%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : GRP167-5 : 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 : n001.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 08:20:04 AM UTC 2026 % Result : Unsatisfiable 43.43s 43.67s % Output : Proof 43.43s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : GRP167-5 : 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 % 0.18/0.35 % Computer : n001.cluster.edu % 0.18/0.35 % Model : x86_64 x86_64 % 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.35 % Memory : 8042.1875MB % 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.35 % CPULimit : 300 % 0.18/0.35 % WCLimit : 300 % 0.18/0.35 % DateTime : Tue Jun 2 00:55:05 EDT 2026 % 0.18/0.35 % CPUTime : % 0.30/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.30/0.51 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 15.71/15.95 --- Run --no-e-matching --full-saturate-quant at 6... % 21.72/21.97 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 6... % 27.72/28.00 --- Run --finite-model-find --uf-ss=no-minimal at 6... % 33.85/34.05 --- Run --multi-trigger-when-single --full-saturate-quant at 30... % 43.43/43.67 % SZS status Unsatisfiable % 43.43/43.67 % SZS output start Proof % 43.43/43.68 ( % 43.43/43.68 (declare-sort $$unsorted 0) % 43.43/43.68 (declare-const tptp.a $$unsorted) % 43.43/43.68 (declare-const tptp.negative_part (-> $$unsorted $$unsorted)) % 43.43/43.68 (declare-const tptp.positive_part (-> $$unsorted $$unsorted)) % 43.43/43.68 (declare-const tptp.least_upper_bound (-> $$unsorted $$unsorted $$unsorted)) % 43.43/43.68 (declare-const tptp.greatest_lower_bound (-> $$unsorted $$unsorted $$unsorted)) % 43.43/43.68 (declare-const tptp.inverse (-> $$unsorted $$unsorted)) % 43.43/43.68 (declare-const tptp.multiply (-> $$unsorted $$unsorted $$unsorted)) % 43.43/43.68 (declare-const tptp.identity $$unsorted) % 43.43/43.68 (define @t1 () (@var "X" $$unsorted)) % 43.43/43.68 (define @t2 () (tptp.multiply tptp.identity @t1)) % 43.43/43.68 (define @t3 () (@list @t1)) % 43.43/43.68 (define @t4 () (forall @t3 (= @t2 @t1))) % 43.43/43.68 (define @t5 () (tptp.multiply (tptp.inverse @t1) @t1)) % 43.43/43.68 (define @t6 () (forall @t3 (= @t5 tptp.identity))) % 43.43/43.68 (define @t7 () (@var "Z" $$unsorted)) % 43.43/43.68 (define @t8 () (@var "Y" $$unsorted)) % 43.43/43.68 (define @t9 () (tptp.multiply @t1 @t8)) % 43.43/43.68 (define @t10 () (@list @t1 @t8 @t7)) % 43.43/43.68 (define @t11 () (forall @t10 (= (tptp.multiply @t9 @t7) (tptp.multiply @t1 (tptp.multiply @t8 @t7))))) % 43.43/43.68 (define @t12 () (tptp.greatest_lower_bound @t1 @t8)) % 43.43/43.68 (define @t13 () (@list @t1 @t8)) % 43.43/43.68 (define @t14 () (forall @t13 (= @t12 (tptp.greatest_lower_bound @t8 @t1)))) % 43.43/43.68 (define @t15 () (tptp.least_upper_bound @t1 @t8)) % 43.43/43.68 (define @t16 () (tptp.greatest_lower_bound @t8 @t7)) % 43.43/43.68 (define @t17 () (tptp.least_upper_bound @t8 @t7)) % 43.43/43.68 (define @t18 () (tptp.greatest_lower_bound @t1 @t1)) % 43.43/43.68 (define @t19 () (forall @t3 (= @t18 @t1))) % 43.43/43.68 (define @t20 () (tptp.least_upper_bound @t1 @t12)) % 43.43/43.68 (define @t21 () (forall @t13 (= @t20 @t1))) % 43.43/43.68 (define @t22 () (tptp.greatest_lower_bound @t1 @t15)) % 43.43/43.68 (define @t23 () (forall @t13 (= @t22 @t1))) % 43.43/43.68 (define @t24 () (tptp.multiply @t1 @t7)) % 