%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : GRP179-2 : TPTP v9.2.1. Bugfixed v1.2.1. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n017.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 08:20:07 AM UTC 2026 % Result : Unsatisfiable 160.17s 160.44s % Output : Proof 160.17s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : GRP179-2 : TPTP v9.2.1. Bugfixed v1.2.1. % 0.00/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.15/0.34 % Computer : n017.cluster.edu % 0.15/0.34 % Model : x86_64 x86_64 % 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.34 % Memory : 8042.1875MB % 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.34 % CPULimit : 300 % 0.15/0.34 % WCLimit : 300 % 0.15/0.34 % DateTime : Tue Jun 2 00:53:46 EDT 2026 % 0.15/0.34 % CPUTime : % 0.31/0.49 %----Proving TF0_NAR, FOF, or CNF % 0.31/0.50 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 15.85/16.11 --- Run --no-e-matching --full-saturate-quant at 6... % 21.95/22.14 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 6... % 27.97/28.16 --- Run --finite-model-find --uf-ss=no-minimal at 6... % 34.06/34.20 --- Run --multi-trigger-when-single --full-saturate-quant at 30... % 34.07/64.42 --- Run --trigger-sel=max --full-saturate-quant at 15... % 79.41/79.64 --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 33... % 112.70/112.90 --- Run --multi-trigger-cache --full-saturate-quant at 15... % 127.81/128.07 --- Run --prenex-quant=none --full-saturate-quant at 30... % 157.96/158.27 --- Run --enum-inst-interleave --decision=internal --full-saturate-quant at 15... % 160.17/160.44 % SZS status Unsatisfiable % 160.17/160.44 % SZS output start Proof % 160.17/160.45 ( % 160.17/160.45 (declare-sort $$unsorted 0) % 160.17/160.45 (declare-const tptp.a $$unsorted) % 160.17/160.45 (declare-const tptp.least_upper_bound (-> $$unsorted $$unsorted $$unsorted)) % 160.17/160.45 (declare-const tptp.greatest_lower_bound (-> $$unsorted $$unsorted $$unsorted)) % 160.17/160.45 (declare-const tptp.inverse (-> $$unsorted $$unsorted)) % 160.17/160.45 (declare-const tptp.multiply (-> $$unsorted $$unsorted $$unsorted)) % 160.17/160.45 (declare-const tptp.identity $$unsorted) % 160.17/160.45 (define @t1 () (@var "X" $$unsorted)) % 160.17/160.45 (define @t2 () (tptp.multiply tptp.identity @t1)) % 160.17/160.45 (define @t3 () (@list @t1)) % 160.17/160.45 (define @t4 () (forall @t3 (= @t2 @t1))) % 160.17/160.45 (define @t5 () (tptp.multiply (tptp.inverse @t1) @t1)) % 160.17/160.45 (define @t6 () (forall @t3 (= @t5 tptp.identity))) % 160.17/160.45 (define @t7 () (@var "Z" $$unsorted)) % 160.17/160.45 (define @t8 () (@var "Y" $$unsorted)) % 160.17/160.45 (define @t9 () (tptp.multiply @t1 @t8)) % 160.17/160.45 (define @t10 () (@list @t1 @t8 @t7)) % 160.17/160.45 (define @t11 () (forall @t10 (= (tptp.multiply @t9 @t7) (tptp.multiply @t1 (tptp.multiply @t8 @t7))))) % 160.17/160.45 (define @t12 () (tptp.greatest_lower_bound @t1 @t8)) % 160.17/160.45 (define @t13 () (@list @t1 @t8)) % 160.17/160.45 (define @t14 () (tptp.least_upper_bound @t1 @t8)) % 160.17/160.45 (define @t15 () (tptp.greatest_lower_bound @t8 @t7)) % 160.17/160.45 (define @t16 () (tptp.least_upper_bound @t8 @t7)) % 160.17/160.45 (define @t17 () (tptp.least_upper_bound @t1 @t1)) % 160.17/160.45 (define @t18 () (forall @t3 (= @t17 @t1))) % 160.17/160.45 (define @t19 () (tptp.greatest_lower_bound @t1 @t1)) % 160.17/160.45 (define @t20 () (forall @t3 (= @t19 @t1))) % 160.17/160.45 (define @t21 () (tptp.least_upper_bound @t1 @t12)) % 160.17/160.45 (define @t22 () (forall @t13 (= @t21 @t1))) % 160.17/160.45 (define @t23 () (tptp.greatest_lower_bound @t1 @t14)) % 160.17/160.45 (define @t24 () (forall @t13 (= @t23 @t1))) % 160.17/160.45 (define @t25 () (tptp.multiply @t1 @t7)) % 160.17/160.45 (define @t26 () (tptp.multiply @t7 @t1)) % 160.17/160.45 (define @t27 () (tptp.multiply @t8 @t1)) % 160.17/160.45 (define @t28 () (@list @t8 @t7 @t1)) % 160.17/160.45 (define @t29 () (tptp.greatest_lower_bound tptp.a tptp.identity)) % 160.17/160.45 (define @t30 () (tptp.inverse @t29)) % 160.17/160.45 (define @t31 () (tptp.inverse tptp.a)) % 160.17/160.45 (define @t32 () (tptp.least_upper_bound @t31 tptp.identity)) % 160.17/160.45 (define @t33 () (tptp.greatest_lower_bound tptp.identity tptp.a)) % 160.17/160.45 (define @t34 () (tptp.multiply @t33 @t30)) % 160.17/160.45 (define @t35 () (tptp.multiply @t30 tptp.identity)) % 160.17/160.45 (define @t36 () (tptp.multiply @t35 @t34)) % 160.17/160.45 (define @t37 () (tptp.multiply @t35 @t33)) % 160.17/160.45 (define @t38 () (tptp.multiply @t37 @t30)) % 160.17/160.45 (define @t39 () (= @t38 @t36)) % 160.17/160.45 (define @t40 () (= @t36 @t38)) % 160.17/160.45 (define @t41 () (@list @t30)) % 160.17/160.45 (define @t42 () (@list tptp.a tptp.identity)) % 160.17/160.45 (define @t43 () (@list tptp.a)) % 160.17/160.45 (define @t44 () (@list tptp.identity)) % 160.17/160.45 (define @t45 () (tptp.multiply tptp.identity tptp.a)) % 160.17/160.45 (define @t46 () (tptp.multiply tptp.identity tptp.identity)) % 160.17/160.45 (define @t47 () (tptp.multiply tptp.identity @t33)) % 160.17/160.45 (define @t48 () (@list @t31)) % 160.17/160.45 (define @t49 () (tptp.multiply @t31 tptp.a)) % 160.17/160.45 (define @t50 () (tptp.inverse @t31)) % 160.17/160.45 (define @t51 () (tptp.multiply @t50 @t31)) % 160.17/160.45 (define @t52 () (tptp.multiply @t50 tptp.identity)) % 160.17/160.45 (define @t53 () (tptp.multiply @t31 tptp.identity)) % 160.17/160.45 (define @t54 () (@list @t32)) % 160.17/160.45 (define @t55 () (tptp.inverse @t32)) % 160.17/160.45 (define @t56 () (tptp.inverse @t30)) % 160.17/160.45 (define @t57 () (tptp.multiply @t50 @t49)) % 160.17/160.45 (define @t58 () (tptp.greatest_lower_bound tptp.identity @t31)) % 160.17/160.45 (define @t59 () (@list tptp.identity @t31)) % 