint @ F) & (F = E) & (ron @ C @ A)) => (? [G:$i]: (~ (E = G) & (ron @ G @ A) & (rpoint @ G) & ~ (C = G)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[57])). 19.26/7.24 thf(23,axiom,((! [A:$i,B:$i]: (((A = B) & (rreal @ B)) => ((vplus @ A @ v0) = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(141), 0), imp(cond(axiom(141), 0)))')). 19.26/7.24 thf(231,plain,((! [A:$i,B:$i]: (((A = B) & (rreal @ B)) => ((vplus @ A @ v0) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[23])). 19.26/7.24 thf(45,axiom,((! [A:$i,B:$i,C:$i]: ((? [D:$i]: ((D = C) & (rpoint @ D)) & ? [D:$i]: ((rpoint @ D) & (D = B)) & ? [D:$i]: ((rpoint @ D) & (A = D))) => (? [D:$i]: ((C != D) & (A != D) & (rpoint @ D) & (D != B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(11), 0), imp(cond(axiom(11), 0)))')). 19.26/7.24 thf(363,plain,((! [A:$i,B:$i,C:$i]: ((? [D:$i]: ((D = C) & (rpoint @ D)) & ? [D:$i]: ((rpoint @ D) & (D = B)) & ? [D:$i]: ((rpoint @ D) & (A = D))) => (? [D:$i]: (~ (C = D) & ~ (A = D) & (rpoint @ D) & ~ (D = B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[45])). 19.26/7.24 thf(66,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i]: ((~ (ron @ G @ C) & (ron @ F @ C) & (ron @ E @ C) & (rcenter @ F @ B) & (rintersect @ A @ B) & ? [H:$i]: ((rcircle @ H) & (B = H)) & ? [H:$i]: ((rcircle @ H) & (H = A)) & (rline @ D) & (C = D) & (rcenter @ E @ A)) => (? [H:$i]: ((rS @ H @ G @ C) & (rpoint @ H) & (ron @ H @ A) & (ron @ H @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(69), 0), imp(cond(axiom(69), 0)))')). 19.26/7.24 thf(556,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i]: ((~ (ron @ G @ C) & (ron @ F @ C) & (ron @ E @ C) & (rcenter @ F @ B) & (rintersect @ A @ B) & ? [H:$i]: ((rcircle @ H) & (B = H)) & ? [H:$i]: ((rcircle @ H) & (H = A)) & (rline @ D) & (C = D) & (rcenter @ E @ A)) => (? [H:$i]: ((rS @ H @ G @ C) & (rpoint @ H) & (ron @ H @ A) & (ron @ H @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[66])). 19.26/7.24 thf(107,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((ron @ C @ A) & ? [E:$i]: ((E = D) & (rpoint @ E)) & ? [E:$i]: ((E = C) & (rpoint @ E)) & (A = B) & (rline @ B) & (ron @ D @ A) & (D != C)) => (? [E:$i]: ((rR @ D @ C @ E) & (rpoint @ E)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(29), 0), imp(cond(axiom(29), 0)))')). 19.26/7.24 thf(931,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((ron @ C @ A) & ? [E:$i]: ((E = D) & (rpoint @ E)) & ? [E:$i]: ((E = C) & (rpoint @ E)) & (A = B) & (rline @ B) & (ron @ D @ A) & ~ (D = C)) => (? [E:$i]: ((rR @ D @ C @ E) & (rpoint @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[107])). 19.26/7.24 thf(19,axiom,((! [A:$i,B:$i,C:$i]: ((((vg @ A @ B @ C) = (vg @ C @ A @ B)) & ((vg @ A @ C @ B) = (vg @ A @ B @ C))) <= (? [D:$i]: ((rpoint @ D) & (C = D)) & ? [D:$i]: ((rpoint @ D) & (B = D)) & ? [D:$i]: ((rpoint @ D) & (A = D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(176), 0), imp(cond(axiom(176), 0)))')). 