43.43/43.68 (define @t25 () (tptp.multiply @t7 @t1)) % 43.43/43.68 (define @t26 () (tptp.multiply @t8 @t1)) % 43.43/43.68 (define @t27 () (@list @t8 @t7 @t1)) % 43.43/43.68 (define @t28 () (@var "B" $$unsorted)) % 43.43/43.68 (define @t29 () (@var "A" $$unsorted)) % 43.43/43.68 (define @t30 () (tptp.positive_part tptp.a)) % 43.43/43.68 (define @t31 () (@list tptp.a)) % 43.43/43.68 (define @t32 () (@list tptp.a tptp.identity)) % 43.43/43.68 (define @t33 () (tptp.least_upper_bound tptp.a tptp.identity)) % 43.43/43.68 (define @t34 () (tptp.greatest_lower_bound tptp.a @t33)) % 43.43/43.68 (define @t35 () (@list @t33)) % 43.43/43.68 (define @t36 () (tptp.inverse @t33)) % 43.43/43.68 (define @t37 () (tptp.multiply @t33 tptp.a)) % 43.43/43.68 (define @t38 () (@list tptp.identity)) % 43.43/43.68 (define @t39 () (tptp.inverse tptp.identity)) % 43.43/43.68 (define @t40 () (tptp.multiply @t39 tptp.identity)) % 43.43/43.68 (define @t41 () (tptp.multiply @t39 @t36)) % 43.43/43.68 (define @t42 () (tptp.multiply @t39 tptp.a)) % 43.43/43.68 (define @t43 () (tptp.inverse tptp.a)) % 43.43/43.68 (define @t44 () (tptp.multiply @t36 tptp.a)) % 43.43/43.68 (define @t45 () (tptp.multiply @t30 @t44)) % 43.43/43.68 (define @t46 () (tptp.greatest_lower_bound @t43 @t39)) % 43.43/43.68 (define @t47 () (tptp.multiply tptp.identity tptp.a)) % 43.43/43.68 (define @t48 () (@list @t43 tptp.identity tptp.a)) % 43.43/43.68 (define @t49 () (tptp.multiply @t43 tptp.identity)) % 43.43/43.68 (define @t50 () (tptp.multiply @t49 tptp.a)) % 43.43/43.68 (define @t51 () (tptp.inverse @t46)) % 43.43/43.68 (define @t52 () (tptp.multiply tptp.a @t36)) % 43.43/43.68 (define @t53 () (tptp.multiply @t43 @t49)) % 43.43/43.68 (define @t54 () (tptp.multiply @t43 @t33)) % 43.43/43.68 (define @t55 () (tptp.multiply @t39 @t33)) % 43.43/43.68 (define @t56 () (tptp.least_upper_bound tptp.identity tptp.a)) % 43.43/43.68 (define @t57 () (tptp.least_upper_bound @t49 tptp.identity)) % 43.43/43.68 (define @t58 () (tptp.multiply tptp.identity @t33)) % 43.43/43.68 (define @t59 () (tptp.greatest_lower_bound @t37 @t33)) % 43.43/43.68 (define @t60 () (tptp.greatest_lower_bound @t33 @t37)) % 43.43/43.68 (define @t61 () (= @t59 @t60)) % 43.43/43.68 (define @t62 () (@list tptp.identity tptp.a tptp.a)) % 43.43/43.68 (define @t63 () (tptp.multiply tptp.a tptp.a)) % 43.43/43.68 (define @t64 () (tptp.least_upper_bound @t34 @t63)) % 43.43/43.68 (define @t65 () (tptp.least_upper_bound tptp.a @t63)) % 43.43/43.68 (define @t66 () (tptp.multiply @t39 @t49)) % 43.43/43.68 (define @t67 () (tptp.multiply @t39 @t54)) % 43.43/43.68 (define @t68 () (@list @t39)) % 43.43/43.68 (define @t69 () (tptp.multiply @t39 @t39)) % 43.43/43.68 (define @t70 () (tptp.inverse @t39)) % 43.43/43.68 (define @t71 () (tptp.multiply @t43 @t39)) % 43.43/43.68 (define @t72 () (tptp.multiply @t43 @t54)) % 43.43/43.68 (define @t73 () (tptp.least_upper_bound tptp.identity @t49)) % 43.43/43.68 (define @t74 () (tptp.multiply @t30 @t36)) % 43.43/43.68 (define @t75 () (tptp.multiply @t74 tptp.a)) % 43.43/43.68 (define @t76 () (= @t75 @t45)) % 43.43/43.68 (assume @p1 @t4) % 43.43/43.68 (assume @p2 @t6) % 43.43/43.68 (assume @p3 @t11) % 43.43/43.68 (assume @p4 @t14) % 43.43/43.68 (assume @p5 (forall @t13 (= @t15 (tptp.least_upper_bound @t8 @t1)))) % 43.43/43.68 (assume @p6 (forall @t10 (= (tptp.greatest_lower_bound @t1 @t16) (tptp.greatest_lower_bound @t12 @t7)))) % 43.43/43.68 (assume @p7 (forall @t10 (= (tptp.least_upper_bound @t1 @t17) (tptp.least_upper_bound @t15 @t7)))) % 43.43/43.68 (assume @p8 (forall @t3 (= (tptp.least_upper_bound @t1 @t1) @t1))) % 43.43/43.68 (assume @p9 @t19) % 43.43/43.68 (assume @p10 @t21) % 43.43/43.68 (assume @p11 @t23) % 43.43/43.68 (assume @p12 (forall @t10 (= (tptp.multiply @t1 @t17) (tptp.least_upper_bound @t9 @t24)))) % 43.43/43.68 (assume @p13 (forall @t10 (= (tptp.multiply @t1 @t16) (tptp.greatest_lower_bound @t9 @t24)))) % 43.43/43.68 (assume @p14 (forall @t27 (= (tptp.multiply @t17 @t1) (tptp.least_upper_bound @t26 @t25)))) % 43.43/43.68 (assume @p15 (forall @t27 (= (tptp.multiply @t16 @t1) (tptp.greatest_lower_bound @t26 @t25)))) % 43.43/43.68 (assume @p16 (forall (@list @t29 @t28) (= (tptp.inverse (tptp.least_upper_bound @t29 @t28)) (tptp.greatest_lower_bound (tptp.inverse @t29) (tptp.inverse @t28))))) % 43.43/43.68 (assume @p17 (forall @t3 (= (tptp.positive_part @t1) (tptp.least_upper_bound @t1 tptp.identity)))) % 43.43/43.68 (assume @p18 (forall @t3 (= (tptp.negative_part @t1) (tptp.greatest_lower_bound @t1 tptp.identity)))) % 43.43/43.68 (assume @p19 (forall @t10 (= (tptp.least_upper_bound @t1 @t16) (tptp.greatest_lower_bound @t15 (tptp.least_upper_bound @t1 @t7))))) % 43.43/43.68 (assume @p20 (forall @t10 (= (tptp.greatest_lower_bound @t1 @t17) (tptp.least_upper_bound @t12 (tptp.greatest_lower_bound @t1 @t7))))) % 43.43/43.68 (assume @p21 (not (= tptp.a (tptp.multiply @t30 (tptp.negative_part tptp.a))))) % 43.43/43.68 (step @p22 :rule false_intro :premises (@p21)) % 43.43/43.68 (step @p23 :rule instantiate :premises (@p18) :args (@t31)) % 43.43/43.68 (step @p24 :rule symm :premises (@p23)) % 43.43/43.68 (step @p25 :rule instantiate :premises (@p4) :args (@t32)) % 43.43/43.68 (step @p26 :rule symm :premises (@p25)) % 43.43/43.68 (step @p27 :rule eq-symm :args (@t22 @t1)) % 43.43/43.68 (step @p28 :rule cong :premises (@p27) :args (@t23)) % 43.43/43.68 (step @p29 :rule eq_resolve :premises (@p11 @p28)) % 43.43/43.68 (step @p30 :rule instantiate :premises (@p29) :args (@t32)) % 43.43/43.68 (step @p31 :rule symm :premises (@p30)) % 43.43/43.68 (step @p32 :rule refl :args (tptp.identity)) % 43.43/43.68 (step @p33 :rule cong :premises (@p32 @p31) :args ((tptp.greatest_lower_bound tptp.identity @t34))) % 43.43/43.68 (step @p34 :rule eq-symm :args (@t2 @t1)) % 43.43/43.68 (step @p35 :rule cong :premises (@p34) :args (@t4)) % 43.43/43.68 (step @p36 :rule eq_resolve :premises (@p1 @p35)) % 43.43/43.68 (step @p37 :rule instantiate :premises (@p36) :args (@t31)) % 43.43/43.68 (step @p38 :rule symm :premises (@p37)) % 43.43/43.68 (step @p39 :rule refl :args (tptp.a)) % 43.43/43.68 (step @p40 :rule eq-symm :args (@t5 tptp.identity)) % 43.43/43.68 (step @p41 :rule cong :premises (@p40) :args (@t6)) % 43.43/43.68 (step @p42 :rule eq_resolve :premises (@p2 @p41)) % 43.43/43.68 (step @p43 :rule instantiate :premises (@p42) :args (@t35)) % 43.43/43.68 (step @p44 :rule symm :premises (@p43)) % 43.43/43.68 (step @p45 :rule cong :premises (@p44 @p39) :args ((tptp.multiply (tptp.multiply @t36 @t33) tptp.a))) % 43.43/43.68 (step @p46 :rule instantiate :premises (@p3) :args ((@list @t36 @t33 tptp.a))) % 43.43/43.68 (step @p47 :rule symm :premises (@p46)) % 43.43/43.68 (step @p48 :rule refl :args (@t37)) % 