%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : GEO181+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 : n004.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 08:16:35 AM UTC 2026 % Result : Theorem 0.62s 0.81s % Output : Proof 0.62s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : GEO181+2 : 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 % 0.17/0.35 % Computer : n004.cluster.edu % 0.17/0.35 % Model : x86_64 x86_64 % 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.35 % Memory : 8042.1875MB % 0.17/0.35 % 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 23:39:07 EDT 2026 % 0.17/0.35 % CPUTime : % 0.26/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.62/0.81 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.62/0.81 % SZS status Theorem % 0.62/0.81 % SZS output start Proof % 0.62/0.81 ( % 0.62/0.81 (declare-sort $$unsorted 0) % 0.62/0.81 (declare-const tptp.intersection_point (-> $$unsorted $$unsorted $$unsorted)) % 0.62/0.81 (declare-const tptp.apart_point_and_line (-> $$unsorted $$unsorted Bool)) % 0.62/0.81 (declare-const tptp.line_connecting (-> $$unsorted $$unsorted $$unsorted)) % 0.62/0.81 (declare-const tptp.convergent_lines (-> $$unsorted $$unsorted Bool)) % 0.62/0.81 (declare-const tptp.distinct_lines (-> $$unsorted $$unsorted Bool)) % 0.62/0.81 (declare-const tptp.distinct_points (-> $$unsorted $$unsorted Bool)) % 0.62/0.81 (define @t1 () (@var "X" $$unsorted)) % 0.62/0.81 (define @t2 () (@list @t1)) % 0.62/0.81 (define @t3 () (@var "Z" $$unsorted)) % 0.62/0.81 (define @t4 () (@var "Y" $$unsorted)) % 0.62/0.81 (define @t5 () (tptp.distinct_points @t4 @t3)) % 0.62/0.81 (define @t6 () (tptp.distinct_points @t1 @t3)) % 0.62/0.81 (define @t7 () (or @t6 @t5)) % 0.62/0.81 (define @t8 () (tptp.distinct_points @t1 @t4)) % 0.62/0.81 (define @t9 () (@list @t1 @t4 @t3)) % 0.62/0.81 (define @t10 () (forall @t9 (=> @t8 @t7))) % 0.62/0.81 (define @t11 () (tptp.distinct_lines @t4 @t3)) % 0.62/0.81 (define @t12 () (tptp.distinct_lines @t1 @t4)) % 0.62/0.81 (define @t13 () (tptp.convergent_lines @t1 @t4)) % 0.62/0.81 (define @t14 () (and (tptp.distinct_points @t3 @t1) (tptp.distinct_points @t3 @t4))) % 0.62/0.81 (define @t15 () (tptp.apart_point_and_line @t3 (tptp.line_connecting @t1 @t4))) % 0.62/0.81 (define @t16 () (=> @t15 @t14)) % 0.62/0.81 (define @t17 () (forall @t9 (=> @t8 @t16))) % 0.62/0.81 (define @t18 () (tptp.apart_point_and_line @t3 @t4)) % 0.62/0.81 (define @t19 () (@var "V" $$unsorted)) % 0.62/0.81 (define @t20 () (tptp.apart_point_and_line @t4 @t19)) % 0.62/0.81 (define @t21 () (@var "U" $$unsorted)) % 0.62/0.81 (define @t22 () (tptp.apart_point_and_line @t4 @t21)) % 