19.26/7.24 thf(203,plain,((! [A:$i,B:$i,C:$i]: ((((vg @ A @ B @ C) = (vg @ C @ A @ B)) & ((vg @ A @ C @ B) = (vg @ A @ B @ C))) | ~ (? [D:$i]: ((rpoint @ D) & (C = D)) & ? [D:$i]: ((rpoint @ D) & (B = D)) & ? [D:$i]: ((rpoint @ D) & (A = D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[19])). 19.26/7.24 thf(111,axiom,((! [A:$i,B:$i]: ((? [C:$i,D:$i]: ((ron @ D @ A) & (ron @ C @ A) & (rpoint @ C) & (ron @ C @ B) & (rpoint @ D) & (ron @ D @ B) & (C != D))) <= ((rintersect @ A @ B) & ? [C:$i]: ((rcircle @ C) & (A = C)) & ? [C:$i]: ((rcircle @ C) & (B = C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(67), 0), imp(cond(axiom(67), 0)))')). 19.26/7.24 thf(963,plain,((! [A:$i,B:$i]: (? [C:$i,D:$i]: ((ron @ D @ A) & (ron @ C @ A) & (rpoint @ C) & (ron @ C @ B) & (rpoint @ D) & (ron @ D @ B) & ~ (C = D)) | ~ ((rintersect @ A @ B) & ? [C:$i]: ((rcircle @ C) & (A = C)) & ? [C:$i]: ((rcircle @ C) & (B = C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[111])). 19.26/7.24 thf(126,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i]: (((E != D) & ~ (rS @ E @ G @ B) & (rS @ F @ G @ A) & (ron @ F @ B) & (ron @ D @ B) & ? [H:$i]: ((G = H) & (rpoint @ H)) & ? [H:$i]: ((rpoint @ H) & (E = H)) & ? [H:$i]: ((rpoint @ H) & (H = D)) & ? [H:$i]: ((rline @ H) & (C = H)) & ? [H:$i]: ((rline @ H) & (H = B)) & ? [H:$i]: ((rline @ H) & (H = A)) & ? [H:$i]: ((H = F) & (rpoint @ H)) & (ron @ D @ A) & (ron @ D @ C) & (ron @ E @ A) & (ron @ G @ C) & ~ (ron @ G @ B)) => (rS @ E @ F @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(115), 0), imp(cond(axiom(115), 0)))')). 19.26/7.24 thf(1101,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i]: ((~ (E = D) & ~ (rS @ E @ G @ B) & (rS @ F @ G @ A) & (ron @ F @ B) & (ron @ D @ B) & ? [H:$i]: ((G = H) & (rpoint @ H)) & ? [H:$i]: ((rpoint @ H) & (E = H)) & ? [H:$i]: ((rpoint @ H) & (H = D)) & ? [H:$i]: ((rline @ H) & (C = H)) & ? [H:$i]: ((rline @ H) & (H = B)) & ? [H:$i]: ((rline @ H) & (H = A)) & ? [H:$i]: ((H = F) & (rpoint @ H)) & (ron @ D @ A) & (ron @ D @ C) & (ron @ E @ A) & (ron @ G @ C) & ~ (ron @ G @ B)) => (rS @ E @ F @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[126])). 19.26/7.24 thf(42,axiom,((! [A:$i,B:$i,C:$i]: (((vf @ A @ C) = (vf @ A @ B)) <= (((vangle @ A @ B @ C) = (vangle @ A @ C @ B)) & (C != A) & ? [D:$i]: ((rpoint @ D) & (D = C)) & ? [D:$i]: ((rpoint @ D) & (D = A)) & ? [D:$i]: ((rpoint @ D) & (B = D)) & (B != A) & (C != B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(382), 0), 0)')). 19.26/7.24 thf(351,plain,((! [A:$i,B:$i,C:$i]: (((vf @ A @ C) = (vf @ A @ B)) | ~ (((vangle @ A @ B @ C) = (vangle @ A @ C @ B)) & ~ (C = A) & ? [D:$i]: ((rpoint @ D) & (D = C)) & ? [D:$i]: ((rpoint @ D) & (D = A)) & ? [D:$i]: ((rpoint @ D) & (B = D)) & ~ (B = A) & ~ (C = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[42])). 19.26/7.24 thf(6,axiom,((! [A:$i,B:$i]: ((? [C:$i]: ((C = B) & (rpoint @ C)) & ? [C:$i]: ((A = C) & (rpoint @ C))) => (? [C:$i]: ((rreal @ C) & (C = (vf @ A @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(160), 0), imp(cond(axiom(160), 0)))')). 