%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : GEO226+1 : 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 : n027.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 08:16:50 AM UTC 2026 % Result : Theorem 0.35s 0.58s % Output : Proof 0.35s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : GEO226+1 : TPTP v9.2.1. Released v3.3.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n027.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.35 % CPULimit : 300 % 0.17/0.35 % WCLimit : 300 % 0.17/0.35 % DateTime : Mon Jun 1 23:41:21 EDT 2026 % 0.17/0.35 % CPUTime : % 0.35/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.35/0.58 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.35/0.58 % SZS status Theorem % 0.35/0.58 % SZS output start Proof % 0.35/0.58 ( % 0.35/0.58 (declare-sort $$unsorted 0) % 0.35/0.58 (declare-const tptp.parallel_through_point (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.58 (declare-const tptp.intersection_point (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.58 (declare-const tptp.apart_point_and_line (-> $$unsorted $$unsorted Bool)) % 0.35/0.58 (declare-const tptp.orthogonal_through_point (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.58 (declare-const tptp.line_connecting (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.58 (declare-const tptp.convergent_lines (-> $$unsorted $$unsorted Bool)) % 0.35/0.58 (declare-const tptp.line (-> $$unsorted Bool)) % 0.35/0.58 (declare-const tptp.distinct_lines (-> $$unsorted $$unsorted Bool)) % 0.35/0.58 (declare-const tptp.point (-> $$unsorted Bool)) % 0.35/0.58 (declare-const tptp.distinct_points (-> $$unsorted $$unsorted Bool)) % 0.35/0.58 (define @t1 () (@var "X" $$unsorted)) % 0.35/0.58 (define @t2 () (@list @t1)) % 0.35/0.58 (define @t3 () (@var "Z" $$unsorted)) % 0.35/0.58 (define @t4 () (@var "Y" $$unsorted)) % 0.35/0.58 (define @t5 () (tptp.distinct_points @t1 @t3)) % 0.35/0.58 (define @t6 () (tptp.distinct_points @t1 @t4)) % 0.35/0.58 (define @t7 () (@list @t1 @t4 @t3)) % 0.35/0.58 (define @t8 () (tptp.distinct_lines @t4 @t3)) % 0.35/0.58 (define @t9 () (tptp.convergent_lines @t1 @t3)) % 0.35/0.58 (define @t10 () (tptp.convergent_lines @t1 @t4)) % 0.35/0.58 (define @t11 () (tptp.line_connecting @t1 @t4)) % 0.35/0.58 (define @t12 () (@list @t1 @t4)) % 0.35/0.58 (define @t13 () (tptp.intersection_point @t1 @t4)) % 0.35/0.58 (define @t14 () (not (tptp.apart_point_and_line @t13 @t1))) % 0.35/0.58 (define @t15 () (forall @t12 (=> @t10 @t14))) % 0.35/0.58 (define @t16 () (not (tptp.apart_point_and_line @t13 @t4))) % 0.35/0.58 (define @t17 () (forall @t12 (=> @t10 @t16))) % 0.35/0.58 (define @t18 () (@var "V" $$unsorted)) % 0.35/0.58 (define @t19 () (@var "U" $$unsorted)) % 0.35/0.58 (define @t20 () (tptp.apart_point_and_line @t1 @t4)) % 