43.43/43.68 (step @p49 :rule instantiate :premises (@p36) :args ((@list @t36))) % 43.43/43.68 (step @p50 :rule symm :premises (@p49)) % 43.43/43.68 (step @p51 :rule refl :args (@t36)) % 43.43/43.68 (step @p52 :rule instantiate :premises (@p42) :args (@t38)) % 43.43/43.68 (step @p53 :rule symm :premises (@p52)) % 43.43/43.68 (step @p54 :rule cong :premises (@p53 @p51) :args ((tptp.multiply @t40 @t36))) % 43.43/43.68 (step @p55 :rule instantiate :premises (@p3) :args ((@list @t39 tptp.identity @t36))) % 43.43/43.68 (step @p56 :rule symm :premises (@p55)) % 43.43/43.68 (step @p57 :rule refl :args (@t39)) % 43.43/43.68 (step @p58 :rule cong :premises (@p57 @p49) :args (@t41)) % 43.43/43.68 (step @p59 :rule trans :premises (@p58 @p56 @p54 @p50)) % 43.43/43.68 (step @p60 :rule cong :premises (@p59 @p48) :args ((tptp.multiply @t41 @t37))) % 43.43/43.68 (step @p61 :rule instantiate :premises (@p3) :args ((@list @t39 @t36 @t37))) % 43.43/43.68 (step @p62 :rule symm :premises (@p61)) % 43.43/43.68 (step @p63 :rule symm :premises (@p45)) % 43.43/43.68 (step @p64 :rule trans :premises (@p37 @p63 @p46)) % 43.43/43.68 (step @p65 :rule cong :premises (@p57 @p64) :args (@t42)) % 43.43/43.68 (step @p66 :rule trans :premises (@p65 @p62 @p60 @p47 @p45 @p38 @p30)) % 43.43/43.68 (step @p67 :rule instantiate :premises (@p42) :args (@t31)) % 43.43/43.68 (step @p68 :rule symm :premises (@p67)) % 43.43/43.68 (step @p69 :rule cong :premises (@p68 @p66) :args ((tptp.greatest_lower_bound (tptp.multiply @t43 tptp.a) @t42))) % 43.43/43.68 (step @p70 :rule instantiate :premises (@p15) :args ((@list @t43 @t39 tptp.a))) % 43.43/43.68 (step @p71 :rule instantiate :premises (@p16) :args (@t32)) % 43.43/43.68 (step @p72 :rule cong :premises (@p71 @p39) :args (@t44)) % 43.43/43.68 (step @p73 :rule trans :premises (@p72 @p70 @p69 @p33 @p26 @p24)) % 43.43/43.68 (step @p74 :rule refl :args (@t30)) % 43.43/43.68 (step @p75 :rule cong :premises (@p74 @p73) :args (@t45)) % 43.43/43.68 (step @p76 :rule instantiate :premises (@p42) :args ((@list @t46))) % 43.43/43.68 (step @p77 :rule symm :premises (@p76)) % 43.43/43.68 (step @p78 :rule refl :args (@t43)) % 43.43/43.68 (step @p79 :rule cong :premises (@p78 @p38) :args ((tptp.multiply @t43 @t47))) % 43.43/43.68 (step @p80 :rule instantiate :premises (@p3) :args (@t48)) % 43.43/43.68 (step @p81 :rule trans :premises (@p80 @p79 @p68)) % 43.43/43.68 (step @p82 :rule cong :premises (@p81 @p51) :args ((tptp.multiply @t50 @t36))) % 43.43/43.68 (step @p83 :rule instantiate :premises (@p3) :args ((@list @t49 tptp.a @t36))) % 43.43/43.68 (step @p84 :rule symm :premises (@p83)) % 43.43/43.68 (step @p85 :rule trans :premises (@p84 @p82 @p50 @p71)) % 43.43/43.68 (step @p86 :rule refl :args (@t51)) % 43.43/43.68 (step @p87 :rule cong :premises (@p86 @p85) :args ((tptp.multiply @t51 (tptp.multiply @t49 @t52)))) % 43.43/43.68 (step @p88 :rule instantiate :premises (@p3) :args ((@list @t51 @t49 @t52))) % 43.43/43.68 (step @p89 :rule refl :args (@t52)) % 43.43/43.68 (step @p90 :rule cong :premises (@p78 @p81) :args ((tptp.multiply @t43 @t50))) % 43.43/43.68 (step @p91 :rule instantiate :premises (@p3) :args ((@list @t43 @t49 tptp.a))) % 43.43/43.68 (step @p92 :rule refl :args (@t53)) % 43.43/43.68 (step @p93 :rule cong :premises (@p92 @p31) :args ((tptp.multiply @t53 @t34))) % 43.43/43.68 (step @p94 :rule refl :args (@t33)) % 43.43/43.68 (step @p95 :rule symm :premises (@p71)) % 43.43/43.68 (step @p96 :rule instantiate :premises (@p4) :args ((@list @t43 @t39))) % 43.43/43.68 (step @p97 :rule symm :premises (@p96)) % 43.43/43.68 (step @p98 :rule trans :premises (@p97 @p95)) % 43.43/43.68 (step @p99 :rule cong :premises (@p98 @p94) :args ((tptp.multiply (tptp.greatest_lower_bound @t39 @t43) @t33))) % 43.43/43.68 (step @p100 :rule instantiate :premises (@p15) :args ((@list @t39 @t43 @t33))) % 43.43/43.68 (step @p101 :rule symm :premises (@p100)) % 43.43/43.68 (step @p102 :rule trans :premises (@p101 @p99 @p44)) % 43.43/43.68 (step @p103 :rule cong :premises (@p102 @p39) :args ((tptp.multiply (tptp.greatest_lower_bound @t55 @t54) tptp.a))) % 43.43/43.68 (step @p104 :rule instantiate :premises (@p15) :args ((@list @t55 @t54 tptp.a))) % 43.43/43.68 (step @p105 :rule symm :premises (@p104)) % 43.43/43.68 (step @p106 :rule instantiate :premises (@p5) :args (@t32)) % 43.43/43.68 (step @p107 :rule symm :premises (@p106)) % 43.43/43.68 (step @p108 :rule cong :premises (@p78 @p107) :args ((tptp.multiply @t43 @t56))) % 43.43/43.68 (step @p109 :rule instantiate :premises (@p12) :args (@t48)) % 43.43/43.68 (step @p110 :rule symm :premises (@p109)) % 43.43/43.68 (step @p111 :rule refl :args (@t49)) % 43.43/43.68 (step @p112 :rule cong :premises (@p111 @p67) :args (@t57)) % 43.43/43.68 (step @p113 :rule trans :premises (@p112 @p110 @p108)) % 43.43/43.68 (step @p114 :rule cong :premises (@p113 @p39) :args ((tptp.multiply @t57 tptp.a))) % 43.43/43.68 (step @p115 :rule instantiate :premises (@p14) :args ((@list @t49 tptp.identity tptp.a))) % 43.43/43.68 (step @p116 :rule symm :premises (@p115)) % 43.43/43.68 (step @p117 :rule eq-symm :args (@t20 @t1)) % 43.43/43.68 (step @p118 :rule cong :premises (@p117) :args (@t21)) % 43.43/43.68 (step @p119 :rule eq_resolve :premises (@p10 @p118)) % 43.43/43.68 (step @p120 :rule instantiate :premises (@p119) :args (@t32)) % 43.43/43.68 (step @p121 :rule symm :premises (@p120)) % 43.43/43.68 (step @p122 :rule trans :premises (@p121 @p37)) % 43.43/43.68 (step @p123 :rule symm :premises (@p81)) % 43.43/43.68 (step @p124 :rule cong :premises (@p123 @p122) :args ((tptp.least_upper_bound tptp.identity (tptp.least_upper_bound tptp.a (tptp.greatest_lower_bound tptp.a tptp.identity))))) % 43.43/43.68 (step @p125 :rule cong :premises (@p32 @p120) :args (@t56)) % 43.43/43.68 (step @p126 :rule trans :premises (@p106 @p125 @p124 @p116 @p114)) % 43.43/43.68 (step @p127 :rule instantiate :premises (@p36) :args (@t38)) % 43.43/43.68 (step @p128 :rule symm :premises (@p127)) % 43.43/43.68 (step @p129 :rule cong :premises (@p38 @p128) :args ((tptp.least_upper_bound @t47 (tptp.multiply tptp.identity tptp.identity)))) % 43.43/43.68 (step @p130 :rule instantiate :premises (@p12) :args ((@list tptp.identity tptp.a tptp.identity))) % 43.43/43.68 (step @p131 :rule trans :premises (@p130 @p129)) % 43.43/43.68 (step @p132 :rule cong :premises (@p57 @p131) :args ((tptp.multiply @t39 @t58))) % 43.43/43.68 (step @p133 :rule instantiate :premises (@p3) :args ((@list @t39 tptp.identity @t33))) % 43.43/43.68 (step @p134 :rule cong :premises (@p52 @p94) :args (@t58)) % 43.43/43.68 (step @p135 :rule symm :premises (@p130)) % 43.43/43.68 (step @p136 :rule symm :premises (@p129)) % 43.43/43.68 (step @p137 :rule instantiate :premises (@p17) :args (@t31)) % 43.43/43.68 (step @p138 :rule trans :premises (@p137 @p136 @p135 @p134 @p133 @p132)) % 43.43/43.68 (step @p139 :rule cong :premises (@p138 @p39) :args ((tptp.multiply @t30 tptp.a))) % 43.43/43.68 (step @p140 :rule symm :premises (@p137)) % 43.43/43.68 (step @p141 :rule cong :premises (@p140 @p39) :args (@t37)) % 43.43/43.68 (step @p142 :rule trans :premises (@p141 @p139)) % 43.43/43.68 (step @p143 :rule cong :premises (@p142 @p126) :args (@t59)) % 43.43/43.68 (step @p144 :rule eq-symm :args (@t59 @t60)) % 43.43/43.68 (step @p145 :rule refl :args (@t14)) % 43.43/43.68 (step @p146 :rule cong :premises (@p145 @p144) :args ((=> @t14 @t61))) % 43.43/43.68 (assume-push @p266 @t14) % 43.43/43.68 (step @p148 :rule instantiate :premises (@p4) :args ((@list @t37 @t33))) % 43.43/43.68 (step-pop @p267 :rule scope :premises (@p148)) % 43.43/43.68 (step @p149 :rule process_scope :premises (@p267) :args (@t61)) % 43.43/43.68 (step @p151 :rule eq_resolve :premises (@p149 @p146)) % 43.43/43.68 (step @p152 :rule implies_elim :premises (@p151)) % 43.43/43.68 (step @p153 :rule chain_m_resolution :premises (@p152 @p4) :args ((= @t60 @t59) (@list false) (@list @t14))) % 43.43/43.68 (step @p154 :rule trans :premises (@p153 @p143 @p105 @p103 @p38 @p30)) % 43.43/43.68 (step @p155 :rule cong :premises (@p92 @p154) :args ((tptp.multiply @t53 @t60))) % 43.43/43.68 (step @p156 :rule instantiate :premises (@p13) :args ((@list @t53 @t33 @t37))) % 43.43/43.68 (step @p157 :rule symm :premises (@p156)) % 43.43/43.68 (step @p158 :rule instantiate :premises (@p3) :args ((@list @t43 @t49 @t37))) % 43.43/43.68 (step @p159 :rule symm :premises (@p158)) % 43.43/43.68 (step @p160 :rule instantiate :premises (@p3) :args ((@list @t43 tptp.identity @t37))) % 43.43/43.68 (step @p161 :rule symm :premises (@p160)) % 43.43/43.68 (step @p162 :rule symm :premises (@p141)) % 43.43/43.68 (step @p163 :rule trans :premises (@p107 @p140)) % 43.43/43.68 (step @p164 :rule cong :premises (@p163 @p39) :args ((tptp.multiply @t56 tptp.a))) % 43.43/43.68 (step @p165 :rule instantiate :premises (@p14) :args (@t62)) % 43.43/43.68 (step @p166 :rule symm :premises (@p165)) % 43.43/43.68 (step @p167 :rule refl :args (@t63)) % 43.43/43.68 (step @p168 :rule trans :premises (@p31 @p37)) % 43.43/43.68 (step @p169 :rule cong :premises (@p168 @p167) :args (@t64)) % 43.43/43.68 (step @p170 :rule cong :premises (@p30 @p167) :args (@t65)) % 43.43/43.68 (step @p171 :rule trans :premises (@p170 @p169 @p166 @p164 @p162)) % 43.43/43.68 (step @p172 :rule cong :premises (@p32 @p171) :args ((tptp.multiply tptp.identity @t65))) % 43.43/43.68 (step @p173 :rule instantiate :premises (@p12) :args ((@list tptp.identity tptp.a @t63))) % 43.43/43.68 (step @p174 :rule symm :premises (@p173)) % 43.43/43.68 (step @p175 :rule instantiate :premises (@p3) :args (@t62)) % 43.43/43.68 (step @p176 :rule cong :premises (@p37 @p39) :args (@t63)) % 43.43/43.68 (step @p177 :rule trans :premises (@p176 @p175)) % 43.43/43.68 (step @p178 :rule cong :premises (@p168 @p177) :args (@t64)) % 43.43/43.68 (step @p179 :rule symm :premises (@p169)) % 43.43/43.68 (step @p180 :rule symm :premises (@p164)) % 43.43/43.68 (step @p181 :rule trans :premises (@p141 @p180 @p165 @p179 @p178 @p174 @p172)) % 43.43/43.68 (step @p182 :rule cong :premises (@p78 @p181) :args ((tptp.multiply @t43 @t37))) % 43.43/43.68 (step @p183 :rule instantiate :premises (@p3) :args ((@list @t43 @t33 tptp.a))) % 43.43/43.68 (step @p184 :rule trans :premises (@p106 @p125 @p124 @p116 @p114 @p183 @p182 @p161)) % 43.43/43.68 (step @p185 :rule cong :premises (@p78 @p184) :args (@t54)) % 43.43/43.68 (step @p186 :rule instantiate :premises (@p36) :args ((@list @t49))) % 43.43/43.68 (step @p187 :rule symm :premises (@p186)) % 43.43/43.68 (step @p188 :rule cong :premises (@p53 @p111) :args ((tptp.multiply @t40 @t49))) % 43.43/43.68 (step @p189 :rule instantiate :premises (@p3) :args ((@list @t39 tptp.identity @t49))) % 43.43/43.68 (step @p190 :rule symm :premises (@p189)) % 43.43/43.68 (step @p191 :rule cong :premises (@p57 @p186) :args (@t66)) % 43.43/43.68 (step @p192 :rule trans :premises (@p191 @p190 @p188 @p187)) % 43.43/43.68 (step @p193 :rule cong :premises (@p192 @p53) :args ((tptp.least_upper_bound @t66 @t40))) % 43.43/43.68 (step @p194 :rule instantiate :premises (@p12) :args ((@list @t39 @t49 tptp.identity))) % 43.43/43.68 (step @p195 :rule symm :premises (@p113)) % 43.43/43.68 (step @p196 :rule cong :premises (@p57 @p195) :args (@t67)) % 43.43/43.68 (step @p197 :rule trans :premises (@p196 @p194 @p193 @p112 @p110 @p108 @p185 @p159)) % 43.43/43.68 (step @p198 :rule instantiate :premises (@p3) :args ((@list @t43 @t49 @t33))) % 43.43/43.68 (step @p199 :rule symm :premises (@p198)) % 43.43/43.68 (step @p200 :rule eq-symm :args (@t18 @t1)) % 43.43/43.68 (step @p201 :rule cong :premises (@p200) :args (@t19)) % 43.43/43.68 (step @p202 :rule eq_resolve :premises (@p9 @p201)) % 43.43/43.68 (step @p203 :rule instantiate :premises (@p202) :args (@t35)) % 43.43/43.68 (step @p204 :rule symm :premises (@p203)) % 43.43/43.68 (step @p205 :rule instantiate :premises (@p42) :args (@t68)) % 43.43/43.68 (step @p206 :rule symm :premises (@p205)) % 43.43/43.68 (step @p207 :rule instantiate :premises (@p36) :args (@t68)) % 43.43/43.68 (step @p208 :rule symm :premises (@p207)) % 43.43/43.68 (step @p209 :rule cong :premises (@p53 @p57) :args ((tptp.multiply @t40 @t39))) % 43.43/43.68 (step @p210 :rule instantiate :premises (@p3) :args ((@list @t39 tptp.identity @t39))) % 43.43/43.68 (step @p211 :rule symm :premises (@p210)) % 43.43/43.68 (step @p212 :rule cong :premises (@p57 @p207) :args (@t69)) % 43.43/43.68 (step @p213 :rule trans :premises (@p212 @p211 @p209 @p208)) % 43.43/43.68 (step @p214 :rule refl :args (@t70)) % 43.43/43.68 (step @p215 :rule cong :premises (@p214 @p213) :args ((tptp.multiply @t70 @t69))) % 43.43/43.68 (step @p216 :rule instantiate :premises (@p3) :args ((@list @t70 @t39 @t39))) % 43.43/43.68 (step @p217 :rule cong :premises (@p205 @p57) :args ((tptp.multiply tptp.identity @t39))) % 43.43/43.68 (step @p218 :rule trans :premises (@p212 @p211 @p209 @p217 @p216 @p215 @p206)) % 43.43/43.68 (step @p219 :rule cong :premises (@p78 @p218) :args ((tptp.multiply @t43 @t69))) % 43.43/43.68 (step @p220 :rule symm :premises (@p213)) % 43.43/43.68 (step @p221 :rule cong :premises (@p78 @p220) :args (@t71)) % 43.43/43.68 (step @p222 :rule trans :premises (@p221 @p219)) % 43.43/43.68 (step @p223 :rule cong :premises (@p222 @p204) :args ((tptp.multiply @t71 (tptp.greatest_lower_bound @t33 @t33)))) % 43.43/43.68 (step @p224 :rule refl :args (@t71)) % 43.43/43.68 (step @p225 :rule cong :premises (@p224 @p203) :args ((tptp.multiply @t71 @t33))) % 