19.26/7.24 thf(139,plain,((! [A:$i,B:$i]: ((? [C:$i]: ((C = B) & (rpoint @ C)) & ? [C:$i]: ((A = C) & (rpoint @ C))) => (? [C:$i]: ((rreal @ C) & (C = (vf @ A @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])). 19.26/7.24 thf(52,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: ((? [G:$i]: ((rpoint @ G) & (rS @ G @ C @ A) & (C != G) & (G != E))) <= ((E = F) & (rS @ E @ C @ A) & (A = B) & (rline @ B) & (rpoint @ D) & ~ (ron @ C @ A) & (rpoint @ F) & (C = D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(35), 0), imp(cond(axiom(35), 0)))')). 19.26/7.24 thf(418,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: (? [G:$i]: ((rpoint @ G) & (rS @ G @ C @ A) & ~ (C = G) & ~ (G = E)) | ~ ((E = F) & (rS @ E @ C @ A) & (A = B) & (rline @ B) & (rpoint @ D) & ~ (ron @ C @ A) & (rpoint @ F) & (C = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[52])). 19.26/7.24 thf(117,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i]: ((~ (rS @ E @ G @ B)) <= ((rS @ F @ G @ A) & (ron @ G @ C) & (ron @ E @ A) & (ron @ D @ C) & (ron @ D @ B) & (ron @ D @ A) & ? [H:$i]: ((rpoint @ H) & (D = H)) & ? [H:$i]: ((rline @ H) & (H = B)) & ? [H:$i]: ((H = A) & (rline @ H)) & ? [H:$i]: ((rline @ H) & (C = H)) & ? [H:$i]: ((rpoint @ H) & (E = H)) & ? [H:$i]: ((H = F) & (rpoint @ H)) & ? [H:$i]: ((rpoint @ H) & (H = G)) & (ron @ F @ C) & (rS @ E @ F @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(113), 0), imp(cond(axiom(113), 0)))')). 19.26/7.24 thf(1030,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i]: (~ (rS @ E @ G @ B) | ~ ((rS @ F @ G @ A) & (ron @ G @ C) & (ron @ E @ A) & (ron @ D @ C) & (ron @ D @ B) & (ron @ D @ A) & ? [H:$i]: ((rpoint @ H) & (D = H)) & ? [H:$i]: ((rline @ H) & (H = B)) & ? [H:$i]: ((H = A) & (rline @ H)) & ? [H:$i]: ((rline @ H) & (C = H)) & ? [H:$i]: ((rpoint @ H) & (E = H)) & ? [H:$i]: ((H = F) & (rpoint @ H)) & ? [H:$i]: ((rpoint @ H) & (H = G)) & (ron @ F @ C) & (rS @ E @ F @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[117])). 19.26/7.24 thf(89,axiom,(((vd1406 = vd1407) & (ron @ vd1399 @ vd1406) & (vd1401 != vd1400) & (vd1401 != vd1399) & ? [A:$i]: ((A = vd1401) & (rpoint @ A)) & ? [A:$i]: ((A = vd1400) & (rpoint @ A)) & ? [A:$i]: ((vd1399 = A) & (rpoint @ A)) & (vd1400 != vd1399) & (rline @ vd1407) & (ron @ vd1400 @ vd1406))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','and(pred(conjunct2(405), 5), and(pred(s2(plural(conjunct2(405))), 0), and(pred(s1(plural(conjunct2(405))), 0), and(pred(conjunct2(405), 1), and(pred(conjunct1(405), 9), and(pred(conjunct1(405), 8), and(pred(conjunct1(405), 7), and(qe(s3(plural(405))), and(qe(s2(plural(405))), qe(s1(plural(405))))))))))))')). 19.26/7.24 thf(763,plain,(((vd1406 = vd1407) & (ron @ vd1399 @ vd1406) & ~ (vd1401 = vd1400) & ~ (vd1401 = vd1399) & ? [A:$i]: ((A = vd1401) & (rpoint @ A)) & ? [A:$i]: ((A = vd1400) & (rpoint @ A)) & ? [A:$i]: ((vd1399 = A) & (rpoint @ A)) & ~ (vd1400 = vd1399) & (rline @ vd1407) & (ron @ vd1400 @ vd1406))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[89])). 