0.35/0.58 (define @t21 () (@var "B" $$unsorted)) % 0.35/0.58 (define @t22 () (@var "A" $$unsorted)) % 0.35/0.58 (define @t23 () (tptp.point @t22)) % 0.35/0.58 (define @t24 () (@var "M" $$unsorted)) % 0.35/0.58 (define @t25 () (@var "L" $$unsorted)) % 0.35/0.58 (define @t26 () (tptp.convergent_lines @t25 @t24)) % 0.35/0.58 (define @t27 () (tptp.line @t24)) % 0.35/0.58 (define @t28 () (tptp.line @t25)) % 0.35/0.58 (define @t29 () (and @t28 @t27 @t26)) % 0.35/0.58 (define @t30 () (@list @t25 @t24)) % 0.35/0.58 (define @t31 () (and @t28 @t23)) % 0.35/0.58 (define @t32 () (@list @t25 @t22)) % 0.35/0.58 (define @t33 () (tptp.apart_point_and_line @t1 @t24)) % 0.35/0.58 (define @t34 () (not @t33)) % 0.35/0.58 (define @t35 () (tptp.apart_point_and_line @t1 @t25)) % 0.35/0.58 (define @t36 () (not @t35)) % 0.35/0.58 (define @t37 () (and @t36 @t34)) % 0.35/0.58 (define @t38 () (tptp.point @t1)) % 0.35/0.58 (define @t39 () (=> @t38 @t37)) % 0.35/0.58 (define @t40 () (exists @t2 @t39)) % 0.35/0.58 (define @t41 () (=> @t29 @t40)) % 0.35/0.58 (define @t42 () (forall @t30 @t41)) % 0.35/0.58 (define @t43 () (not @t42)) % 0.35/0.58 (define @t44 () (@var "BOUND_VARIABLE_7614" $$unsorted)) % 0.35/0.58 (define @t45 () (@list @t44)) % 0.35/0.58 (define @t46 () (forall @t45 (or (tptp.apart_point_and_line @t44 @t25) (tptp.apart_point_and_line @t44 @t24)))) % 0.35/0.58 (define @t47 () (not @t46)) % 0.35/0.58 (define @t48 () (not @t26)) % 0.35/0.58 (define @t49 () (not @t27)) % 0.35/0.58 (define @t50 () (not @t28)) % 0.35/0.58 (define @t51 () (or @t50 @t49 @t48 @t47)) % 0.35/0.58 (define @t52 () (forall @t30 @t51)) % 0.35/0.58 (define @t53 () (@var "BOUND_VARIABLE_7609" $$unsorted)) % 0.35/0.58 (define @t54 () (forall (@list @t53) (tptp.point @t53))) % 0.35/0.58 (define @t55 () (not @t54)) % 0.35/0.58 (define @t56 () (or @t55 @t51)) % 0.35/0.58 (define @t57 () (or @t50 @t49 @t48 @t55 @t47)) % 0.35/0.58 (define @t58 () (or @t50 @t49 @t48)) % 0.35/0.58 (define @t59 () (not (and @t54 @t46))) % 0.35/0.58 (define @t60 () (or @t35 @t33)) % 0.35/0.58 (define @t61 () (forall @t2 @t60)) % 0.35/0.58 (define @t62 () (@list @t1)) % 0.35/0.58 (define @t63 () (forall @t2 @t38)) % 0.35/0.58 (define @t64 () (and @t63 @t61)) % 0.35/0.58 (define @t65 () (forall @t2 (not @t39))) % 0.35/0.58 (define @t66 () (not @t65)) % 0.35/0.58 (define @t67 () (@quantifiers_skolemize @t52 1)) % 0.35/0.58 (define @t68 () (@quantifiers_skolemize @t52 0)) % 0.35/0.58 (define @t69 () (forall @t45 (or (tptp.apart_point_and_line @t44 @t68) (tptp.apart_point_and_line @t44 @t67)))) % 0.35/0.58 (define @t70 () (not @t69)) % 0.35/0.58 (define @t71 () (tptp.convergent_lines @t68 @t67)) % 0.35/0.58 (define @t72 () (not @t71)) % 0.35/0.58 (define @t73 () (or (not (tptp.line @t68)) (not (tptp.line @t67)) @t72 @t70)) % 0.35/0.58 (define @t74 () (@list true)) % 0.35/0.58 (define @t75 () (@list @t73)) % 0.35/0.58 (define @t76 () (@list @t68 @t67)) % 0.35/0.58 (define @t77 () (tptp.intersection_point @t68 @t67)) % 0.35/0.58 (define @t78 () (tptp.apart_point_and_line @t77 @t67)) % 0.35/0.58 (define @t79 () (not @t78)) % 0.35/0.58 (define @t80 () (or @t72 @t79)) % 0.35/0.58 (define @t81 () (@list false false)) % 0.35/0.58 (define @t82 () (tptp.apart_point_and_line @t77 @t68)) % 0.35/0.58 (define @t83 () (not @t82)) % 0.35/0.58 (define @t84 () (or @t72 @t83)) % 0.35/0.58 (define @t85 () (or @t82 @t78)) % 0.35/0.58 (define @t86 () (not @t85)) % 0.35/0.58 (assume @p1 (forall @t2 (not (tptp.distinct_points @t1 @t1)))) % 0.35/0.58 (assume @p2 (forall @t2 (not (tptp.distinct_lines @t1 @t1)))) % 0.35/0.58 (assume @p3 (forall @t2 (not (tptp.convergent_lines @t1 @t1)))) % 0.35/0.58 (assume @p4 (forall @t7 (=> @t6 (or @t5 (tptp.distinct_points @t4 @t3))))) % 0.35/0.58 (assume @p5 (forall @t7 (=> (tptp.distinct_lines @t1 @t4) (or (tptp.distinct_lines @t1 @t3) @t8)))) % 0.35/0.58 (assume @p6 (forall @t7 (=> @t10 (or @t9 (tptp.convergent_lines @t4 @t3))))) % 0.35/0.58 (assume @p7 (forall @t12 (=> @t6 (not (tptp.apart_point_and_line @t1 @t11))))) % 0.35/0.58 (assume @p8 (forall @t12 (=> @t6 (not (tptp.apart_point_and_line @t4 @t11))))) % 0.35/0.58 (assume @p9 @t15) % 0.35/0.58 (assume @p10 @t17) % 0.35/0.58 (assume @p11 (forall (@list @t1 @t4 @t19 @t18) (=> (and @t6 (tptp.distinct_lines @t19 @t18)) (or (tptp.apart_point_and_line @t1 @t19) (tptp.apart_point_and_line @t1 @t18) (tptp.apart_point_and_line @t4 @t19) (tptp.apart_point_and_line @t4 @t18))))) % 0.35/0.58 (assume @p12 (forall @t7 (=> @t20 (or @t5 (tptp.apart_point_and_line @t3 @t4))))) % 0.35/0.58 (assume @p13 (forall @t7 (=> @t20 (or @t8 (tptp.apart_point_and_line @t1 @t3))))) % 0.35/0.58 (assume @p14 (forall @t7 (=> @t10 (or @t8 @t9)))) % 0.35/0.58 (assume @p15 (forall (@list @t22 @t21) (=> (and @t23 (tptp.point @t21) (tptp.distinct_points @t22 @t21)) (tptp.line (tptp.line_connecting @t22 @t21))))) % 0.35/0.58 (assume @p16 (forall @t30 (=> @t29 (tptp.point (tptp.intersection_point @t25 @t24))))) % 0.35/0.58 (assume @p17 (forall @t32 (=> @t31 (tptp.line (tptp.parallel_through_point @t25 @t22))))) % 0.35/0.58 (assume @p18 (forall @t32 (=> @t31 (tptp.line (tptp.orthogonal_through_point @t25 @t22))))) % 0.35/0.58 (assume @p19 @t43) % 0.35/0.58 (assume @p20 true) % 0.35/0.58 (step @p21 :rule quant-miniscope-or :args ((= (forall @t30 @t56) (or @t55 @t52)))) % 0.35/0.58 (step @p22 :rule aci_norm :args ((= @t57 @t56))) % 0.35/0.58 (step @p23 :rule cong :premises (@p22) :args ((forall @t30 @t57))) % 0.35/0.58 (step @p24 :rule trans :premises (@p23 @p21)) % 0.35/0.58 (step @p25 :rule aci_norm :args ((= (or @t58 (or @t55 @t47)) @t57))) % 0.35/0.58 (step @p26 :rule bool-and-de-morgan :args (@t54 @t46 true)) % 0.35/0.58 (step @p27 :rule aci_norm :args ((= (or @t50 (or @t49 @t48)) @t58))) % 0.35/0.58 (step @p28 :rule bool-and-de-morgan :args (@t27 @t26 true)) % 0.35/0.58 (step @p29 :rule refl :args (@t50)) % 0.35/0.58 (step @p30 :rule nary_cong :premises (@p29 @p28) :args ((or @t50 (not (and @t27 @t26))))) % 0.35/0.58 (step @p31 :rule bool-and-de-morgan :args (@t28 @t27 (and @t26))) % 0.35/0.58 (step @p32 :rule trans :premises (@p31 @p30)) % 0.35/0.58 (step @p33 :rule trans :premises (@p32 @p27)) % 0.35/0.58 (step @p34 :rule nary_cong :premises (@p33 @p26) :args ((or (not @t29) @t59))) % 0.35/0.58 (step @p35 :rule trans :premises (@p34 @p25)) % 0.35/0.58 (step @p36 :rule bool-impl-elim :args (@t29 @t59)) % 0.35/0.58 (step @p37 :rule trans :premises (@p36 @p35)) % 0.35/0.58 (step @p38 :rule cong :premises (@p37) :args ((forall @t30 (=> @t29 @t59)))) % 0.35/0.58 (step @p39 :rule trans :premises (@p38 @p24)) % 0.35/0.58 (step @p40 :rule alpha_equiv :args (@t61 @t62 (@list @t44))) % 0.35/0.58 (step @p41 :rule alpha_equiv :args (@t63 @t62 (@list @t53))) % 0.35/0.58 (step @p42 :rule nary_cong :premises (@p41 @p40) :args (@t64)) % 0.35/0.58 (step @p43 :rule quant-miniscope-and :args ((= (forall @t2 (and @t38 @t60)) @t64))) % 0.35/0.58 (step @p44 :rule trans :premises (@p43 @p42)) % 0.35/0.58 (step @p45 :rule bool-double-not-elim :args (@t33)) % 0.35/0.58 (step @p46 :rule bool-double-not-elim :args (@t35)) % 0.35/0.58 (step @p47 :rule nary_cong :premises (@p46 @p45) :args ((or (not @t36) (not @t34)))) % 0.35/0.58 (step @p48 :rule bool-and-de-morgan :args (@t36 @t34 true)) % 0.35/0.58 (step @p49 :rule trans :premises (@p48 @p47)) % 0.35/0.58 (step @p50 :rule refl :args (@t38)) % 0.35/0.58 (step @p51 :rule nary_cong :premises (@p50 @p49) :args ((and @t38 (not @t37)))) % 0.35/0.58 (step @p52 :rule bool-implies-de-morgan :args (@t38 @t37)) % 0.35/0.58 (step @p53 :rule trans :premises (@p52 @p51)) % 0.35/0.58 (step @p54 :rule cong :premises (@p53) :args (@t65)) % 0.35/0.58 (step @p55 :rule trans :premises (@p54 @p44)) % 0.35/0.58 (step @p56 :rule cong :premises (@p55) :args (@t66)) % 0.35/0.58 (step @p57 :rule exists-elim :args ((= @t40 @t66))) % 0.35/0.58 (step @p58 :rule trans :premises (@p57 @p56)) % 0.35/0.58 (step @p59 :rule refl :args (@t29)) % 0.35/0.58 (step @p60 :rule cong :premises (@p59 @p58) :args (@t41)) % 0.35/0.58 (step @p61 :rule cong :premises (@p60) :args (@t42)) % 0.35/0.58 (step @p62 :rule trans :premises (@p61 @p39)) % 0.35/0.58 (step @p63 :rule cong :premises (@p62) :args (@t43)) % 0.35/0.58 (step @p64 :rule eq_resolve :premises (@p19 @p63)) % 0.35/0.58 (step @p65 :rule not_or_elim :premises (@p64) :args (1)) % 0.35/0.58 (step @p66 :rule skolemize :premises (@p65)) % 0.35/0.58 (step @p67 :rule bool-double-not-elim :args (@t69)) % 0.35/0.58 (step @p68 :rule refl :args (@t73)) % 0.35/0.58 (step @p69 :rule nary_cong :premises (@p68 @p67) :args ((or @t73 (not @t70)))) % 0.35/0.58 (step @p70 :rule cnf_or_neg :args (@t73 3)) % 0.35/0.58 (step @p71 :rule eq_resolve :premises (@p70 @p69)) % 0.35/0.58 (step @p72 :rule reordering :premises (@p71) :args ((or @t69 @t73))) % 0.35/0.58 (step @p73 :rule chain_m_resolution :premises (@p72 @p66) :args (@t69 @t74 @t75)) % 0.35/0.58 (step @p74 :rule bool-impl-elim :args (@t10 @t16)) % 0.35/0.58 (step @p75 :rule cong :premises (@p74) :args (@t17)) % 0.35/0.58 (step @p76 :rule eq_resolve :premises (@p10 @p75)) % 0.35/0.58 (step @p77 :rule instantiate :premises (@p76) :args (@t76)) % 0.35/0.58 (step @p78 :rule bool-double-not-elim :args (@t71)) % 0.35/0.58 (step @p79 :rule nary_cong :premises (@p68 @p78) :args ((or @t73 (not @t72)))) % 0.35/0.58 (step @p80 :rule cnf_or_neg :args (@t73 2)) % 0.35/0.58 (step @p81 :rule eq_resolve :premises (@p80 @p79)) % 0.35/0.58 (step @p82 :rule reordering :premises (@p81) :args ((or @t71 @t73))) % 0.35/0.58 (step @p83 :rule chain_m_resolution :premises (@p82 @p66) :args (@t71 @t74 @t75)) % 0.35/0.58 (step @p84 :rule cnf_or_pos :args (@t80)) % 0.35/0.58 (step @p85 :rule reordering :premises (@p84) :args ((or @t72 @t79 (not @t80)))) % 0.35/0.58 (step @p86 :rule chain_m_resolution :premises (@p85 @p83 @p77) :args (@t79 @t81 (@list @t71 @t80))) % 0.35/0.58 (step @p87 :rule bool-impl-elim :args (@t10 @t14)) % 0.35/0.58 (step @p88 :rule cong :premises (@p87) :args (@t15)) % 0.35/0.58 (step @p89 :rule eq_resolve :premises (@p9 @p88)) % 0.35/0.58 (step @p90 :rule instantiate :premises (@p89) :args (@t76)) % 0.35/0.58 (step @p91 :rule cnf_or_pos :args (@t84)) % 0.35/0.58 (step @p92 :rule reordering :premises (@p91) :args ((or @t72 @t83 (not @t84)))) % 0.35/0.58 (step @p93 :rule chain_m_resolution :premises (@p92 @p83 @p90) :args (@t83 @t81 (@list @t71 @t84))) % 0.35/0.58 (step @p94 :rule cnf_or_pos :args (@t85)) % 0.35/0.58 (step @p95 :rule reordering :premises (@p94) :args ((or @t82 @t78 @t86))) % 0.35/0.58 (step @p96 :rule chain_m_resolution :premises (@p95 @p93 @p86) :args (@t86 (@list true true) (@list @t82 @t78))) % 0.35/0.58 (assume-push @p103 @t69) % 0.35/0.58 (step @p98 :rule instantiate :premises (@p73) :args ((@list @t77))) % 0.35/0.58 (step-pop @p104 :rule scope :premises (@p98)) % 0.35/0.58 (step @p99 :rule process_scope :premises (@p104) :args (@t85)) % 0.35/0.58 (step @p101 :rule implies_elim :premises (@p99)) % 0.35/0.58 (step @p102 false :rule chain_m_resolution :premises (@p101 @p96 @p73) :args (false (@list true false) (@list @t85 @t69))) % 0.35/0.58 ) % 0.35/0.58 % SZS output end Proof % 0.35/0.58 % cvc5 exiting %------------------------------------------------------------------------------