%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : GRP183-1 : TPTP v9.2.1. Bugfixed v1.2.1. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n016.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 08:20:08 AM UTC 2026 % Result : Unsatisfiable 172.96s 173.22s % Output : Proof 172.96s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : GRP183-1 : TPTP v9.2.1. Bugfixed v1.2.1. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n016.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Tue Jun 2 00:55:24 EDT 2026 % 0.16/0.34 % CPUTime : % 0.30/0.49 %----Proving TF0_NAR, FOF, or CNF % 0.30/0.50 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 15.83/16.03 --- Run --no-e-matching --full-saturate-quant at 6... % 21.83/22.06 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 6... % 27.82/28.08 --- Run --finite-model-find --uf-ss=no-minimal at 6... % 33.94/34.18 --- Run --multi-trigger-when-single --full-saturate-quant at 30... % 64.19/64.44 --- Run --trigger-sel=max --full-saturate-quant at 15... % 79.39/79.67 --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 33... % 112.69/112.93 --- Run --multi-trigger-cache --full-saturate-quant at 15... % 127.92/128.17 --- Run --prenex-quant=none --full-saturate-quant at 30... % 127.97/158.42 --- Run --enum-inst-interleave --decision=internal --full-saturate-quant at 15... % 172.96/173.22 % SZS status Unsatisfiable % 172.96/173.22 % SZS output start Proof % 172.96/173.23 ( % 172.96/173.23 (declare-sort $$unsorted 0) % 172.96/173.23 (declare-const tptp.a $$unsorted) % 172.96/173.23 (declare-const tptp.least_upper_bound (-> $$unsorted $$unsorted $$unsorted)) % 172.96/173.23 (declare-const tptp.greatest_lower_bound (-> $$unsorted $$unsorted $$unsorted)) % 172.96/173.23 (declare-const tptp.inverse (-> $$unsorted $$unsorted)) % 172.96/173.23 (declare-const tptp.multiply (-> $$unsorted $$unsorted $$unsorted)) % 172.96/173.23 (declare-const tptp.identity $$unsorted) % 172.96/173.23 (define @t1 () (@var "X" $$unsorted)) % 172.96/173.23 (define @t2 () (tptp.multiply tptp.identity @t1)) % 172.96/173.23 (define @t3 () (@list @t1)) % 172.96/173.23 (define @t4 () (forall @t3 (= @t2 @t1))) % 172.96/173.23 (define @t5 () (tptp.multiply (tptp.inverse @t1) @t1)) % 172.96/173.23 (define @t6 () (forall @t3 (= @t5 tptp.identity))) % 172.96/173.23 (define @t7 () (@var "Z" $$unsorted)) % 172.96/173.23 (define @t8 () (@var "Y" $$unsorted)) % 172.96/173.23 (define @t9 () (tptp.multiply @t1 @t8)) % 172.96/173.23 (define @t10 () (@list @t1 @t8 @t7)) % 172.96/173.23 (define @t11 () (forall @t10 (= (tptp.multiply @t9 @t7) (tptp.multiply @t1 (tptp.multiply @t8 @t7))))) % 172.96/173.23 (define @t12 () (tptp.greatest_lower_bound @t1 @t8)) % 172.96/173.23 (define @t13 () (@list @t1 @t8)) % 172.96/173.23 (define @t14 () (tptp.least_upper_bound @t1 @t8)) % 172.96/173.23 (define @t15 () (tptp.greatest_lower_bound @t8 @t7)) % 172.96/173.23 (define @t16 () (tptp.least_upper_bound @t8 @t7)) % 172.96/173.23 (define @t17 () (tptp.greatest_lower_bound @t1 @t1)) % 172.96/173.23 (define @t18 () (forall @t3 (= @t17 @t1))) % 172.96/173.23 (define @t19 () (tptp.least_upper_bound @t1 @t12)) % 172.96/173.23 (define @t20 () (forall @t13 (= @t19 @t1))) % 172.96/173.23 (define @t21 () (tptp.greatest_lower_bound @t1 @t14)) % 172.96/173.23 (define @t22 () (forall @t13 (= @t21 @t1))) % 172.96/173.23 (define @t23 () (tptp.multiply @t1 @t7)) % 172.96/173.23 (define @t24 () (tptp.multiply @t7 @t1)) % 172.96/173.23 (define @t25 () (tptp.multiply @t8 @t1)) % 172.96/173.23 (define @t26 () (@list @t8 @t7 @t1)) % 172.96/173.23 (define @t27 () (tptp.greatest_lower_bound tptp.a tptp.identity)) % 172.96/173.23 (define @t28 () (tptp.inverse @t27)) % 172.96/173.23 (define @t29 () (tptp.least_upper_bound tptp.a tptp.identity)) % 172.96/173.23 (define @t30 () (tptp.greatest_lower_bound @t29 @t28)) % 172.96/173.23 (define @t31 () (tptp.multiply @t30 @t30)) % 172.96/173.23 (define @t32 () (tptp.inverse @t30)) % 172.96/173.23 (define @t33 () (tptp.multiply @t32 @t31)) % 172.96/173.23 (define @t34 () (tptp.multiply (tptp.multiply @t32 @t30) @t30)) % 172.96/173.23 (define @t35 () (= @t34 @t33)) % 172.96/173.23 (define @t36 () (= @t33 @t34)) % 172.96/173.23 (define @t37 () (tptp.least_upper_bound @t30 tptp.identity)) % 172.96/173.23 (define @t38 () (@list tptp.identity @t28)) % 172.96/173.23 (define @t39 () (tptp.greatest_lower_bound @t28 @t29)) % 172.96/173.23 (define @t40 () (tptp.least_upper_bound @t28 @t39)) % 172.96/173.23 (define @t41 () (tptp.greatest_lower_bound tptp.identity @t28)) % 172.96/173.23 (define @t42 () (@list @t28 @t39)) % 172.96/173.23 (define @t43 () (tptp.greatest_lower_bound @t28 tptp.identity)) % 172.96/173.23 (define @t44 () (tptp.least_upper_bound @t43 @t43)) % 172.96/173.23 (define @t45 () (@list @t28)) % 172.96/173.23 (define @t46 () (tptp.inverse @t29)) % 172.96/173.23 (define @t47 () (tptp.multiply @t46 @t29)) % 172.96/173.23 (define @t48 () (tptp.inverse @t28)) % 172.96/173.23 (define @t49 () (tptp.multiply @t48 (tptp.multiply @t46 (tptp.multiply @t29 @t28)))) % 172.96/173.23 (define @t50 () (tptp.multiply tptp.identity @t28)) % 172.96/173.23 (define @t51 () (tptp.multiply @t48 @t50)) % 172.96/173.23 (define @t52 () (tptp.multiply @t28 tptp.identity)) % 172.96/173.23 (define @t53 () (tptp.multiply @t52 @t28)) % 172.96/173.23 (define @t54 () (tptp.multiply @t48 @t53)) % 172.96/173.23 (define @t55 () (tptp.multiply @t28 @t27)) % 172.96/173.23 (define @t56 () (@list @t28 @t27 tptp.identity)) % 172.96/173.23 (define @t57 () (@list tptp.a tptp.identity)) % 172.96/173.23 (define @t58 () (tptp.greatest_lower_bound tptp.identity