19.26/7.24 thf(47,axiom,((! [A:$i,B:$i]: (((A = B) & (rreal @ B)) => (~ (rless @ A @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(149), 0), imp(cond(axiom(149), 0)))')). 19.26/7.24 thf(383,plain,((! [A:$i,B:$i]: (((A = B) & (rreal @ B)) => (~ (rless @ A @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[47])). 19.26/7.24 thf(95,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: (((ron @ A @ E) & (rinside @ A @ C) & (rline @ F) & (rpoint @ B) & (B = A) & (rcircle @ D) & (D = C) & (E = F)) => (rintersect @ E @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(131), 0), imp(cond(axiom(131), 0)))')). 19.26/7.24 thf(832,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: (((ron @ A @ E) & (rinside @ A @ C) & (rline @ F) & (rpoint @ B) & (B = A) & (rcircle @ D) & (D = C) & (E = F)) => (rintersect @ E @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[95])). 19.26/7.24 thf(35,axiom,((! [A:$i,B:$i,C:$i]: ((? [D:$i]: ((rpoint @ D) & (A = D)) & ? [D:$i]: ((rpoint @ D) & (D = B)) & ? [D:$i]: ((rpoint @ D) & (D = C))) => (? [D:$i]: (((vg @ A @ B @ C) = D) & (rreal @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(198), 0), imp(cond(axiom(198), 0)))')). 19.26/7.24 thf(300,plain,((! [A:$i,B:$i,C:$i]: ((? [D:$i]: ((rpoint @ D) & (A = D)) & ? [D:$i]: ((rpoint @ D) & (D = B)) & ? [D:$i]: ((rpoint @ D) & (D = C))) => (? [D:$i]: (((vg @ A @ B @ C) = D) & (rreal @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[35])). 19.26/7.24 thf(53,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((rintersect @ C @ D) <= (~ (rinside @ B @ D) & ~ (ron @ B @ D) & (rinside @ A @ D) & ((rinside @ B @ C) | (ron @ B @ C)) & (ron @ A @ C) & ? [E:$i]: ((rcircle @ E) & (E = C)) & ? [E:$i]: ((B = E) & (rpoint @ E)) & ? [E:$i]: ((E = A) & (rpoint @ E)) & ? [E:$i]: ((rcircle @ E) & (E = D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(133), 0), imp(cond(axiom(133), 0)))')). 19.26/7.24 thf(432,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((rintersect @ C @ D) | ~ (~ (rinside @ B @ D) & ~ (ron @ B @ D) & (rinside @ A @ D) & ((rinside @ B @ C) | (ron @ B @ C)) & (ron @ A @ C) & ? [E:$i]: ((rcircle @ E) & (E = C)) & ? [E:$i]: ((B = E) & (rpoint @ E)) & ? [E:$i]: ((E = A) & (rpoint @ E)) & ? [E:$i]: ((rcircle @ E) & (E = D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[53])). 19.26/7.24 thf(7,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((vf @ A @ C) = (vf @ C @ (vskolem1052 @ A @ B @ C @ D))) <= ((C = D) & (rpoint @ D) & (A = B) & (rpoint @ B) & (A != C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(206), 0), 1)')). 19.26/7.24 thf(146,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((vf @ A @ C) = (vf @ C @ (vskolem1052 @ A @ B @ C @ D))) | ~ ((C = D) & (rpoint @ D) & (A = B) & (rpoint @ B) & ~ (A = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])). 