%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : GEO226+2 : TPTP v9.2.1. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n005.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 08:16:51 AM UTC 2026 % Result : Theorem 0.39s 0.58s % Output : Proof 0.39s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : GEO226+2 : TPTP v9.2.1. Released v3.3.0. % 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.18/0.34 % Computer : n005.cluster.edu % 0.18/0.34 % Model : x86_64 x86_64 % 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.34 % Memory : 8042.1875MB % 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.34 % CPULimit : 300 % 0.18/0.35 % WCLimit : 300 % 0.18/0.35 % DateTime : Mon Jun 1 23:41:03 EDT 2026 % 0.18/0.35 % CPUTime : % 0.27/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.39/0.58 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.39/0.58 % SZS status Theorem % 0.39/0.58 % SZS output start Proof % 0.39/0.58 ( % 0.39/0.58 (declare-sort $$unsorted 0) % 0.39/0.58 (declare-const tptp.parallel_through_point (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.58 (declare-const tptp.point (-> $$unsorted Bool)) % 0.39/0.58 (declare-const tptp.line (-> $$unsorted Bool)) % 0.39/0.58 (declare-const tptp.intersection_point (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.58 (declare-const tptp.apart_point_and_line (-> $$unsorted $$unsorted Bool)) % 0.39/0.58 (declare-const tptp.line_connecting (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.58 (declare-const tptp.convergent_lines (-> $$unsorted $$unsorted Bool)) % 0.39/0.58 (declare-const tptp.orthogonal_through_point (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.58 (declare-const tptp.distinct_lines (-> $$unsorted $$unsorted Bool)) % 0.39/0.58 (declare-const tptp.distinct_points (-> $$unsorted $$unsorted Bool)) % 0.39/0.58 (define @t1 () (@var "X" $$unsorted)) % 0.39/0.58 (define @t2 () (@list @t1)) % 0.39/0.58 (define @t3 () (@var "Z" $$unsorted)) % 0.39/0.58 (define @t4 () (@var "Y" $$unsorted)) % 0.39/0.58 (define @t5 () (tptp.distinct_points @t1 @t3)) % 0.39/0.58 (define @t6 () (tptp.distinct_points @t1 @t4)) % 0.39/0.58 (define @t7 () (@list @t1 @t4 @t3)) % 0.39/0.58 (define @t8 () (tptp.distinct_lines @t4 @t3)) % 0.39/0.58 (define @t9 () (tptp.distinct_lines @t1 @t4)) % 0.39/0.58 (define @t10 () (tptp.convergent_lines @t1 @t4)) % 0.39/0.58 (define @t11 () (tptp.distinct_points @t3 (tptp.intersection_point @t1 @t4))) % 0.39/0.58 (define @t12 () (tptp.apart_point_and_line @t3 @t4)) % 0.39/0.58 (define @t13 () (tptp.apart_point_and_line @t3 @t1)) % 0.39/0.58 (define @t14 () (or @t13 @t12)) % 0.39/0.58 (define @t15 () (=> @t14 @t11)) % 0.39/0.58 (define @t16 () (forall @t7 (=> @t10 @t15))) % 0.39/0.58 (define @t17 () (@var "V" $$unsorted)) % 0.39/0.58 (define @t18 () (@var "U" $$unsorted)) % 0.39/0.58 (define @t19 () (tptp.apart_point_and_line @t1 @t4)) % 0.39/0.58 (define @t20 () (@var "B" $$unsorted)) % 0.39/0.58 (define @t21 () (@var "A" $$unsorted)) % 0.39/0.58 (define @t22 () (tptp.point @t21)) % 0.39/0.58 (define @t23 () (@var "M" $$unsorted)) % 0.39/0.58 (define @t24 () (@var "L" $$unsorted)) % 0.39/0.58 (define @t25 () (tptp.convergent_lines @t24 @t23)) % 0.39/0.58 (define @t26 () (tptp.line @t23)) % 0.39/0.58 (define @t27 () (tptp.line @t24)) % 0.39/0.58 (define @t28 () (and @t27 @t26 @t25)) % 0.39/0.58 (define @t29 () (@list @t24 @t23)) % 0.39/0.58 (define @t30 () (and @t27 @t22)) % 0.39/0.58 (define @t31 () (@list @t24 @t21)) % 0.39/0.58 (define @t32 () (tptp.apart_point_and_line @t1 @t23)) % 0.39/0.58 (define @t33 () (not @t32)) % 0.39/0.58 (define @t34 () (tptp.apart_point_and_line @t1 @t24)) % 0.39/0.58 (define @t35 () (not @t34)) % 0.39/0.58 (define @t36 () (and @t35 @t33)) % 0.39/0.58 (define @t37 () (tptp.point @t1)) % 0.39/0.58 (define @t38 () (=> @t37 @t36)) % 0.39/0.58 (define @t39 () (exists @t2 @t38)) % 0.39/0.58 (define @t40 () (=> @t28 @t39)) % 0.39/0.58 (define @t41 () (forall @t29 @t40)) % 0.39/0.58 (define @t42 () (not @t41)) % 0.39/0.58 (define @t43 () (@var "BOUND_VARIABLE_7611" $$unsorted)) % 0.39/0.58 (define @t44 () (@list @t43)) % 0.39/0.58 (define @t45 () (forall @t44 (or (tptp.apart_point_and_line @t43 @t24) (tptp.apart_point_and_line @t43 @t23)))) % 0.39/0.58 (define @t46 () (not @t45)) % 0.39/0.58 (define @t47 () (not @t25)) % 0.39/0.58 (define @t48 () (not @t26)) % 0.39/0.58 (define @t49 () (not @t27)) % 0.39/0.58 (define @t50 () (or @t49 @t48 @t47 @t46)) % 0.39/0.58 (define @t51 () (forall @t29 @t50)) % 0.39/0.58 (define @t52 () (@var "BOUND_VARIABLE_7606" $$unsorted)) % 0.39/0.58 (define @t53 () (forall (@list @t52) (tptp.point @t52))) % 0.39/0.58 (define @t54 () (not @t53)) % 0.39/0.58 (define @t55 () (or @t54 @t50)) % 0.39/0.58 (define @t56 () (or @t49 @t48 @t47 @t54 @t46)) % 0.39/0.58 (define @t57 () (or @t49 @t48 @t47)) % 0.39/0.58 (define @t58 () (not (and @t53 @t45))) % 0.39/0.58 (define @t59 () (or @t34 @t32)) % 0.39/0.58 (define @t60 () (forall @t2 @t59)) % 0.39/0.58 (define @t61 () (@list @t1)) % 0.39/0.58 (define @t62 () (forall @t2 @t37)) % 0.39/0.58 (define @t63 () (and @t62 @t60)) % 0.39/0.58 (define @t64 () (forall @t2 (not @t38))) % 0.39/0.58 (define @t65 () (not @t64)) % 0.39/0.58 (define @t66 () (@quantifiers_skolemize @t51 1)) % 0.39/0.58 (define @t67 () (@quantifiers_skolemize @t51 0)) % 0.39/0.58 (define @t68 () (forall @t44 (or (tptp.apart_point_and_line @t43 @t67) (tptp.apart_point_and_line @t43 @t66)))) % 0.39/0.58 (define @t69 () (not @t68)) % 0.39/0.58 (define @t70 () (tptp.convergent_lines @t67 @t66)) % 0.39/0.58 (define @t71 () (not @t70)) % 0.39/0.58 (define @t72 () (or (not (tptp.line @t67)) (not (tptp.line @t66)) @t71 @t69)) % 0.39/0.58 (define @t73 () (@list true)) % 0.39/0.58 (define @t74 () (@list @t72)) % 0.39/0.58 (define @t75 () (tptp.intersection_point @t67 @t66)) % 0.39/0.58 (define @t76 () (@list @t75)) % 0.39/0.58 (define @t77 () (and (not @t13) (not @t12))) % 0.39/0.58 (define @t78 () (not @t10)) % 0.39/0.58 (define @t79 () (tptp.distinct_points @t75 @t75)) % 0.39/0.58 (define @t80 () (tptp.apart_point_and_line @t75 @t66)) % 0.39/0.58 (define @t81 () (not @t80)) % 0.39/0.58 (define @t82 () (tptp.apart_point_and_line @t75 @t67)) % 0.39/0.58 (define @t83 () (not @t82)) % 0.39/0.58 (define @t84 () (and @t83 @t81)) % 0.39/0.58 (define @t85 () (or @t71 @t84 @t79)) % 0.39/0.58 (define @t86 () (not @t84)) % 0.39/0.58 (define @t87 () (@list false)) % 0.39/0.58 (define @t88 () (@list @t84)) % 0.39/0.58 (define @t89 () (or @t82 @t80)) % 0.39/0.58 (assume @p1 (forall @t2 (not (tptp.distinct_points @t1 @t1)))) % 0.39/0.58 (assume @p2 (forall @t2 (not (tptp.distinct_lines @t1 @t1)))) % 0.39/0.58 (assume @p3 (forall @t2 (not (tptp.convergent_lines @t1 @t1)))) % 0.39/0.58 (assume @p4 (forall @t7 (=> @t6 (or @t5 (tptp.distinct_points @t4 @t3))))) % 0.39/0.58 (assume @p5 (forall @t7 (=> @t9 (or (tptp.distinct_lines @t1 @t3) @t8)))) % 0.39/0.58 (assume @p6 (forall @t7 (=> @t10 (or (tptp.convergent_lines @t1 @t3) (tptp.convergent_lines @t4 @t3))))) % 0.39/0.58 (assume @p7 (forall @t7 (=> @t6 (=> (tptp.apart_point_and_line @t3 (tptp.line_connecting @t1 @t4)) (and (tptp.distinct_points @t3 @t1) (tptp.distinct_points @t3 @t4)))))) % 0.39/0.58 (assume @p8 @t16) % 0.39/0.58 (assume @p9 (forall (@list @t1 @t4 @t18 @t17) (=> (and @t6 (tptp.distinct_lines @t18 @t17)) (or (tptp.apart_point_and_line @t1 @t18) (tptp.apart_point_and_line @t1 @t17) (tptp.apart_point_and_line @t4 @t18) (tptp.apart_point_and_line @t4 @t17))))) % 0.39/0.58 (assume @p10 (forall @t7 (=> @t19 (or @t5 @t12)))) % 0.39/0.58 (assume @p11 (forall @t7 (=> @t19 (or @t8 (tptp.apart_point_and_line @t1 @t3))))) % 0.39/0.58 (assume @p12 (forall (@list @t1 @t4) (=> @t10 @t9))) % 0.39/0.58 (assume @p13 (forall (@list @t21 @t20) (=> (and @t22 (tptp.point @t20) (tptp.distinct_points @t21 @t20)) (tptp.line (tptp.line_connecting @t21 @t20))))) % 0.39/0.58 (assume @p14 (forall @t29 (=> @t28 (tptp.point (tptp.intersection_point @t24 @t23))))) % 0.39/0.58 (assume @p15 (forall @t31 (=> @t30 (tptp.line (tptp.parallel_through_point @t24 @t21))))) % 0.39/0.58 (assume @p16 (forall @t31 (=> @t30 (tptp.line (tptp.orthogonal_through_point @t24 @t21))))) % 0.39/0.58 (assume @p17 @t42) % 0.39/0.58 (assume @p18 true) % 0.39/0.58 (step @p19 :rule quant-miniscope-or :args ((= (forall @t29 @t55) (or @t54 @t51)))) % 0.39/0.58 (step @p20 :rule aci_norm :args ((= @t56 @t55))) % 0.39/0.58 (step @p21 :rule cong :premises (@p20) :args ((forall @t29 @t56))) % 0.39/0.58 (step @p22 :rule trans :premises (@p21 @p19)) % 0.39/0.58 (step @p23 :rule aci_norm :args ((= (or @t57 (or @t54 @t46)) @t56))) % 0.39/0.58 (step @p24 :rule bool-and-de-morgan :args (@t53 @t45 true)) % 0.39/0.58 (step @p25 :rule aci_norm :args ((= (or @t49 (or @t48 @t47)) @t57))) % 0.39/0.58 (step @p26 :rule bool-and-de-morgan :args (@t26 @t25 true)) % 0.39/0.58 (step @p27 :rule refl :args (@t49)) % 0.39/0.58 (step @p28 :rule nary_cong :premises (@p27 @p26) :args ((or @t49 (not (and @t26 @t25))))) % 0.39/0.58 (step @p29 :rule bool-and-de-morgan :args (@t27 @t26 (and @t25))) % 0.39/0.58 (step @p30 :rule trans :premises (@p29 @p28)) % 0.39/0.58 (step @p31 :rule trans :premises (@p30 @p25)) % 0.39/0.58 (step @p32 :rule nary_cong :premises (@p31 @p24) :args ((or (not @t28) @t58))) % 0.39/0.58 (step @p33 :rule trans :premises (@p32 @p23)) % 0.39/0.58 (step @p34 :rule bool-impl-elim :args (@t28 @t58)) % 0.39/0.58 (step @p35 :rule trans :premises (@p34 @p33)) % 0.39/0.58 (step @p36 :rule cong :premises (@p35) :args ((forall @t29 (=> @t28 @t58)))) % 0.39/0.58 (step @p37 :rule trans :premises (@p36 @p22)) % 0.39/0.58 (step @p38 :rule alpha_equiv :args (@t60 @t61 (@list @t43))) % 0.39/0.58 (step @p39 :rule alpha_equiv :args (@t62 @t61 (@list @t52))) % 0.39/0.58 (step @p40 :rule nary_cong :premises (@p39 @p38) :args (@t63)) % 0.39/0.58 (step @p41 :rule quant-miniscope-and :args ((= (forall @t2 (and @t37 @t59)) @t63))) % 0.39/0.58 (step @p42 :rule trans :premises (@p41 @p40)) % 0.39/0.58 (step @p43 :rule bool-double-not-elim :args (@t32)) % 0.39/0.58 (step @p44 :rule bool-double-not-elim :args (@t34)) % 0.39/0.58 (step @p45 :rule nary_cong :premises (@p44 @p43) :args ((or (not @t35) (not @t33)))) % 0.39/0.58 (step @p46 :rule bool-and-de-morgan :args (@t35 @t33 true)) % 0.39/0.58 (step @p47 :rule trans :premises (@p46 @p45)) % 0.39/0.58 (step @p48 :rule refl :args (@t37)) % 0.39/0.58 (step @p49 :rule nary_cong :premises (@p48 @p47) :args ((and @t37 (not @t36)))) % 0.39/0.58 (step @p50 :rule bool-implies-de-morgan :args (@t37 @t36)) % 0.39/0.58 (step @p51 :rule trans :premises (@p50 @p49)) % 0.39/0.58 (step @p52 :rule cong :premises (@p51) :args (@t64)) % 0.39/0.58 (step @p53 :rule trans :premises (@p52 @p42)) % 0.39/0.58 (step @p54 :rule cong :premises (@p53) :args (@t65)) % 0.39/0.58 (step @p55 :rule exists-elim :args ((= @t39 @t65))) % 0.39/0.59 (step @p56 :rule trans :premises (@p55 @p54)) % 0.39/0.59 (step @p57 :rule refl :args (@t28)) % 0.39/0.59 (step @p58 :rule cong :premises (@p57 @p56) :args (@t40)) % 0.39/0.59 (step @p59 :rule cong :premises (@p58) :args (@t41)) % 0.39/0.59 (step @p60 :rule trans :premises (@p59 @p37)) % 0.39/0.59 (step @p61 :rule cong :premises (@p60) :args (@t42)) % 0.39/0.59 (step @p62 :rule eq_resolve :premises (@p17 @p61)) % 0.39/0.59 (step @p63 :rule not_or_elim :premises (@p62) :args (1)) % 0.39/0.59 (step @p64 :rule skolemize :premises (@p63)) % 0.39/0.59 (step @p65 :rule bool-double-not-elim :args (@t68)) % 0.39/0.59 (step @p66 :rule refl :args (@t72)) % 0.39/0.59 (step @p67 :rule nary_cong :premises (@p66 @p65) :args ((or @t72 (not @t69)))) % 0.39/0.59 (step @p68 :rule cnf_or_neg :args (@t72 3)) % 0.39/0.59 (step @p69 :rule eq_resolve :premises (@p68 @p67)) % 