tptp.a)) % 172.96/173.23 (define @t59 () (@list tptp.identity tptp.identity tptp.a)) % 172.96/173.23 (define @t60 () (@list tptp.identity)) % 172.96/173.23 (define @t61 () (@list @t29 @t28)) % 172.96/173.23 (define @t62 () (tptp.least_upper_bound tptp.identity @t30)) % 172.96/173.23 (define @t63 () (tptp.least_upper_bound tptp.identity @t39)) % 172.96/173.23 (define @t64 () (@list @t30)) % 172.96/173.23 (define @t65 () (tptp.multiply tptp.identity tptp.identity)) % 172.96/173.23 (define @t66 () (tptp.multiply @t29 @t30)) % 172.96/173.23 (define @t67 () (@list tptp.identity tptp.a)) % 172.96/173.23 (define @t68 () (tptp.multiply @t29 tptp.identity)) % 172.96/173.23 (define @t69 () (tptp.inverse tptp.identity)) % 172.96/173.23 (define @t70 () (tptp.multiply @t69 tptp.identity)) % 172.96/173.23 (define @t71 () (tptp.greatest_lower_bound @t29 @t69)) % 172.96/173.23 (define @t72 () (tptp.multiply @t71 @t46)) % 172.96/173.23 (define @t73 () (@list tptp.identity tptp.a tptp.identity)) % 172.96/173.23 (define @t74 () (tptp.multiply tptp.a tptp.identity)) % 172.96/173.23 (define @t75 () (@list tptp.a)) % 172.96/173.23 (define @t76 () (tptp.multiply tptp.identity tptp.a)) % 172.96/173.23 (define @t77 () (tptp.multiply @t65 tptp.a)) % 172.96/173.23 (define @t78 () (tptp.multiply @t68 tptp.a)) % 172.96/173.23 (define @t79 () (tptp.least_upper_bound @t27 tptp.identity)) % 172.96/173.23 (define @t80 () (tptp.multiply @t27 tptp.a)) % 172.96/173.23 (define @t81 () (tptp.multiply @t29 tptp.a)) % 172.96/173.23 (define @t82 () (tptp.multiply tptp.identity @t29)) % 172.96/173.23 (define @t83 () (tptp.multiply tptp.identity @t78)) % 172.96/173.23 (define @t84 () (tptp.inverse tptp.a)) % 172.96/173.23 (define @t85 () (tptp.multiply @t84 @t76)) % 172.96/173.23 (define @t86 () (tptp.multiply tptp.a tptp.a)) % 172.96/173.23 (define @t87 () (tptp.multiply @t84 @t86)) % 172.96/173.23 (define @t88 () (@list @t84 @t76 @t86)) % 172.96/173.23 (define @t89 () (@list tptp.identity tptp.a tptp.a)) % 172.96/173.23 (define @t90 () (tptp.multiply @t84 @t78)) % 172.96/173.23 (define @t91 () (@list tptp.identity @t84)) % 172.96/173.23 (define @t92 () (tptp.greatest_lower_bound tptp.identity @t84)) % 172.96/173.23 (define @t93 () (tptp.multiply @t69 @t29)) % 172.96/173.23 (define @t94 () (tptp.multiply @t93 tptp.identity)) % 172.96/173.23 (define @t95 () (tptp.multiply @t74 tptp.a)) % 172.96/173.23 (define @t96 () (tptp.multiply tptp.a @t76)) % 172.96/173.23 (define @t97 () (= @t95 @t96)) % 172.96/173.23 (define @t98 () (@list false)) % 172.96/173.23 (define @t99 () (@list @t11)) % 172.96/173.23 (define @t100 () (tptp.least_upper_bound @t27 @t80)) % 172.96/173.23 (define @t101 () (tptp.multiply tptp.identity @t80)) % 172.96/173.23 (define @t102 () (tptp.multiply @t84 @t80)) % 172.96/173.23 (define @t103 () (tptp.multiply @t80 tptp.identity)) % 172.96/173.23 (define @t104 () (tptp.multiply @t27 @t74)) % 172.96/173.23 (define @t105 () (= @t103 @t104)) % 172.96/173.23 (define @t106 () (tptp.multiply @t27 @t65)) % 172.96/173.23 (define @t107 () (tptp.multiply @t27 @t68)) % 172.96/173.23 (define @t108 () (tptp.multiply (tptp.multiply (tptp.multiply @t27 @t84) @t78) tptp.identity)) % 172.96/173.23 (define @t109 () (tptp.multiply (tptp.multiply @t27 @t29) tptp.identity)) % 172.96/173.23 (define @t110 () (= @t109 @t107)) % 172.96/173.23 (define @t111 () (tptp.multiply @t28 @t46)) % 172.96/173.23 (define @t112 () (tptp.multiply @t29 @t46)) % 172.96/173.23 (define @t113 () (tptp.multiply @t39 @t46)) % 172.96/173.23 (assume @p1 @t4) % 172.96/173.23 (assume @p2 @t6) % 172.96/173.23 (assume @p3 @t11) % 172.96/173.23 (assume @p4 (forall @t13 (= @t12 (tptp.greatest_lower_bound @t8 @t1)))) % 172.96/173.23 (assume @p5 (forall @t13 (= @t14 (tptp.least_upper_bound @t8 @t1)))) % 172.96/173.23 (assume @p6 (forall @t10 (= (tptp.greatest_lower_bound @t1 @t15) (tptp.greatest_lower_bound @t12 @t7)))) % 172.96/173.23 (assume @p7 (forall @t10 (= (tptp.least_upper_bound @t1 @t16) (tptp.least_upper_bound @t14 @t7)))) % 172.96/173.23 (assume @p8 (forall @t3 (= (tptp.least_upper_bound @t1 @t1) @t1))) % 172.96/173.23 (assume @p9 @t18) % 172.96/173.23 (assume @p10 @t20) % 172.96/173.23 (assume @p11 @t22) % 172.96/173.23 (assume @p12 (forall @t10 (= (tptp.multiply @t1 @t16) (tptp.least_upper_bound @t9 @t23)))) % 172.96/173.23 (assume @p13 (forall @t10 (= (tptp.multiply @t1 @t15) (tptp.greatest_lower_bound @t9 @t23)))) % 172.96/173.23 (assume @p14 (forall @t26 (= (tptp.multiply @t16 @t1) (tptp.least_upper_bound @t25 @t24)))) % 172.96/173.23 (assume @p15 (forall @t26 (= (tptp.multiply @t15 @t1) (tptp.greatest_lower_bound @t25 @t24)))) % 172.96/173.23 (assume @p16 (not (= @t30 tptp.identity))) % 172.96/173.23 (step @p17 :rule bool-eq-false :args (@t35)) % 172.96/173.23 (step @p18 :rule symm :premises (@p17)) % 172.96/173.23 (step @p19 :rule eq-symm :args (@t33 @t34)) % 172.96/173.23 (step @p20 :rule cong :premises (@p19) :args ((not @t36))) % 172.96/173.23 (step @p21 :rule bool-eq-false :args (@t36)) % 172.96/173.23 (step @p22 :rule trans :premises (@p21 @p20)) % 172.96/173.23 (step @p23 :rule trans :premises (@p22 @p18)) % 172.96/173.23 (step @p24 :rule symm :premises (@p16)) % 172.96/173.23 (step @p25 :rule false_intro :premises (@p24)) % 172.96/173.23 (step @p26 :rule eq-symm :args (@t21 @t1)) % 172.96/173.23 (step @p27 :rule cong :premises (@p26) :args (@t22)) % 172.96/173.23 (step @p28 :rule eq_resolve :premises (@p11 @p27)) % 172.96/173.23 (step @p29 :rule instantiate :premises (@p28) :args ((@list @t30 tptp.identity))) % 172.96/173.23 (step @p30 :rule symm :premises (@p29)) % 172.96/173.23 (step @p31 :rule