19.26/7.24 thf(99,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((~ (ron @ A @ C)) <= ((rS @ A @ B @ C) & (rline @ D) & ? [E:$i]: ((rpoint @ E) & (A = E)) & ? [E:$i]: ((E = B) & (rpoint @ E)) & (C = D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(99), 0), imp(cond(axiom(99), 0)))')). 19.26/7.24 thf(854,plain,((! [A:$i,B:$i,C:$i,D:$i]: (~ (ron @ A @ C) | ~ ((rS @ A @ B @ C) & (rline @ D) & ? [E:$i]: ((rpoint @ E) & (A = E)) & ? [E:$i]: ((E = B) & (rpoint @ E)) & (C = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[99])). 19.26/7.24 thf(30,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: (((rless @ C @ E) & (rless @ A @ C) & (rreal @ F) & (D = C) & (rreal @ B) & (B = A) & (rreal @ D) & (F = E)) => (rless @ A @ E)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(151), 0), imp(cond(axiom(151), 0)))')). 19.26/7.24 thf(273,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: (((rless @ C @ E) & (rless @ A @ C) & (rreal @ F) & (D = C) & (rreal @ B) & (B = A) & (rreal @ D) & (F = E)) => (rless @ A @ E)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[30])). 19.26/7.24 thf(20,axiom,((! [A:$i,B:$i,C:$i]: ((? [D:$i]: ((rpoint @ D) & (C = D)) & ? [D:$i]: ((rpoint @ D) & (D = A)) & ? [D:$i]: ((D = B) & (rpoint @ D)) & (rR @ B @ A @ C)) => (~ (rR @ A @ B @ C) & (A != C) & (B != A) & (rR @ B @ C @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(81), 0), imp(cond(axiom(81), 0)))')). 19.26/7.24 thf(210,plain,((! [A:$i,B:$i,C:$i]: ((? [D:$i]: ((rpoint @ D) & (C = D)) & ? [D:$i]: ((rpoint @ D) & (D = A)) & ? [D:$i]: ((D = B) & (rpoint @ D)) & (rR @ B @ A @ C)) => (~ (rR @ A @ B @ C) & ~ (A = C) & ~ (B = A) & (rR @ B @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[20])). 19.26/7.24 thf(84,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: (((ron @ A @ D) <=> ((vf @ C @ E) = (vf @ C @ A))) <= ((rpoint @ B) & (B = A) & (rcenter @ C @ D) & (rpoint @ F) & (E = F) & (ron @ E @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(184), 0), imp(cond(axiom(184), 0)))')). 19.26/7.24 thf(720,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: ((((ron @ A @ D) => ((vf @ C @ E) = (vf @ C @ A))) & (((vf @ C @ E) = (vf @ C @ A)) => (ron @ A @ D))) | ~ ((rpoint @ B) & (B = A) & (rcenter @ C @ D) & (rpoint @ F) & (E = F) & (ron @ E @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[84])). 19.26/7.24 thf(32,axiom,((! [A:$i,B:$i]: ((? [C:$i]: ((rpoint @ C) & (C != A))) <= ((A = B) & (rpoint @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(7), 0), imp(cond(axiom(7), 0)))')). 19.26/7.24 thf(283,plain,((! [A:$i,B:$i]: (? [C:$i]: ((rpoint @ C) & ~ (C = A)) | ~ ((A = B) & (rpoint @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[32])). 