0.62/0.81 (define @t23 () (tptp.apart_point_and_line @t1 @t19)) % 0.62/0.81 (define @t24 () (tptp.apart_point_and_line @t1 @t21)) % 0.62/0.81 (define @t25 () (or @t24 @t23 @t22 @t20)) % 0.62/0.81 (define @t26 () (tptp.distinct_lines @t21 @t19)) % 0.62/0.81 (define @t27 () (and @t8 @t26)) % 0.62/0.81 (define @t28 () (forall (@list @t1 @t4 @t21 @t19) (=> @t27 @t25))) % 0.62/0.81 (define @t29 () (tptp.apart_point_and_line @t1 @t4)) % 0.62/0.81 (define @t30 () (tptp.apart_point_and_line @t1 @t3)) % 0.62/0.81 (define @t31 () (or @t11 @t30)) % 0.62/0.81 (define @t32 () (forall @t9 (=> @t29 @t31))) % 0.62/0.81 (define @t33 () (tptp.apart_point_and_line @t4 (tptp.line_connecting @t1 @t3))) % 0.62/0.81 (define @t34 () (=> @t15 @t33)) % 0.62/0.81 (define @t35 () (forall @t9 (=> @t8 @t34))) % 0.62/0.81 (define @t36 () (not @t35)) % 0.62/0.81 (define @t37 () (not @t15)) % 0.62/0.81 (define @t38 () (not @t8)) % 0.62/0.81 (define @t39 () (or @t38 @t37 @t33)) % 0.62/0.81 (define @t40 () (forall @t9 @t39)) % 0.62/0.81 (define @t41 () (@quantifiers_skolemize @t40 2)) % 0.62/0.81 (define @t42 () (@quantifiers_skolemize @t40 0)) % 0.62/0.81 (define @t43 () (tptp.line_connecting @t42 @t41)) % 0.62/0.81 (define @t44 () (@quantifiers_skolemize @t40 1)) % 0.62/0.81 (define @t45 () (tptp.apart_point_and_line @t44 @t43)) % 0.62/0.81 (define @t46 () (tptp.line_connecting @t42 @t44)) % 0.62/0.81 (define @t47 () (tptp.apart_point_and_line @t41 @t46)) % 0.62/0.81 (define @t48 () (not @t47)) % 0.62/0.81 (define @t49 () (tptp.distinct_points @t42 @t44)) % 0.62/0.81 (define @t50 () (not @t49)) % 0.62/0.81 (define @t51 () (or @t50 @t48 @t45)) % 0.62/0.81 (define @t52 () (@list true)) % 0.62/0.81 (define @t53 () (@list @t51)) % 0.62/0.81 (define @t54 () (@list @t42 @t44 @t42)) % 0.62/0.81 (define @t55 () (tptp.distinct_points @t44 @t42)) % 0.62/0.81 (define @t56 () (tptp.distinct_points @t42 @t42)) % 0.62/0.81 (define @t57 () (or @t50 @t56 @t55)) % 0.62/0.81 (define @t58 () (@list false true false)) % 0.62/0.81 (define @t59 () (and @t56 @t49)) % 0.62/0.81 (define @t60 () (not @t59)) % 0.62/0.81 (define @t61 () (@list @t56)) % 0.62/0.81 (define @t62 () (tptp.apart_point_and_line @t42 @t46)) % 0.62/0.81 (define @t63 () (not @t62)) % 0.62/0.81 (define @t64 () (or @t50 @t63 @t59)) % 0.62/0.81 (define @t65 () (tptp.distinct_points @t44 @t44)) % 0.62/0.81 (define @t66 () (and @t55 @t65)) % 0.62/0.81 (define @t67 () (not @t66)) % 0.62/0.81 (define @t68 () (tptp.apart_point_and_line @t44 @t46)) % 0.62/0.81 (define @t69 () (not @t68)) % 0.62/0.81 (define @t70 () (or @t50 @t69 @t66)) % 0.62/0.81 (define @t71 () (not @t26)) % 0.62/0.81 (define @t72 () (tptp.distinct_points @t42 @t41)) % 0.62/0.81 (define @t73 () (and @t56 @t72)) % 0.62/0.81 (define @t74 () (not @t73)) % 0.62/0.81 (define @t75 () (tptp.distinct_points @t41 @t42)) % 0.62/0.81 (define @t76 () (and @t75 (tptp.distinct_points @t41 @t44))) % 0.62/0.81 (define @t77 () (or @t50 @t48 @t76)) % 0.62/0.81 (define @t78 () (tptp.distinct_points @t41 @t41)) % 0.62/0.81 (define @t79 () (not @t75)) % 0.62/0.81 (define @t80 () (or @t79 @t78 @t72)) % 0.62/0.81 (define @t81 () (tptp.apart_point_and_line @t42 @t43)) % 0.62/0.81 (define @t82 () (not @t81)) % 0.62/0.81 (define @t83 () (not @t72)) % 0.62/0.81 (define @t84 () (or @t83 @t82 @t73)) % 0.62/0.81 (define @t85 () (not @t29)) % 0.62/0.81 (define @t86 () (and @t75 @t78)) % 0.62/0.81 (define @t87 () (not @t86)) % 0.62/0.81 (define @t88 () (tptp.apart_point_and_line @t41 @t43)) % 0.62/0.81 (define @t89 () (not @t88)) % 0.62/0.81 (define @t90 () (or @t83 @t89 @t86)) % 0.62/0.81 (define @t91 () (tptp.distinct_lines @t46 @t43)) % 0.62/0.81 (define @t92 () (or @t48 @t91 @t88)) % 0.62/0.81 (define @t93 () (not @t91)) % 0.62/0.81 (define @t94 () (not @t55)) % 0.62/0.81 (define @t95 () (or @t94 @t93 @t68 @t45 @t62 @t81)) % 0.62/0.81 (assume @p1 (forall @t2 (not (tptp.distinct_points @t1 @t1)))) % 0.62/0.81 (assume @p2 (forall @t2 (not (tptp.distinct_lines @t1 @t1)))) % 0.62/0.81 (assume @p3 (forall @t2 (not (tptp.convergent_lines @t1 @t1)))) % 0.62/0.81 (assume @p4 @t10) % 0.62/0.81 (assume @p5 (forall @t9 (=> @t12 (or (tptp.distinct_lines @t1 @t3) @t11)))) % 0.62/0.81 (assume @p6 (forall @t9 (=> @t13 (or (tptp.convergent_lines @t1 @t3) (tptp.convergent_lines @t4 @t3))))) % 0.62/0.81 (assume @p7 @t17) % 0.62/0.81 (assume @p8 (forall @t9 (=> @t13 (=> (or (tptp.apart_point_and_line @t3 @t1) @t18) (tptp.distinct_points @t3 (tptp.intersection_point @t1 @t4)))))) % 0.62/0.81 (assume @p9 @t28) % 0.62/0.81 (assume @p10 (forall @t9 (=> @t29 (or @t6 @t18)))) % 0.62/0.81 (assume @p11 @t32) % 0.62/0.81 (assume @p12 (forall (@list @t1 @t4) (=> @t13 @t12))) % 0.62/0.81 (assume @p13 @t36) % 0.62/0.81 (assume @p14 true) % 0.62/0.81 (step @p15 :rule aci_norm :args ((= (or @t38 (or @t37 @t33)) @t39))) % 0.62/0.81 (step @p16 :rule bool-impl-elim :args (@t15 @t33)) % 0.62/0.81 (step @p17 :rule refl :args (@t38)) % 0.62/0.81 (step @p18 :rule nary_cong :premises (@p17 @p16) :args ((or @t38 @t34))) % 0.62/0.81 (step @p19 :rule trans :premises (@p18 @p15)) % 0.62/0.81 (step @p20 :rule bool-impl-elim :args (@t8 @t34)) % 0.62/0.81 (step @p21 :rule trans :premises (@p20 @p19)) % 0.62/0.81 (step @p22 :rule cong :premises (@p21) :args (@t35)) % 0.62/0.81 (step @p23 :rule cong :premises (@p22) :args (@t36)) % 0.62/0.81 (step @p24 :rule