43.43/43.68 (step @p226 :rule instantiate :premises (@p3) :args ((@list @t43 @t39 @t33))) % 43.43/43.68 (step @p227 :rule symm :premises (@p226)) % 43.43/43.68 (step @p228 :rule trans :premises (@p136 @p135 @p134 @p133 @p132)) % 43.43/43.68 (step @p229 :rule cong :premises (@p78 @p228) :args (@t54)) % 43.43/43.68 (step @p230 :rule trans :premises (@p229 @p227 @p225 @p223)) % 43.43/43.68 (step @p231 :rule cong :premises (@p78 @p230) :args (@t72)) % 43.43/43.68 (step @p232 :rule trans :premises (@p231 @p199)) % 43.43/43.68 (step @p233 :rule cong :premises (@p232 @p197) :args ((tptp.greatest_lower_bound @t72 @t67))) % 43.43/43.68 (step @p234 :rule instantiate :premises (@p15) :args ((@list @t43 @t39 @t54))) % 43.43/43.68 (step @p235 :rule trans :premises (@p234 @p233 @p157 @p155 @p93 @p91 @p90)) % 43.43/43.68 (step @p236 :rule cong :premises (@p86 @p235) :args ((tptp.multiply @t51 (tptp.multiply @t46 @t54)))) % 43.43/43.68 (step @p237 :rule instantiate :premises (@p3) :args ((@list @t51 @t46 @t54))) % 43.43/43.68 (step @p238 :rule refl :args (@t54)) % 43.43/43.68 (step @p239 :rule cong :premises (@p76 @p238) :args ((tptp.multiply tptp.identity @t54))) % 43.43/43.68 (step @p240 :rule instantiate :premises (@p12) :args ((@list @t43 tptp.a tptp.identity))) % 43.43/43.68 (step @p241 :rule symm :premises (@p240)) % 43.43/43.68 (step @p242 :rule cong :premises (@p67 @p111) :args (@t73)) % 43.43/43.68 (step @p243 :rule trans :premises (@p242 @p241)) % 43.43/43.68 (step @p244 :rule cong :premises (@p32 @p243) :args ((tptp.multiply tptp.identity @t73))) % 43.43/43.68 (step @p245 :rule instantiate :premises (@p12) :args ((@list tptp.identity tptp.identity @t49))) % 43.43/43.68 (step @p246 :rule symm :premises (@p245)) % 43.43/43.68 (step @p247 :rule cong :premises (@p127 @p186) :args (@t73)) % 43.43/43.68 (step @p248 :rule symm :premises (@p242)) % 43.43/43.68 (step @p249 :rule trans :premises (@p240 @p248 @p247 @p246 @p244 @p239 @p237 @p236)) % 43.43/43.68 (step @p250 :rule cong :premises (@p249 @p89) :args ((tptp.multiply @t54 @t52))) % 43.43/43.68 (step @p251 :rule instantiate :premises (@p3) :args ((@list @t54 tptp.a @t36))) % 43.43/43.68 (step @p252 :rule trans :premises (@p137 @p106 @p125 @p124 @p116 @p114)) % 43.43/43.68 (step @p253 :rule cong :premises (@p252 @p51) :args (@t74)) % 43.43/43.68 (step @p254 :rule trans :premises (@p253 @p251 @p250 @p88 @p87 @p77)) % 43.43/43.68 (step @p255 :rule cong :premises (@p254 @p39) :args (@t75)) % 43.43/43.68 (step @p256 :rule trans :premises (@p255 @p38)) % 43.43/43.68 (step @p257 :rule cong :premises (@p256 @p75) :args (@t76)) % 43.43/43.68 (step @p258 :rule trans :premises (@p257 @p22)) % 43.43/43.68 (step @p259 :rule false_elim :premises (@p258)) % 43.43/43.68 (assume-push @p268 @t11) % 43.43/43.68 (step @p261 :rule instantiate :premises (@p3) :args ((@list @t30 @t36 tptp.a))) % 43.43/43.68 (step-pop @p269 :rule scope :premises (@p261)) % 43.43/43.68 (step @p262 :rule process_scope :premises (@p269) :args (@t76)) % 43.43/43.68 (step @p264 :rule implies_elim :premises (@p262)) % 43.43/43.68 (step @p265 false :rule chain_m_resolution :premises (@p264 @p259 @p3) :args (false (@list true false) (@list @t76 @t11))) % 43.43/43.68 ) % 43.43/43.69 % SZS output end Proof % 43.43/43.69 % cvc5 exiting %------------------------------------------------------------------------------