19.26/7.24 thf(85,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i]: (((rintersect @ F @ G) & ((rS @ E @ A @ G) <= ((ron @ E @ F) & (ron @ E @ G)))) <= ((rless @ (vplus @ (vangle @ A @ B @ C) @ (vangle @ B @ C @ D)) @ (vplus @ vperp @ vperp)) & (rS @ A @ D @ G) & (B != C) & (ron @ C @ H) & (ron @ C @ G) & (ron @ A @ F) & ? [I:$i]: ((D = I) & (rpoint @ I)) & ? [I:$i]: ((rpoint @ I) & (I = C)) & ? [I:$i]: ((rpoint @ I) & (A = I)) & ? [I:$i]: ((B = I) & (rpoint @ I)) & ? [I:$i]: ((I = E) & (rpoint @ I)) & ? [I:$i]: ((rline @ I) & (F = I)) & ? [I:$i]: ((G = I) & (rline @ I)) & ? [I:$i]: ((rline @ I) & (I = H)) & (ron @ B @ F) & (ron @ B @ G) & (ron @ D @ H))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(196), 0), imp(cond(axiom(196), 0)))')). 19.26/7.24 thf(728,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i]: (((rintersect @ F @ G) & ((rS @ E @ A @ G) | ~ ((ron @ E @ F) & (ron @ E @ G)))) | ~ ((rless @ (vplus @ (vangle @ A @ B @ C) @ (vangle @ B @ C @ D)) @ (vplus @ vperp @ vperp)) & (rS @ A @ D @ G) & ~ (B = C) & (ron @ C @ H) & (ron @ C @ G) & (ron @ A @ F) & ? [I:$i]: ((D = I) & (rpoint @ I)) & ? [I:$i]: ((rpoint @ I) & (I = C)) & ? [I:$i]: ((rpoint @ I) & (A = I)) & ? [I:$i]: ((B = I) & (rpoint @ I)) & ? [I:$i]: ((I = E) & (rpoint @ I)) & ? [I:$i]: ((rline @ I) & (F = I)) & ? [I:$i]: ((G = I) & (rline @ I)) & ? [I:$i]: ((rline @ I) & (I = H)) & (ron @ B @ F) & (ron @ B @ G) & (ron @ D @ H))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[85])). 19.26/7.24 thf(116,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i]: (((v0 = (vangle @ C @ A @ E)) <=> ((ron @ E @ G) & ~ (rR @ A @ C @ E))) <= ((C != A) & (E = F) & (C = D) & (A = B) & (rpoint @ B) & (rpoint @ D) & (rpoint @ F) & (rline @ H) & (H = G) & (A != E) & (ron @ A @ G) & (ron @ C @ G))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(188), 0), imp(cond(axiom(188), 0)))')). 19.26/7.24 thf(1019,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i]: ((((v0 = (vangle @ C @ A @ E)) => ((ron @ E @ G) & ~ (rR @ A @ C @ E))) & (((ron @ E @ G) & ~ (rR @ A @ C @ E)) => (v0 = (vangle @ C @ A @ E)))) | ~ (~ (C = A) & (E = F) & (C = D) & (A = B) & (rpoint @ B) & (rpoint @ D) & (rpoint @ F) & (rline @ H) & (H = G) & ~ (A = E) & (ron @ A @ G) & (ron @ C @ G))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[116])). 19.26/7.24 thf(104,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: (((vangle @ D @ E @ F) = (vangle @ A @ B @ C)) <= (? [G:$i]: ((rpoint @ G) & (G = F)) & ? [G:$i]: ((rpoint @ G) & (E = G)) & ? [G:$i]: ((rpoint @ G) & (D = G)) & (C != B) & (A != B) & ? [G:$i]: ((rpoint @ G) & (C = G)) & ? [G:$i]: ((A = G) & (rpoint @ G)) & ? [G:$i]: ((rpoint @ G) & (G = B)) & (C != A) & ((vf @ A @ B) = (vf @ D @ E)) & ((vf @ A @ C) = (vf @ D @ F)) & ((vangle @ B @ A @ C) = (vangle @ E @ D @ F)) & ~ (? [G:$i]: ((ron @ E @ G) & (rline @ G) & (ron @ D @ G) & (ron @ F @ G))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(264), 0), 1)')). 