eq_resolve :premises (@p13 @p23)) % 0.62/0.81 (step @p25 :rule skolemize :premises (@p24)) % 0.62/0.81 (step @p26 :rule cnf_or_neg :args (@t51 2)) % 0.62/0.81 (step @p27 :rule chain_m_resolution :premises (@p26 @p25) :args ((not @t45) @t52 @t53)) % 0.62/0.81 (step @p28 :rule aci_norm :args ((= (or @t38 @t7) (or @t38 @t6 @t5)))) % 0.62/0.81 (step @p29 :rule bool-impl-elim :args (@t8 @t7)) % 0.62/0.81 (step @p30 :rule trans :premises (@p29 @p28)) % 0.62/0.81 (step @p31 :rule cong :premises (@p30) :args (@t10)) % 0.62/0.81 (step @p32 :rule eq_resolve :premises (@p4 @p31)) % 0.62/0.81 (step @p33 :rule instantiate :premises (@p32) :args (@t54)) % 0.62/0.81 (step @p34 :rule instantiate :premises (@p1) :args ((@list @t42))) % 0.62/0.81 (step @p35 :rule bool-double-not-elim :args (@t49)) % 0.62/0.81 (step @p36 :rule refl :args (@t51)) % 0.62/0.81 (step @p37 :rule nary_cong :premises (@p36 @p35) :args ((or @t51 (not @t50)))) % 0.62/0.81 (step @p38 :rule cnf_or_neg :args (@t51 0)) % 0.62/0.81 (step @p39 :rule eq_resolve :premises (@p38 @p37)) % 0.62/0.81 (step @p40 :rule reordering :premises (@p39) :args ((or @t49 @t51))) % 0.62/0.81 (step @p41 :rule chain_m_resolution :premises (@p40 @p25) :args (@t49 @t52 @t53)) % 0.62/0.81 (step @p42 :rule cnf_or_pos :args (@t57)) % 0.62/0.81 (step @p43 :rule reordering :premises (@p42) :args ((or @t50 @t56 @t55 (not @t57)))) % 0.62/0.81 (step @p44 :rule chain_m_resolution :premises (@p43 @p41 @p34 @p33) :args (@t55 @t58 (@list @t49 @t56 @t57))) % 0.62/0.81 (step @p45 :rule aci_norm :args ((= (or @t38 (or @t37 @t14)) (or @t38 @t37 @t14)))) % 0.62/0.81 (step @p46 :rule bool-impl-elim :args (@t15 @t14)) % 0.62/0.81 (step @p47 :rule nary_cong :premises (@p17 @p46) :args ((or @t38 @t16))) % 0.62/0.81 (step @p48 :rule trans :premises (@p47 @p45)) % 0.62/0.81 (step @p49 :rule bool-impl-elim :args (@t8 @t16)) % 0.62/0.81 (step @p50 :rule trans :premises (@p49 @p48)) % 0.62/0.81 (step @p51 :rule cong :premises (@p50) :args (@t17)) % 0.62/0.81 (step @p52 :rule eq_resolve :premises (@p7 @p51)) % 0.62/0.81 (step @p53 :rule instantiate :premises (@p52) :args (@t54)) % 0.62/0.81 (step @p54 :rule cnf_and_pos :args (@t59 0)) % 0.62/0.81 (step @p55 :rule reordering :premises (@p54) :args ((or @t56 @t60))) % 0.62/0.81 (step @p56 :rule chain_m_resolution :premises (@p55 @p34) :args (@t60 @t52 @t61)) % 0.62/0.81 (step @p57 :rule cnf_or_pos :args (@t64)) % 0.62/0.81 (step @p58 :rule reordering :premises (@p57) :args ((or @t50 @t63 @t59 (not @t64)))) % 0.62/0.81 (step @p59 :rule chain_m_resolution :premises (@p58 @p41 @p56 @p53) :args (@t63 @t58 (@list @t49 @t59 @t64))) % 0.62/0.81 (step @p60 :rule instantiate :premises (@p52) :args ((@list @t42 @t44 @t44))) % 0.62/0.81 (step @p61 :rule instantiate :premises (@p1) :args ((@list @t44))) % 0.62/0.81 (step @p62 :rule cnf_and_pos :args (@t66 1)) % 0.62/0.81 (step @p63 :rule reordering :premises (@p62) :args ((or @t65 @t67))) % 0.62/0.81 (step @p64 :rule chain_m_resolution :premises (@p63 @p61) :args (@t67 @t52 (@list @t65))) % 0.62/0.81 (step @p65 :rule cnf_or_pos :args (@t70)) % 0.62/0.81 (step @p66 :rule reordering :premises (@p65) :args ((or @t50 @t69 @t66 (not @t70)))) % 0.62/0.81 (step @p67 :rule chain_m_resolution :premises (@p66 @p41 @p64 @p60) :args (@t69 @t58 (@list @t49 @t66 @t70))) % 0.62/0.81 (step @p68 :rule aci_norm :args ((= (or (or @t38 @t71) @t25) (or @t38 @t71 @t24 @t23 @t22 @t20)))) % 0.62/0.81 (step @p69 :rule refl :args (@t25)) % 0.62/0.81 (step @p70 :rule bool-and-de-morgan :args (@t8 @t26 true)) % 0.62/0.81 (step @p71 :rule nary_cong :premises (@p70 @p69) :args ((or (not @t27) @t25))) % 0.62/0.81 (step @p72 :rule trans :premises (@p71 @p68)) % 0.62/0.81 (step @p73 :rule bool-impl-elim :args (@t27 @t25)) % 0.62/0.81 (step @p74 :rule trans :premises (@p73 @p72)) % 0.62/0.81 (step @p75 :rule cong :premises (@p74) :args (@t28)) % 0.62/0.81 (step @p76 :rule eq_resolve :premises (@p9 @p75)) % 0.62/0.81 (step @p77 :rule instantiate :premises (@p76) :args ((@list @t44 @t42 @t46 @t43))) % 0.62/0.81 (step @p78 :rule instantiate :premises (@p52) :args ((@list @t42 @t41 @t42))) % 0.62/0.81 (step @p79 :rule cnf_and_pos :args (@t73 0)) % 0.62/0.81 (step @p80 :rule reordering :premises (@p79) :args ((or @t56 @t74))) % 0.62/0.81 (step @p81 :rule chain_m_resolution :premises (@p80 @p34) :args (@t74 @t52 @t61)) % 0.62/0.81 (step @p82 :rule instantiate :premises (@p32) :args ((@list @t41 @t42 @t41))) % 0.62/0.81 (step @p83 :rule instantiate :premises (@p1) :args ((@list @t41))) % 0.62/0.81 (step @p84 :rule instantiate :premises (@p52) :args ((@list @t42 @t44 @t41))) % 0.62/0.81 (step @p85 :rule bool-double-not-elim :args (@t47)) % 0.62/0.81 (step @p86 :rule nary_cong :premises (@p36 @p85) :args ((or @t51 (not @t48)))) % 0.62/0.81 (step @p87 :rule cnf_or_neg :args (@t51 1)) % 0.62/0.81 (step @p88 :rule eq_resolve :premises (@p87 @p86)) % 0.62/0.81 (step @p89 :rule reordering :premises (@p88) :args ((or @t47 @t51))) % 0.62/0.81 (step @p90 :rule chain_m_resolution :premises (@p89 @p25) :args (@t47 @t52 @t53)) % 0.62/0.81 (step @p91 :rule cnf_or_pos :args (@t77)) % 0.62/0.81 (step @p92 :rule reordering :premises (@p91) :args ((or @t50 @t48 @t76 (not @t77)))) % 0.62/0.81 (step @p93 :rule chain_m_resolution :premises (@p92 @p41 @p90 @p84) :args (@t76 (@list false false false) (@list @t49 @t47 @t77))) % 