0.39/0.59 (step @p70 :rule reordering :premises (@p69) :args ((or @t68 @t72))) % 0.39/0.59 (step @p71 :rule chain_m_resolution :premises (@p70 @p64) :args (@t68 @t73 @t74)) % 0.39/0.59 (step @p72 :rule instantiate :premises (@p71) :args (@t76)) % 0.39/0.59 (step @p73 :rule aci_norm :args ((= (or @t78 (or @t77 @t11)) (or @t78 @t77 @t11)))) % 0.39/0.59 (step @p74 :rule refl :args (@t11)) % 0.39/0.59 (step @p75 :rule bool-or-de-morgan :args (@t13 @t12 false)) % 0.39/0.59 (step @p76 :rule nary_cong :premises (@p75 @p74) :args ((or (not @t14) @t11))) % 0.39/0.59 (step @p77 :rule bool-impl-elim :args (@t14 @t11)) % 0.39/0.59 (step @p78 :rule trans :premises (@p77 @p76)) % 0.39/0.59 (step @p79 :rule refl :args (@t78)) % 0.39/0.59 (step @p80 :rule nary_cong :premises (@p79 @p78) :args ((or @t78 @t15))) % 0.39/0.59 (step @p81 :rule trans :premises (@p80 @p73)) % 0.39/0.59 (step @p82 :rule bool-impl-elim :args (@t10 @t15)) % 0.39/0.59 (step @p83 :rule trans :premises (@p82 @p81)) % 0.39/0.59 (step @p84 :rule cong :premises (@p83) :args (@t16)) % 0.39/0.59 (step @p85 :rule eq_resolve :premises (@p8 @p84)) % 0.39/0.59 (step @p86 :rule instantiate :premises (@p85) :args ((@list @t67 @t66 @t75))) % 0.39/0.59 (step @p87 :rule instantiate :premises (@p1) :args (@t76)) % 0.39/0.59 (step @p88 :rule bool-double-not-elim :args (@t70)) % 0.39/0.59 (step @p89 :rule nary_cong :premises (@p66 @p88) :args ((or @t72 (not @t71)))) % 0.39/0.59 (step @p90 :rule cnf_or_neg :args (@t72 2)) % 0.39/0.59 (step @p91 :rule eq_resolve :premises (@p90 @p89)) % 0.39/0.59 (step @p92 :rule reordering :premises (@p91) :args ((or @t70 @t72))) % 0.39/0.59 (step @p93 :rule chain_m_resolution :premises (@p92 @p64) :args (@t70 @t73 @t74)) % 0.39/0.59 (step @p94 :rule cnf_or_pos :args (@t85)) % 0.39/0.59 (step @p95 :rule reordering :premises (@p94) :args ((or @t71 @t79 @t84 (not @t85)))) % 0.39/0.59 (step @p96 :rule chain_m_resolution :premises (@p95 @p93 @p87 @p86) :args (@t84 (@list false true false) (@list @t70 @t79 @t85))) % 0.39/0.59 (step @p97 :rule cnf_and_pos :args (@t84 0)) % 0.39/0.59 (step @p98 :rule reordering :premises (@p97) :args ((or @t83 @t86))) % 0.39/0.59 (step @p99 :rule chain_m_resolution :premises (@p98 @p96) :args (@t83 @t87 @t88)) % 0.39/0.59 (step @p100 :rule cnf_and_pos :args (@t84 1)) % 0.39/0.59 (step @p101 :rule reordering :premises (@p100) :args ((or @t81 @t86))) % 0.39/0.59 (step @p102 :rule chain_m_resolution :premises (@p101 @p96) :args (@t81 @t87 @t88)) % 0.39/0.59 (step @p103 :rule cnf_or_pos :args (@t89)) % 0.39/0.59 (step @p104 :rule reordering :premises (@p103) :args ((or @t82 @t80 (not @t89)))) % 0.39/0.59 (step @p105 false :rule chain_m_resolution :premises (@p104 @p102 @p99 @p72) :args (false (@list true true false) (@list @t80 @t82 @t89))) % 0.39/0.59 ) % 0.39/0.59 % SZS output end Proof % 0.39/0.59 % cvc5 exiting %------------------------------------------------------------------------------