19.26/7.24 thf(908,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: (((vangle @ D @ E @ F) = (vangle @ A @ B @ C)) | ~ (? [G:$i]: ((rpoint @ G) & (G = F)) & ? [G:$i]: ((rpoint @ G) & (E = G)) & ? [G:$i]: ((rpoint @ G) & (D = G)) & ~ (C = B) & ~ (A = B) & ? [G:$i]: ((rpoint @ G) & (C = G)) & ? [G:$i]: ((A = G) & (rpoint @ G)) & ? [G:$i]: ((rpoint @ G) & (G = B)) & ~ (C = A) & ((vf @ A @ B) = (vf @ D @ E)) & ((vf @ A @ C) = (vf @ D @ F)) & ((vangle @ B @ A @ C) = (vangle @ E @ D @ F)) & ~ (? [G:$i]: ((ron @ E @ G) & (rline @ G) & (ron @ D @ G) & (ron @ F @ G))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[104])). 19.26/7.24 thf(22,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((~ (rR @ B @ C @ D)) <= ((rR @ B @ A @ D) & (rR @ B @ A @ C) & ? [E:$i]: ((rpoint @ E) & (D = E)) & ? [E:$i]: ((rpoint @ E) & (A = E)) & ? [E:$i]: ((B = E) & (rpoint @ E)) & ? [E:$i]: ((rpoint @ E) & (C = E)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(93), 0), imp(cond(axiom(93), 0)))')). 19.26/7.24 thf(227,plain,((! [A:$i,B:$i,C:$i,D:$i]: (~ (rR @ B @ C @ D) | ~ ((rR @ B @ A @ D) & (rR @ B @ A @ C) & ? [E:$i]: ((rpoint @ E) & (D = E)) & ? [E:$i]: ((rpoint @ E) & (A = E)) & ? [E:$i]: ((B = E) & (rpoint @ E)) & ? [E:$i]: ((rpoint @ E) & (C = E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[22])). 19.26/7.24 thf(56,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: ((? [G:$i]: ((E != G) & (rpoint @ G) & (rR @ D @ C @ G))) <= ((rpoint @ F) & ? [G:$i]: ((G = D) & (rpoint @ G)) & ? [G:$i]: ((rpoint @ G) & (G = C)) & (B = A) & (rline @ B) & (ron @ C @ A) & (ron @ D @ A) & (rR @ D @ C @ E) & (F = E))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(31), 0), imp(cond(axiom(31), 0)))')). 19.26/7.24 thf(454,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: (? [G:$i]: (~ (E = G) & (rpoint @ G) & (rR @ D @ C @ G)) | ~ ((rpoint @ F) & ? [G:$i]: ((G = D) & (rpoint @ G)) & ? [G:$i]: ((rpoint @ G) & (G = C)) & (B = A) & (rline @ B) & (ron @ C @ A) & (ron @ D @ A) & (rR @ D @ C @ E) & (F = E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[56])). 19.26/7.24 thf(101,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((~ (ron @ A @ C) & (C = D) & (rline @ D) & (rpoint @ B) & (B = A)) => (rS @ A @ A @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(95), 0), imp(cond(axiom(95), 0)))')). 19.26/7.24 thf(882,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((~ (ron @ A @ C) & (C = D) & (rline @ D) & (rpoint @ B) & (B = A)) => (rS @ A @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[101])). 19.26/7.24 thf(1133,plain,($false),inference(cvc4,[status(thm)],[645,809,138,479,846,249,1083,408,308,1078,814,747,1001,841,1046,320,184,638,606,152,316,443,376,574,133,265,507,312,307,942,439,1042,260,349,598,392,693,630,165,710,156,1064,1096,188,388,169,256,193,489,590,837,985,173,569,134,938,921,1054,530,953,926,161,180,291,545,413,236,784,736,996,758,700,520,895,827,278,1015,223,608,241,1034,531,795,355,712,295,705,150,887,717,502,127,576,359,613,859,465,231,363,556,931,203,963,1101,351,139,418,1030,763,383,832,300,432,146,854,273,210,720,283,728,1019,908,227,454,882])). 19.26/7.24 % SZS output end CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p 19.26/7.24 % [INFO] Killing All external provers ... 19.53/7.33 EOF