0.62/0.81 (step @p94 :rule cnf_and_pos :args (@t76 0)) % 0.62/0.81 (step @p95 :rule reordering :premises (@p94) :args ((or @t75 (not @t76)))) % 0.62/0.81 (step @p96 :rule chain_m_resolution :premises (@p95 @p93) :args (@t75 (@list false) (@list @t76))) % 0.62/0.81 (step @p97 :rule cnf_or_pos :args (@t80)) % 0.62/0.81 (step @p98 :rule reordering :premises (@p97) :args ((or @t79 @t78 @t72 (not @t80)))) % 0.62/0.81 (step @p99 :rule chain_m_resolution :premises (@p98 @p96 @p83 @p82) :args (@t72 @t58 (@list @t75 @t78 @t80))) % 0.62/0.81 (step @p100 :rule cnf_or_pos :args (@t84)) % 0.62/0.81 (step @p101 :rule reordering :premises (@p100) :args ((or @t82 @t83 @t73 (not @t84)))) % 0.62/0.81 (step @p102 :rule chain_m_resolution :premises (@p101 @p99 @p81 @p78) :args (@t82 @t58 (@list @t72 @t73 @t84))) % 0.62/0.81 (step @p103 :rule aci_norm :args ((= (or @t85 @t31) (or @t85 @t11 @t30)))) % 0.62/0.81 (step @p104 :rule bool-impl-elim :args (@t29 @t31)) % 0.62/0.81 (step @p105 :rule trans :premises (@p104 @p103)) % 0.62/0.81 (step @p106 :rule cong :premises (@p105) :args (@t32)) % 0.62/0.81 (step @p107 :rule eq_resolve :premises (@p11 @p106)) % 0.62/0.81 (step @p108 :rule instantiate :premises (@p107) :args ((@list @t41 @t46 @t43))) % 0.62/0.81 (step @p109 :rule instantiate :premises (@p52) :args ((@list @t42 @t41 @t41))) % 0.62/0.81 (step @p110 :rule cnf_and_pos :args (@t86 1)) % 0.62/0.81 (step @p111 :rule reordering :premises (@p110) :args ((or @t78 @t87))) % 0.62/0.81 (step @p112 :rule chain_m_resolution :premises (@p111 @p83) :args (@t87 @t52 (@list @t78))) % 0.62/0.81 (step @p113 :rule cnf_or_pos :args (@t90)) % 0.62/0.81 (step @p114 :rule reordering :premises (@p113) :args ((or @t83 @t89 @t86 (not @t90)))) % 0.62/0.81 (step @p115 :rule chain_m_resolution :premises (@p114 @p99 @p112 @p109) :args (@t89 @t58 (@list @t72 @t86 @t90))) % 0.62/0.81 (step @p116 :rule cnf_or_pos :args (@t92)) % 0.62/0.81 (step @p117 :rule reordering :premises (@p116) :args ((or @t48 @t91 @t88 (not @t92)))) % 0.62/0.81 (step @p118 :rule chain_m_resolution :premises (@p117 @p90 @p115 @p108) :args (@t91 @t58 (@list @t47 @t88 @t92))) % 0.62/0.81 (step @p119 :rule cnf_or_pos :args (@t95)) % 0.62/0.81 (step @p120 :rule reordering :premises (@p119) :args ((or @t45 @t62 @t94 @t68 @t81 @t93 (not @t95)))) % 0.62/0.81 (step @p121 false :rule chain_m_resolution :premises (@p120 @p118 @p102 @p77 @p67 @p59 @p44 @p27) :args (false (@list false true false true true false true) (@list @t91 @t81 @t95 @t68 @t62 @t55 @t45))) % 0.62/0.81 ) % 0.62/0.81 % SZS output end Proof % 0.62/0.81 % cvc5 exiting %------------------------------------------------------------------------------