instantiate :premises (@p4) :args ((@list @t30 @t37))) % 172.96/173.23 (step @p32 :rule symm :premises (@p31)) % 172.96/173.23 (step @p33 :rule instantiate :premises (@p6) :args ((@list @t37 @t29 @t28))) % 172.96/173.23 (step @p34 :rule symm :premises (@p33)) % 172.96/173.23 (step @p35 :rule eq-symm :args (@t19 @t1)) % 172.96/173.23 (step @p36 :rule cong :premises (@p35) :args (@t20)) % 172.96/173.23 (step @p37 :rule eq_resolve :premises (@p10 @p36)) % 172.96/173.23 (step @p38 :rule instantiate :premises (@p37) :args ((@list @t28 tptp.identity))) % 172.96/173.23 (step @p39 :rule symm :premises (@p38)) % 172.96/173.23 (step @p40 :rule instantiate :premises (@p4) :args (@t38)) % 172.96/173.23 (step @p41 :rule instantiate :premises (@p37) :args ((@list @t41 @t40))) % 172.96/173.23 (step @p42 :rule symm :premises (@p41)) % 172.96/173.23 (step @p43 :rule instantiate :premises (@p6) :args ((@list tptp.identity @t28 @t40))) % 172.96/173.23 (step @p44 :rule instantiate :premises (@p28) :args (@t42)) % 172.96/173.23 (step @p45 :rule refl :args (tptp.identity)) % 172.96/173.23 (step @p46 :rule cong :premises (@p45 @p44) :args (@t41)) % 172.96/173.23 (step @p47 :rule trans :premises (@p46 @p43)) % 172.96/173.23 (step @p48 :rule refl :args (@t41)) % 172.96/173.23 (step @p49 :rule cong :premises (@p48 @p47) :args ((tptp.least_upper_bound @t41 @t41))) % 172.96/173.23 (step @p50 :rule symm :premises (@p40)) % 172.96/173.23 (step @p51 :rule cong :premises (@p50 @p50) :args (@t44)) % 172.96/173.23 (step @p52 :rule trans :premises (@p51 @p49 @p42 @p40)) % 172.96/173.23 (step @p53 :rule refl :args (@t28)) % 172.96/173.23 (step @p54 :rule cong :premises (@p53 @p52) :args ((tptp.least_upper_bound @t28 @t44))) % 172.96/173.23 (step @p55 :rule symm :premises (@p51)) % 172.96/173.23 (step @p56 :rule symm :premises (@p49)) % 172.96/173.23 (step @p57 :rule eq-symm :args (@t5 tptp.identity)) % 172.96/173.23 (step @p58 :rule cong :premises (@p57) :args (@t6)) % 172.96/173.23 (step @p59 :rule eq_resolve :premises (@p2 @p58)) % 172.96/173.23 (step @p60 :rule instantiate :premises (@p59) :args (@t45)) % 172.96/173.23 (step @p61 :rule symm :premises (@p60)) % 172.96/173.23 (step @p62 :rule eq-symm :args (@t2 @t1)) % 172.96/173.23 (step @p63 :rule cong :premises (@p62) :args (@t4)) % 172.96/173.23 (step @p64 :rule eq_resolve :premises (@p1 @p63)) % 172.96/173.23 (step @p65 :rule instantiate :premises (@p64) :args (@t45)) % 172.96/173.23 (step @p66 :rule symm :premises (@p65)) % 172.96/173.23 (step @p67 :rule instantiate :premises (@p59) :args ((@list @t29))) % 172.96/173.23 (step @p68 :rule symm :premises (@p67)) % 172.96/173.23 (step @p69 :rule cong :premises (@p68 @p53) :args ((tptp.multiply @t47 @t28))) % 172.96/173.23 (step @p70 :rule instantiate :premises (@p3) :args ((@list @t46 @t29 @t28))) % 172.96/173.23 (step @p71 :rule symm :premises (@p70)) % 172.96/173.23 (step @p72 :rule trans :premises (@p71 @p69 @p66)) % 172.96/173.23 (step @p73 :rule refl :args (@t48)) % 172.96/173.23 (step @p74 :rule cong :premises (@p73 @p72) :args (@t49)) % 172.96/173.23 (step @p75 :rule symm :premises (@p69)) % 172.96/173.23 (step @p76 :rule trans :premises (@p75 @p70)) % 172.96/173.23 (step @p77 :rule cong :premises (@p73 @p76) :args (@t51)) % 172.96/173.23 (step @p78 :rule trans :premises (@p77 @p74 @p61)) % 172.96/173.23 (step @p79 :rule cong :premises (@p61 @p53) :args ((tptp.multiply (tptp.multiply @t48 @t28) @t28))) % 172.96/173.23 (step @p80 :rule instantiate :premises (@p3) :args ((@list @t48 @t28 @t28))) % 172.96/173.23 (step @p81 :rule symm :premises (@p80)) % 172.96/173.23 (step @p82 :rule cong :premises (@p53 @p66) :args ((tptp.multiply @t28 @t50))) % 172.96/173.23 (step @p83 :rule instantiate :premises (@p3) :args ((@list @t28 tptp.identity @t28))) % 172.96/173.23 (step @p84 :rule trans :premises (@p83 @p82)) % 172.96/173.23 (step @p85 :rule cong :premises (@p73 @p84) :args (@t54)) % 172.96/173.23 (step @p86 :rule trans :premises (@p85 @p81 @p79 @p66)) % 172.96/173.23 (step @p87 :rule cong :premises (@p86 @p78) :args ((tptp.greatest_lower_bound @t54 @t51))) % 172.96/173.23 (step @p88 :rule instantiate :premises (@p13) :args ((@list @t48 @t53 @t50))) % 172.96/173.23 (step @p89 :rule instantiate :premises (@p15) :args ((@list @t52 tptp.identity @t28))) % 172.96/173.23 (step @p90 :rule instantiate :premises (@p59) :args ((@list @t27))) % 172.96/173.23 (step @p91 :rule symm :premises (@p90)) % 172.96/173.23 (step @p92 :rule refl :args (@t52)) % 172.96/173.23 (step @p93 :rule cong :premises (@p92 @p91) :args ((tptp.greatest_lower_bound @t52 @t55))) % 172.96/173.23 (step @p94 :rule instantiate :premises (@p4) :args ((@list @t55 @t52))) % 172.96/173.23 (step @p95 :rule instantiate :premises (@p13) :args (@t56)) % 172.96/173.23 (step @p96 :rule instantiate :premises (@p4) :args ((@list tptp.identity @t27))) % 172.96/173.23 (step @p97 :rule instantiate :premises (@p4) :args (@t57)) % 172.96/173.23 (step @p98 :rule symm :premises (@p97)) % 172.96/173.23 (step @p99 :rule cong :premises (@p45 @p98) :args ((tptp.greatest_lower_bound tptp.identity @t58))) % 172.96/173.23 (step @p100 :rule instantiate :premises (@p6) :args (@t59)) % 172.96/173.23 (step @p101 :rule symm :premises (@p100)) % 172.96/173.23 (step @p102 :rule refl :args (tptp.a)) % 172.96/173.23 (step @p103 :rule eq-symm :args (@t17 @t1)) % 172.96/173.23 (step @p104 :rule cong :premises (@p103) :args (@t18)) % 172.96/173.23 (step @p105 :rule eq_resolve :premises (@p9 @p104)) % 172.96/173.23 (step @p106 :rule instantiate :premises (@p105) :args (@t60)) % 172.96/173.23 (step @p107 :rule cong :premises (@p106 @p102) :args (@t58)) % 172.96/173.23 (step @p108 :rule trans :premises (@p97 @p107 @p101 @p99 @p96)) % 172.96/173.23 (step @p109 :rule cong :premises (@p53 @p108) :args (@t55)) % 172.96/173.23 (step @p110 :rule trans :premises (@p90 @p109 @p95 @p94 @p93)) % 172.96/173.23 (step @p111 :rule cong :premises (@p110 @p53) :args (@t50)) % 172.96/173.23 (step @p112 :rule trans :premises (@p71 @p69 @p111 @p89)) % 172.96/173.23 (step @p113 :rule cong :premises (@p73 @p112) :args (@t49)) % 172.96/173.23 (step @p114 :rule symm :premises (@p74)) % 172.96/173.23 (step @p115 :rule trans :premises (@p60 @p114 @p113 @p88 @p87 @p50 @p41 @p56 @p55)) % 172.96/173.23 (step @p116 :rule cong :premises (@p53 @p115) :args ((tptp.least_upper_bound @t28 tptp.identity))) % 172.96/173.23 (step @p117 :rule instantiate :premises (@p5) :args (@t38)) % 172.96/173.23 (step @p118 :rule instantiate :premises (@p37) :args ((@list @t28 @t29))) % 172.96/173.23 (step @p119 :rule symm :premises (@p118)) % 172.96/173.23 (step @p120 :rule instantiate :premises (@p5) :args (@t42)) % 172.96/173.23 (step @p121 :rule symm :premises (@p120)) % 172.96/173.23 (step @p122 :rule trans :premises (@p121 @p119)) % 172.96/173.23 (step @p123 :rule cong :premises (@p45 @p122) :args ((tptp.least_upper_bound tptp.identity (tptp.least_upper_bound @t39 @t28)))) % 172.96/173.23 (step @p124 :rule instantiate :premises (@p7) :args ((@list tptp.identity @t39 @t28))) % 172.96/173.23 (step @p125 :rule symm :premises (@p124)) % 172.96/173.23 (step @p126 :rule trans :premises (@p125 @p123 @p117 @p116 @p54 @p39)) % 172.96/173.23 (step @p127 :rule instantiate :premises (@p37) :args (@t61)) % 172.96/173.23 (step @p128 :rule symm :premises (@p127)) % 172.96/173.23 (step @p129 :rule instantiate :premises (@p5) :args ((@list @t29 @t30))) % 172.96/173.23 (step @p130 :rule symm :premises (@p129)) % 172.96/173.23 (step @p131 :rule trans :premises (@p130 @p128)) % 172.96/173.23 (step @p132 :rule refl :args (@t37)) % 172.96/173.23 (step @p133 :rule cong :premises (@p132 @p131) :args ((tptp.greatest_lower_bound @t37 (tptp.least_upper_bound @t30 @t29)))) % 172.96/173.23 (step @p134 :rule instantiate :premises (@p7) :args ((@list tptp.a tptp.identity @t30))) % 172.96/173.23 (step @p135 :rule instantiate :premises (@p5) :args ((@list tptp.a @t62))) % 172.96/173.23 (step @p136 :rule symm :premises (@p135)) % 172.96/173.23 (step @p137 :rule trans :premises (@p136 @p134 @p129)) % 172.96/173.23 (step @p138 :rule instantiate :premises (@p5) :args ((@list tptp.identity @t30))) % 172.96/173.23 (step @p139 :rule cong :premises (@p138 @p137) :args ((tptp.greatest_lower_bound @t62 (tptp.least_upper_bound @t62 tptp.a)))) % 172.96/173.23 (step @p140 :rule instantiate :premises (@p28) :args ((@list @t62 tptp.a))) % 172.96/173.23 (step @p141 :rule symm :premises (@p138)) % 172.96/173.23 (step @p142 :rule trans :premises (@p141 @p140 @p139 @p133)) % 172.96/173.23 (step @p143 :rule instantiate :premises (@p4) :args (@t61)) % 172.96/173.23 (step @p144 :rule symm :premises (@p143)) % 172.96/173.23 (step @p145 :rule cong :premises (@p45 @p144) :args (@t63)) % 172.96/173.23 (step @p146 :rule trans :premises (@p145 @p138)) % 172.96/173.23 (step @p147 :rule trans :premises (@p146 @p142)) % 172.96/173.23 (step @p148 :rule cong :premises (@p147 @p126) :args ((tptp.greatest_lower_bound @t63 (tptp.least_upper_bound @t63 @t28)))) % 172.96/173.23 (step @p149 :rule instantiate :premises (@p28) :args ((@list @t63 @t28))) % 172.96/173.23 (step @p150 :rule symm :premises (@p145)) % 172.96/173.23 (step @p151 :rule instantiate :premises (@p64) :args (@t64)) % 172.96/173.23 (step @p152 :rule symm :premises (@p151)) % 172.96/173.23 (step @p153 :rule instantiate :premises (@p64) :args (@t60)) % 172.96/173.23 (step @p154 :rule symm :premises (@p153)) % 172.96/173.23 (step @p155 :rule cong :premises (@p154 @p152) :args ((tptp.least_upper_bound @t65 (tptp.multiply tptp.identity @t30)))) % 172.96/173.23 (step @p156 :rule instantiate :premises (@p12) :args ((@list tptp.identity tptp.identity @t30))) % 172.96/173.23 (step @p157 :rule cong :premises (@p45 @p141) :args ((tptp.multiply tptp.identity @t37))) % 172.96/173.23 (step @p158 :rule symm :premises (@p149)) % 172.96/173.23 (step @p159 :rule symm :premises (@p148)) % 172.96/173.23 (step @p160 :rule trans :premises (@p29 @p31 @p33 @p159 @p158 @p145 @p138)) % 172.96/173.23 (step @p161 :rule instantiate :premises (@p59) :args (@t64)) % 172.96/173.23 (step @p162 :rule symm :premises (@p161)) % 172.96/173.23 (step @p163 :rule cong :premises (@p162 @p160) :args (@t34)) % 172.96/173.23 (step @p164 :rule trans :premises (@p163 @p157 @p156 @p155 @p150 @p149 @p148 @p34 @p32 @p30)) % 172.96/173.23 (step @p165 :rule refl :args (@t30)) % 172.96/173.23 (step @p166 :rule cong :premises (@p68 @p165) :args ((tptp.multiply @t47 @t30))) % 172.96/173.23 (step @p167 :rule instantiate :premises (@p3) :args ((@list @t46 @t29 @t30))) % 172.96/173.23 (step @p168 :rule symm :premises (@p167)) % 172.96/173.23 (step @p169 :rule refl :args (@t66)) % 172.96/173.23 (step @p170 :rule instantiate :premises (@p64) :args ((@list @t46))) % 172.96/173.23 (step @p171 :rule symm :premises (@p170)) % 172.96/173.23 (step @p172 :rule refl :args (@t46)) % 172.96/173.23 (step @p173 :rule instantiate :premises (@p28) :args (@t67)) % 172.96/173.23 (step @p174 :rule symm :premises (@p173)) % 172.96/173.23 (step @p175 :rule instantiate :premises (@p5) :args (@t57)) % 172.96/173.23 (step @p176 :rule cong :premises (@p45 @p175) :args ((tptp.greatest_lower_bound tptp.identity @t29))) % 172.96/173.23 (step @p177 :rule instantiate :premises (@p4) :args ((@list tptp.identity @t29))) % 172.96/173.23 (step @p178 :rule symm :premises (@p177)) % 172.96/173.23 (step @p179 :rule trans :premises (@p178 @p176 @p174)) % 172.96/173.23 (step @p180 :rule cong :premises (@p179 @p45) :args ((tptp.multiply (tptp.greatest_lower_bound @t29 tptp.identity) tptp.identity))) % 172.96/173.23 (step @p181 :rule instantiate :premises (@p15) :args ((@list @t29 tptp.identity tptp.identity))) % 172.96/173.23 (step @p182 :rule symm :premises (@p181)) % 172.96/173.23 (step @p183 :rule instantiate :premises (@p59) :args (@t60)) % 172.96/173.23 (step @p184 :rule symm :premises (@p183)) % 172.96/173.23 (step @p185 :rule trans :premises (@p184 @p153)) % 172.96/173.23 (step @p186 :rule refl :args (@t68)) % 172.96/173.23 (step @p187 :rule cong :premises (@p186 @p185) :args ((tptp.greatest_lower_bound @t68 @t70))) % 172.96/173.23 (step @p188 :rule instantiate :premises (@p15) :args ((@list @t29 @t69 tptp.identity))) % 172.96/173.23 (step @p189 :rule trans :premises (@p188 @p187 @p182 @p180 @p154)) % 172.96/173.23 (step @p190 :rule cong :premises (@p189 @p172) :args ((tptp.multiply (tptp.multiply @t71 tptp.identity) @t46))) % 172.96/173.23 (step @p191 :rule instantiate :premises (@p3) :args ((@list @t71 tptp.identity @t46))) % 172.96/173.23 (step @p192 :rule symm :premises (@p191)) % 172.96/173.23 (step @p193 :rule refl :args (@t71)) % 172.96/173.23 (step @p194 :rule cong :premises (@p193 @p170) :args (@t72)) % 172.96/173.23 (step @p195 :rule trans :premises (@p194 @p192 @p190 @p171)) % 172.96/173.23 (step @p196 :rule cong :premises (@p195 @p169) :args ((tptp.multiply @t72 @t66))) % 172.96/173.23 (step @p197 :rule instantiate :premises (@p3) :args ((@list @t71 @t46 @t66))) % 172.96/173.23 (step @p198 :rule symm :premises (@p197)) % 172.96/173.23 (step @p199 :rule trans :premises (@p198 @p196 @p168 @p166 @p152)) % 172.96/173.23 (step @p200 :rule refl :args (@t32)) % 172.96/173.23 (step @p201 :rule cong :premises (@p200 @p199) :args ((tptp.multiply @t32 (tptp.multiply @t71 (tptp.multiply @t46 @t66))))) % 172.96/173.23 (step @p202 :rule symm :premises (@p196)) % 172.96/173.23 (step @p203 :rule cong :premises (@p91 @p45) :args ((tptp.multiply @t55 tptp.identity))) % 172.96/173.23 (step @p204 :rule instantiate :premises (@p3) :args (@t56)) % 172.96/173.23 (step @p205 :rule symm :premises (@p204)) % 172.96/173.23 (step @p206 :rule cong :premises (@p98 @p45) :args ((tptp.multiply @t58 tptp.identity))) % 172.96/173.23 (step @p207 :rule instantiate :premises (@p15) :args (@t73)) % 172.96/173.23 (step @p208 :rule symm :premises (@p207)) % 172.96/173.23 (step @p209 :rule trans :premises (@p208 @p206)) % 172.96/173.23 (step @p210 :rule cong :premises (@p53 @p209) :args ((tptp.multiply @t28 (tptp.greatest_lower_bound @t65 @t74)))) % 172.96/173.23 (step @p211 :rule instantiate :premises (@p13) :args ((@list @t28 @t65 @t74))) % 172.96/173.23 (step @p212 :rule symm :premises (@p211)) % 172.96/173.23 (step @p213 :rule instantiate :premises (@p64) :args (@t75)) % 172.96/173.23 (step @p214 :rule symm :premises (@p213)) % 172.96/173.23 (step @p215 :rule cong :premises (@p214 @p45) :args ((tptp.multiply @t76 tptp.identity))) % 172.96/173.23 (step @p216 :rule instantiate :premises (@p3) :args (@t73)) % 172.96/173.23 (step @p217 :rule symm :premises (@p216)) % 172.96/173.23 (step @p218 :rule trans :premises (@p217 @p215)) % 172.96/173.23 (step @p219 :rule cong :premises (@p53 @p218) :args ((tptp.multiply @t28 (tptp.multiply tptp.identity @t74)))) % 172.96/173.23 (step @p220 :rule instantiate :premises (@p3) :args ((@list @t28 tptp.identity @t74))) % 172.96/173.23 (step @p221 :rule trans :premises (@p220 @p219)) % 172.96/173.23 (step @p222 :rule cong :premises (@p53 @p153) :args (@t52)) % 172.96/173.23 (step @p223 :rule cong :premises (@p222 @p221) :args ((tptp.greatest_lower_bound @t52 (tptp.multiply @t52 @t74)))) % 172.96/173.23 (step @p224 :rule symm :premises (@p220)) % 172.96/173.23 (step @p225 :rule symm :premises (@p219)) % 172.96/173.23 (step @p226 :rule instantiate :premises (@p28) :args (@t57)) % 172.96/173.23 (step @p227 :rule symm :premises (@p226)) % 172.96/173.23 (step @p228 :rule instantiate :premises (@p4) :args ((@list tptp.a @t29))) % 172.96/173.23 (step @p229 :rule symm :premises (@p228)) % 172.96/173.23 (step @p230 :rule trans :premises (@p182 @p180 @p154)) % 172.96/173.23 (step @p231 :rule cong :premises (@p230 @p102) :args ((tptp.multiply (tptp.greatest_lower_bound @t68 @t65) tptp.a))) % 172.96/173.23 (step @p232 :rule instantiate :premises (@p15) :args ((@list @t68 @t65 tptp.a))) % 172.96/173.23 (step @p233 :rule symm :premises (@p232)) % 172.96/173.23 (step @p234 :rule trans :premises (@p233 @p231 @p214)) % 172.96/173.23 (step @p235 :rule refl :args (@t29)) % 172.96/173.23 (step @p236 :rule cong :premises (@p235 @p234) :args ((tptp.greatest_lower_bound @t29 (tptp.greatest_lower_bound @t78 @t77)))) % 172.96/173.23 (step @p237 :rule instantiate :premises (@p6) :args ((@list @t29 @t78 @t77))) % 172.96/173.23 (step @p238 :rule symm :premises (@p237)) % 172.96/173.23 (step @p239 :rule cong :premises (@p153 @p102) :args (@t76)) % 172.96/173.23 (step @p240 :rule instantiate :premises (@p37) :args (@t57)) % 172.96/173.23 (step @p241 :rule symm :premises (@p240)) % 172.96/173.23 (step @p242 :rule instantiate :premises (@p5) :args ((@list tptp.a @t27))) % 172.96/173.23 (step @p243 :rule symm :premises (@p242)) % 172.96/173.23 (step @p244 :rule instantiate :premises (@p37) :args (@t67)) % 172.96/173.23 (step @p245 :rule symm :premises (@p244)) % 172.96/173.23 (step @p246 :rule instantiate :premises (@p5) :args ((@list tptp.identity @t58))) % 172.96/173.23 (step @p247 :rule symm :premises (@p246)) % 172.96/173.23 (step @p248 :rule cong :premises (@p97 @p45) :args (@t79)) % 172.96/173.23 (step @p249 :rule trans :premises (@p248 @p247 @p245)) % 172.96/173.23 (step @p250 :rule cong :premises (@p249 @p102) :args ((tptp.multiply @t79 tptp.a))) % 172.96/173.23 (step @p251 :rule instantiate :premises (@p14) :args ((@list @t27 tptp.identity tptp.a))) % 172.96/173.23 (step @p252 :rule symm :premises (@p251)) % 172.96/173.23 (step @p253 :rule trans :premises (@p252 @p250 @p214)) % 172.96/173.23 (step @p254 :rule refl :args (@t27)) % 172.96/173.23 (step @p255 :rule cong :premises (@p254 @p253) :args ((tptp.least_upper_bound @t27 (tptp.least_upper_bound @t80 @t76)))) % 172.96/173.23 (step @p256 :rule instantiate :premises (@p7) :args ((@list @t27 @t80 @t76))) % 172.96/173.23 (step @p257 :rule symm :premises (@p256)) % 172.96/173.23 (step @p258 :rule trans :premises (@p257 @p255 @p243 @p241 @p213 @p239)) % 172.96/173.23 (step @p259 :rule instantiate :premises (@p3) :args ((@list @t29 tptp.identity tptp.a))) % 172.96/173.23 (step @p260 :rule symm :premises (@p259)) % 172.96/173.23 (step @p261 :rule cong :premises (@p235 @p213) :args (@t81)) % 172.96/173.23 (step @p262 :rule symm :premises (@p175)) % 172.96/173.23 (step @p263 :rule cong :premises (@p154 @p214) :args ((tptp.least_upper_bound @t65 @t76))) % 172.96/173.23 (step @p264 :rule instantiate :premises (@p12) :args (@t59)) % 172.96/173.23 (step @p265 :rule cong :premises (@p45 @p175) :args (@t82)) % 172.96/173.23 (step @p266 :rule trans :premises (@p265 @p264 @p263 @p262)) % 172.96/173.23 (step @p267 :rule cong :premises (@p266 @p102) :args ((tptp.multiply @t82 tptp.a))) % 172.96/173.23 (step @p268 :rule instantiate :premises (@p3) :args ((@list tptp.identity @t29 tptp.a))) % 172.96/173.23 (step @p269 :rule symm :premises (@p268)) % 172.96/173.23 (step @p270 :rule symm :premises (@p261)) % 172.96/173.23 (step @p271 :rule trans :premises (@p259 @p270)) % 172.96/173.23 (step @p272 :rule cong :premises (@p45 @p271) :args (@t83)) % 172.96/173.23 (step @p273 :rule trans :premises (@p272 @p269 @p267 @p261 @p260)) % 172.96/173.23 (step @p274 :rule instantiate :premises (@p59) :args (@t75)) % 172.96/173.23 (step @p275 :rule symm :premises (@p274)) % 172.96/173.23 (step @p276 :rule cong :premises (@p275 @p102) :args ((tptp.multiply (tptp.multiply @t84 tptp.a) tptp.a))) % 172.96/173.23 (step @p277 :rule instantiate :premises (@p3) :args ((@list @t84 tptp.a tptp.a))) % 172.96/173.23 (step @p278 :rule symm :premises (@p277)) % 172.96/173.23 (step @p279 :rule trans :premises (@p278 @p276 @p214)) % 172.96/173.23 (step @p280 :rule refl :args (@t84)) % 172.96/173.23 (step @p281 :rule cong :premises (@p280 @p214) :args (@t85)) % 172.96/173.23 (step @p282 :rule trans :premises (@p281 @p275)) % 172.96/173.23 (step @p283 :rule cong :premises (@p282 @p279) :args ((tptp.least_upper_bound @t85 @t87))) % 172.96/173.23 (step @p284 :rule instantiate :premises (@p12) :args (@t88)) % 172.96/173.23 (step @p285 :rule instantiate :premises (@p14) :args (@t89)) % 172.96/173.23 (step @p286 :rule cong :premises (@p175 @p102) :args (@t81)) % 172.96/173.23 (step @p287 :rule trans :premises (@p259 @p270 @p286 @p285)) % 172.96/173.23 (step @p288 :rule cong :premises (@p280 @p287) :args (@t90)) % 172.96/173.23 (step @p289 :rule trans :premises (@p288 @p284 @p283 @p262)) % 172.96/173.23 (step @p290 :rule cong :premises (@p289 @p273) :args ((tptp.greatest_lower_bound @t90 @t83))) % 172.96/173.23 (step @p291 :rule instantiate :premises (@p15) :args ((@list @t84 tptp.identity @t78))) % 172.96/173.23 (step @p292 :rule refl :args (@t78)) % 172.96/173.23 (step @p293 :rule instantiate :premises (@p4) :args (@t91)) % 172.96/173.23 (step @p294 :rule cong :premises (@p293 @p292) :args ((tptp.multiply @t92 @t78))) % 172.96/173.23 (step @p295 :rule cong :premises (@p184 @p235) :args ((tptp.multiply @t70 @t29))) % 172.96/173.23 (step @p296 :rule instantiate :premises (@p3) :args ((@list @t69 tptp.identity @t29))) % 172.96/173.23 (step @p297 :rule symm :premises (@p296)) % 172.96/173.23 (step @p298 :rule symm :premises (@p266)) % 172.96/173.23 (step @p299 :rule refl :args (@t69)) % 172.96/173.23 (step @p300 :rule cong :premises (@p299 @p298) :args (@t93)) % 172.96/173.23 (step @p301 :rule trans :premises (@p300 @p297 @p295 @p265 @p264 @p263 @p262)) % 172.96/173.23 (step @p302 :rule cong :premises (@p301 @p45) :args (@t94)) % 172.96/173.23 (step @p303 :rule symm :premises (@p301)) % 172.96/173.23 (step @p304 :rule trans :premises (@p262 @p303)) % 172.96/173.23 (step @p305 :rule cong :premises (@p304 @p45) :args ((tptp.multiply (tptp.least_upper_bound tptp.identity tptp.a) tptp.identity))) % 172.96/173.23 (step @p306 :rule instantiate :premises (@p14) :args (@t73)) % 172.96/173.23 (step @p307 :rule symm :premises (@p306)) % 172.96/173.23 (step @p308 :rule trans :premises (@p307 @p305 @p302)) % 172.96/173.23 (step @p309 :rule cong :premises (@p308 @p102) :args ((tptp.multiply (tptp.least_upper_bound @t65 @t74) tptp.a))) % 172.96/173.23 (step @p310 :rule instantiate :premises (@p14) :args ((@list @t65 @t74 tptp.a))) % 172.96/173.23 (step @p311 :rule symm :premises (@p310)) % 172.96/173.23 (step @p312 :rule trans :premises (@p311 @p309)) % 172.96/173.23 (step @p313 :rule refl :args (@t92)) % 172.96/173.23 (step @p314 :rule cong :premises (@p313 @p312) :args ((tptp.multiply @t92 (tptp.least_upper_bound @t77 @t95)))) % 172.96/173.23 (step @p315 :rule instantiate :premises (@p12) :args ((@list @t92 @t77 @t95))) % 172.96/173.23 (step @p316 :rule symm :premises (@p315)) % 172.96/173.23 (step @p317 :rule eq-symm :args (@t95 @t96)) % 172.96/173.23 (step @p318 :rule refl :args (@t11)) % 172.96/173.23 (step @p319 :rule cong :premises (@p318 @p317) :args ((=> @t11 @t97))) % 172.96/173.23 (assume-push @p454 @t11) % 172.96/173.23 (step @p321 :rule instantiate :premises (@p3) :args ((@list tptp.a tptp.identity tptp.a))) % 172.96/173.23 (step-pop @p455 :rule scope :premises (@p321)) % 172.96/173.23 (step @p322 :rule process_scope :premises (@p455) :args (@t97)) % 172.96/173.23 (step @p324 :rule eq_resolve :premises (@p322 @p319)) % 172.96/173.23 (step @p325 :rule implies_elim :premises (@p324)) % 172.96/173.23 (step @p326 :rule chain_m_resolution :premises (@p325 @p3) :args ((= @t96 @t95) @t98 @t99)) % 172.96/173.23 (step @p327 :rule cong :premises (@p102 @p213) :args (@t86)) % 172.96/173.23 (step @p328 :rule trans :premises (@p327 @p326)) % 172.96/173.23 (step @p329 :rule cong :premises (@p313 @p328) :args ((tptp.multiply @t92 @t86))) % 172.96/173.23 (step @p330 :rule instantiate :premises (@p3) :args ((@list @t92 tptp.a tptp.a))) % 172.96/173.23 (step @p331 :rule instantiate :premises (@p15) :args ((@list tptp.identity @t84 tptp.a))) % 172.96/173.23 (step @p332 :rule symm :premises (@p331)) % 172.96/173.23 (step @p333 :rule cong :premises (@p213 @p274) :args (@t27)) % 172.96/173.23 (step @p334 :rule trans :premises (@p333 @p332)) % 172.96/173.23 (step @p335 :rule cong :premises (@p334 @p102) :args (@t80)) % 172.96/173.23 (step @p336 :rule trans :premises (@p335 @p330 @p329)) % 172.96/173.23 (step @p337 :rule trans :premises (@p213 @p239)) % 172.96/173.23 (step @p338 :rule symm :premises (@p293)) % 172.96/173.23 (step @p339 :rule cong :premises (@p338 @p337) :args ((tptp.multiply (tptp.greatest_lower_bound @t84 tptp.identity) tptp.a))) % 172.96/173.23 (step @p340 :rule instantiate :premises (@p15) :args ((@list @t84 tptp.identity tptp.a))) % 172.96/173.23 (step @p341 :rule symm :premises (@p340)) % 172.96/173.23 (step @p342 :rule cong :premises (@p274 @p213) :args (@t58)) % 172.96/173.23 (step @p343 :rule trans :premises (@p97 @p342 @p341 @p339)) % 172.96/173.23 (step @p344 :rule cong :premises (@p343 @p336) :args (@t100)) % 172.96/173.23 (step @p345 :rule cong :premises (@p154 @p214) :args ((tptp.greatest_lower_bound @t65 @t76))) % 172.96/173.23 (step @p346 :rule instantiate :premises (@p13) :args (@t59)) % 172.96/173.23 (step @p347 :rule trans :premises (@p346 @p345 @p98)) % 172.96/173.23 (step @p348 :rule cong :premises (@p347 @p102) :args ((tptp.multiply (tptp.multiply tptp.identity @t58) tptp.a))) % 172.96/173.23 (step @p349 :rule instantiate :premises (@p3) :args ((@list tptp.identity @t58 tptp.a))) % 172.96/173.23 (step @p350 :rule symm :premises (@p349)) % 172.96/173.23 (step @p351 :rule cong :premises (@p97 @p102) :args (@t80)) % 172.96/173.23 (step @p352 :rule cong :premises (@p45 @p351) :args (@t101)) % 172.96/173.23 (step @p353 :rule trans :premises (@p352 @p350 @p348)) % 172.96/173.23 (step @p354 :rule cong :premises (@p282 @p279) :args ((tptp.greatest_lower_bound @t85 @t87))) % 172.96/173.23 (step @p355 :rule instantiate :premises (@p13) :args (@t88)) % 172.96/173.23 (step @p356 :rule instantiate :premises (@p15) :args (@t89)) % 172.96/173.23 (step @p357 :rule trans :premises (@p351 @p356)) % 172.96/173.23 (step @p358 :rule cong :premises (@p280 @p357) :args (@t102)) % 172.96/173.23 (step @p359 :rule trans :premises (@p358 @p355 @p354 @p98)) % 172.96/173.23 (step @p360 :rule cong :premises (@p359 @p353) :args ((tptp.least_upper_bound @t102 @t101))) % 172.96/173.23 (step @p361 :rule instantiate :premises (@p14) :args ((@list @t84 tptp.identity @t80))) % 172.96/173.23 (step @p362 :rule refl :args (@t80)) % 172.96/173.23 (step @p363 :rule instantiate :premises (@p5) :args (@t91)) % 172.96/173.23 (step @p364 :rule cong :premises (@p363 @p362) :args ((tptp.multiply (tptp.least_upper_bound tptp.identity @t84) @t80))) % 172.96/173.23 (step @p365 :rule trans :premises (@p364 @p361 @p360 @p344 @p316 @p314 @p294 @p291 @p290)) % 172.96/173.23 (step @p366 :rule symm :premises (@p364)) % 172.96/173.23 (step @p367 :rule symm :premises (@p361)) % 172.96/173.23 (step @p368 :rule symm :premises (@p360)) % 172.96/173.23 (step @p369 :rule trans :premises (@p368 @p367 @p366)) % 172.96/173.23 (step @p370 :rule trans :premises (@p369 @p365)) % 172.96/173.23 (step @p371 :rule cong :premises (@p370 @p258) :args ((tptp.greatest_lower_bound @t100 (tptp.least_upper_bound @t100 @t76)))) % 172.96/173.23 (step @p372 :rule instantiate :premises (@p28) :args ((@list @t100 @t76))) % 172.96/173.23 (step @p373 :rule trans :premises (@p372 @p371 @p238 @p236 @p229 @p227)) % 172.96/173.23 (step @p374 :rule cong :premises (@p373 @p45) :args ((tptp.multiply @t100 tptp.identity))) % 172.96/173.23 (step @p375 :rule instantiate :premises (@p14) :args ((@list @t27 @t80 tptp.identity))) % 172.96/173.23 (step @p376 :rule symm :premises (@p375)) % 172.96/173.23 (step @p377 :rule eq-symm :args (@t103 @t104)) % 172.96/173.23 (step @p378 :rule cong :premises (@p318 @p377) :args ((=> @t11 @t105))) % 172.96/173.23 (assume-push @p456 @t11) % 172.96/173.23 (step @p380 :rule instantiate :premises (@p3) :args ((@list @t27 tptp.a tptp.identity))) % 172.96/173.23 (step-pop @p457 :rule scope :premises (@p380)) % 172.96/173.23 (step @p381 :rule process_scope :premises (@p457) :args (@t105)) % 172.96/173.23 (step @p383 :rule eq_resolve :premises (@p381 @p378)) % 172.96/173.23 (step @p384 :rule implies_elim :premises (@p383)) % 172.96/173.23 (step @p385 :rule chain_m_resolution :premises (@p384 @p3) :args ((= @t104 @t103) @t98 @t99)) % 172.96/173.23 (step @p386 :rule cong :premises (@p97 @p154) :args (@t106)) % 172.96/173.23 (step @p387 :rule trans :premises (@p386 @p206)) % 172.96/173.23 (step @p388 :rule cong :premises (@p387 @p385) :args ((tptp.least_upper_bound @t106 @t104))) % 172.96/173.23 (step @p389 :rule instantiate :premises (@p12) :args ((@list @t27 @t65 @t74))) % 172.96/173.23 (step @p390 :rule symm :premises (@p308)) % 172.96/173.23 (step @p391 :rule cong :premises (@p254 @p390) :args (@t107)) % 172.96/173.23 (step @p392 :rule instantiate :premises (@p3) :args ((@list @t27 @t29 tptp.identity))) % 172.96/173.23 (step @p393 :rule cong :premises (@p254 @p289) :args ((tptp.multiply @t27 @t90))) % 172.96/173.23 (step @p394 :rule instantiate :premises (@p3) :args ((@list @t27 @t84 @t78))) % 172.96/173.23 (step @p395 :rule trans :premises (@p394 @p393)) % 172.96/173.23 (step @p396 :rule cong :premises (@p395 @p45) :args (@t108)) % 172.96/173.23 (step @p397 :rule trans :premises (@p396 @p392 @p391 @p389 @p388 @p376 @p374)) % 172.96/173.23 (step @p398 :rule cong :premises (@p53 @p397) :args ((tptp.multiply @t28 @t108))) % 172.96/173.23 (step @p399 :rule symm :premises (@p396)) % 172.96/173.23 (step @p400 :rule eq-symm :args (@t109 @t107)) % 172.96/173.23 (step @p401 :rule cong :premises (@p318 @p400) :args ((=> @t11 @t110))) % 172.96/173.23 (assume-push @p458 @t11) % 172.96/173.23 (step-pop @p459 :rule scope :premises (@p392)) % 172.96/173.23 (step @p403 :rule process_scope :premises (@p459) :args (@t110)) % 172.96/173.23 (step @p405 :rule eq_resolve :premises (@p403 @p401)) % 172.96/173.23 (step @p406 :rule implies_elim :premises (@p405)) % 172.96/173.23 (step @p407 :rule chain_m_resolution :premises (@p406 @p3) :args ((= @t107 @t109) @t98 @t99)) % 172.96/173.23 (step @p408 :rule trans :premises (@p407 @p399)) % 172.96/173.23 (step @p409 :rule cong :premises (@p53 @p408) :args ((tptp.multiply @t28 @t107))) % 172.96/173.23 (step @p410 :rule instantiate :premises (@p3) :args ((@list @t28 @t27 @t68))) % 172.96/173.23 (step @p411 :rule cong :premises (@p90 @p186) :args ((tptp.multiply tptp.identity @t68))) % 172.96/173.23 (step @p412 :rule instantiate :premises (@p3) :args ((@list tptp.identity @t29 tptp.identity))) % 172.96/173.23 (step @p413 :rule trans :premises (@p301 @p298)) % 172.96/173.23 (step @p414 :rule cong :premises (@p413 @p45) :args (@t94)) % 172.96/173.23 (step @p415 :rule symm :premises (@p302)) % 172.96/173.23 (step @p416 :rule trans :premises (@p415 @p414 @p412 @p411 @p410 @p409 @p398 @p225 @p224)) % 172.96/173.23 (step @p417 :rule cong :premises (@p92 @p416) :args ((tptp.greatest_lower_bound @t52 @t68))) % 172.96/173.23 (step @p418 :rule instantiate :premises (@p4) :args ((@list @t68 @t52))) % 172.96/173.23 (step @p419 :rule trans :premises (@p418 @p417 @p223 @p212 @p210 @p205 @p203 @p154)) % 172.96/173.23 (step @p420 :rule cong :premises (@p419 @p172) :args ((tptp.multiply (tptp.greatest_lower_bound @t68 @t52) @t46))) % 172.96/173.23 (step @p421 :rule instantiate :premises (@p15) :args ((@list @t68 @t52 @t46))) % 172.96/173.23 (step @p422 :rule symm :premises (@p421)) % 172.96/173.23 (step @p423 :rule instantiate :premises (@p3) :args ((@list @t28 tptp.identity @t46))) % 172.96/173.23 (step @p424 :rule symm :premises (@p423)) % 172.96/173.23 (step @p425 :rule cong :premises (@p53 @p170) :args (@t111)) % 172.96/173.23 (step @p426 :rule trans :premises (@p425 @p424)) % 172.96/173.23 (step @p427 :rule instantiate :premises (@p3) :args ((@list @t29 tptp.identity @t46))) % 172.96/173.23 (step @p428 :rule symm :premises (@p427)) % 172.96/173.23 (step @p429 :rule cong :premises (@p235 @p170) :args (@t112)) % 172.96/173.23 (step @p430 :rule trans :premises (@p429 @p428)) % 172.96/173.23 (step @p431 :rule cong :premises (@p430 @p426) :args ((tptp.greatest_lower_bound @t112 @t111))) % 172.96/173.23 (step @p432 :rule instantiate :premises (@p15) :args ((@list @t29 @t28 @t46))) % 172.96/173.23 (step @p433 :rule cong :premises (@p144 @p172) :args (@t113)) % 172.96/173.23 (step @p434 :rule trans :premises (@p433 @p432 @p431 @p422 @p420 @p171)) % 172.96/173.23 (step @p435 :rule cong :premises (@p434 @p169) :args ((tptp.multiply @t113 @t66))) % 172.96/173.23 (step @p436 :rule instantiate :premises (@p3) :args ((@list @t39 @t46 @t66))) % 172.96/173.23 (step @p437 :rule symm :premises (@p436)) % 172.96/173.23 (step @p438 :rule symm :premises (@p166)) % 172.96/173.23 (step @p439 :rule trans :premises (@p151 @p438 @p167)) % 172.96/173.23 (step @p440 :rule cong :premises (@p143 @p439) :args (@t31)) % 172.96/173.23 (step @p441 :rule trans :premises (@p440 @p437 @p435 @p202 @p197)) % 172.96/173.23 (step @p442 :rule cong :premises (@p200 @p441) :args (@t33)) % 172.96/173.23 (step @p443 :rule trans :premises (@p442 @p201 @p162)) % 172.96/173.23 (step @p444 :rule cong :premises (@p443 @p164) :args (@t36)) % 172.96/173.23 (step @p445 :rule trans :premises (@p444 @p25)) % 172.96/173.23 (step @p446 :rule eq_resolve :premises (@p445 @p23)) % 172.96/173.23 (step @p447 :rule false_elim :premises (@p446)) % 172.96/173.23 (assume-push @p460 @t11) % 172.96/173.23 (step @p449 :rule instantiate :premises (@p3) :args ((@list @t32 @t30 @t30))) % 172.96/173.23 (step-pop @p461 :rule scope :premises (@p449)) % 172.96/173.23 (step @p450 :rule process_scope :premises (@p461) :args (@t35)) % 172.96/173.23 (step @p452 :rule implies_elim :premises (@p450)) % 172.96/173.23 (step @p453 false :rule chain_m_resolution :premises (@p452 @p447 @p3) :args (false (@list true false) (@list @t35 @t11))) % 172.96/173.23 ) % 172.96/173.25 % SZS output end Proof % 172.96/173.25 % cvc5 exiting %------------------------------------------------------------------------------