160.17/160.45 (define @t60 () (tptp.multiply tptp.identity @t31)) % 160.17/160.45 (define @t61 () (tptp.multiply tptp.identity @t49)) % 160.17/160.45 (define @t62 () (tptp.greatest_lower_bound @t49 @t53)) % 160.17/160.45 (define @t63 () (tptp.multiply @t31 @t29)) % 160.17/160.45 (define @t64 () (tptp.multiply @t60 @t29)) % 160.17/160.45 (define @t65 () (tptp.multiply tptp.identity @t63)) % 160.17/160.45 (define @t66 () (= @t64 @t65)) % 160.17/160.45 (define @t67 () (@list tptp.identity @t31 @t29)) % 160.17/160.45 (define @t68 () (tptp.least_upper_bound @t63 @t33)) % 160.17/160.45 (define @t69 () (tptp.multiply tptp.identity @t29)) % 160.17/160.45 (define @t70 () (tptp.multiply @t32 @t29)) % 160.17/160.45 (define @t71 () (tptp.multiply @t32 tptp.identity)) % 160.17/160.45 (define @t72 () (tptp.multiply @t32 tptp.a)) % 160.17/160.45 (define @t73 () (@list @t31 tptp.identity)) % 160.17/160.45 (define @t74 () (tptp.least_upper_bound tptp.identity @t31)) % 160.17/160.45 (assume @p1 @t4) % 160.17/160.45 (assume @p2 @t6) % 160.17/160.45 (assume @p3 @t11) % 160.17/160.45 (assume @p4 (forall @t13 (= @t12 (tptp.greatest_lower_bound @t8 @t1)))) % 160.17/160.45 (assume @p5 (forall @t13 (= @t14 (tptp.least_upper_bound @t8 @t1)))) % 160.17/160.45 (assume @p6 (forall @t10 (= (tptp.greatest_lower_bound @t1 @t15) (tptp.greatest_lower_bound @t12 @t7)))) % 160.17/160.45 (assume @p7 (forall @t10 (= (tptp.least_upper_bound @t1 @t16) (tptp.least_upper_bound @t14 @t7)))) % 160.17/160.45 (assume @p8 @t18) % 160.17/160.45 (assume @p9 @t20) % 160.17/160.45 (assume @p10 @t22) % 160.17/160.45 (assume @p11 @t24) % 160.17/160.45 (assume @p12 (forall @t10 (= (tptp.multiply @t1 @t16) (tptp.least_upper_bound @t9 @t25)))) % 160.17/160.45 (assume @p13 (forall @t10 (= (tptp.multiply @t1 @t15) (tptp.greatest_lower_bound @t9 @t25)))) % 160.17/160.45 (assume @p14 (forall @t28 (= (tptp.multiply @t16 @t1) (tptp.least_upper_bound @t27 @t26)))) % 160.17/160.45 (assume @p15 (forall @t28 (= (tptp.multiply @t15 @t1) (tptp.greatest_lower_bound @t27 @t26)))) % 160.17/160.45 (assume @p16 (not (= @t32 @t30))) % 160.17/160.45 (step @p17 :rule bool-eq-false :args (@t39)) % 160.17/160.45 (step @p18 :rule symm :premises (@p17)) % 160.17/160.45 (step @p19 :rule eq-symm :args (@t36 @t38)) % 160.17/160.45 (step @p20 :rule cong :premises (@p19) :args ((not @t40))) % 160.17/160.45 (step @p21 :rule bool-eq-false :args (@t40)) % 160.17/160.45 (step @p22 :rule trans :premises (@p21 @p20)) % 160.17/160.45 (step @p23 :rule trans :premises (@p22 @p18)) % 160.17/160.45 (step @p24 :rule false_intro :premises (@p16)) % 160.17/160.45 (step @p25 :rule eq-symm :args (@t2 @t1)) % 160.17/160.45 (step @p26 :rule cong :premises (@p25) :args (@t4)) % 160.17/160.45 (step @p27 :rule eq_resolve :premises (@p1 @p26)) % 160.17/160.45 (step @p28 :rule instantiate :premises (@p27) :args (@t41)) % 160.17/160.45 (step @p29 :rule symm :premises (@p28)) % 160.17/160.45 (step @p30 :rule refl :args (@t30)) % 160.17/160.45 (step @p31 :rule eq-symm :args (@t5 tptp.identity)) % 160.17/160.45 (step @p32 :rule cong :premises (@p31) :args (@t6)) % 160.17/160.45 (step @p33 :rule eq_resolve :premises (@p2 @p32)) % 160.17/160.45 (step @p34 :rule instantiate :premises (@p33) :args ((@list @t29))) % 160.17/160.45 (step @p35 :rule symm :premises (@p34)) % 160.17/160.45 (step @p36 :rule instantiate :premises (@p4) :args (@t42)) % 160.17/160.45 (step @p37 :rule symm :premises (@p36)) % 160.17/160.45 (step @p38 :rule instantiate :premises (@p27) :args (@t43)) % 160.17/160.45 (step @p39 :rule symm :premises (@p38)) % 160.17/160.45 (step @p40 :rule instantiate :premises (@p27) :args (@t44)) % 160.17/160.45 (step @p41 :rule symm :premises (@p40)) % 160.17/160.45 (step @p42 :rule cong :premises (@p41 @p39) :args ((tptp.greatest_lower_bound @t46 @t45))) % 160.17/160.45 (step @p43 :rule instantiate :premises (@p13) :args ((@list tptp.identity tptp.identity tptp.a))) % 160.17/160.45 (step @p44 :rule trans :premises (@p43 @p42 @p37)) % 160.17/160.45 (step @p45 :rule cong :premises (@p30 @p44) :args ((tptp.multiply @t30 @t47))) % 160.17/160.45 (step @p46 :rule instantiate :premises (@p3) :args ((@list @t30 tptp.identity @t33))) % 160.17/160.45 (step @p47 :rule trans :premises (@p46 @p45 @p35)) % 160.17/160.45 (step @p48 :rule cong :premises (@p47 @p30) :args (@t38)) % 160.17/160.45 (step @p49 :rule trans :premises (@p48 @p29)) % 160.17/160.45 (step @p50 :rule eq-symm :args (@t17 @t1)) % 160.17/160.45 (step @p51 :rule cong :premises (@p50) :args (@t18)) % 160.17/160.45 (step @p52 :rule eq_resolve :premises (@p8 @p51)) % 160.17/160.45 (step @p53 :rule instantiate :premises (@p52) :args (@t44)) % 160.17/160.45 (step @p54 :rule symm :premises (@p53)) % 160.17/160.45 (step @p55 :rule refl :args (@t31)) % 160.17/160.45 (step @p56 :rule cong :premises (@p55 @p54) :args ((tptp.least_upper_bound @t31 (tptp.least_upper_bound tptp.identity tptp.identity)))) % 160.17/160.45 (step @p57 :rule instantiate :premises (@p33) :args (@t43)) % 160.17/160.45 (step @p58 :rule symm :premises (@p57)) % 160.17/160.45 (step @p59 :rule trans :premises (@p58 @p53)) % 160.17/160.45 (step @p60 :rule instantiate :premises (@p27) :args (@t48)) % 160.17/160.45 (step @p61 :rule symm :premises (@p60)) % 160.17/160.45 (step @p62 :rule cong :premises (@p58 @p55) :args ((tptp.multiply @t49 @t31))) % 160.17/160.45 (step @p63 :rule instantiate :premises (@p3) :args ((@list @t31 tptp.a @t31))) % 160.17/160.45 (step @p64 :rule symm :premises (@p63)) % 160.17/160.45 (step @p65 :rule refl :args (tptp.a)) % 160.17/160.45 (step @p66 :rule instantiate :premises (@p33) :args (@t48)) % 160.17/160.45 (step @p67 :rule symm :premises (@p66)) % 160.17/160.45 (step @p68 :rule cong :premises (@p67 @p65) :args ((tptp.multiply @t51 tptp.a))) % 160.17/160.45 (step @p69 :rule instantiate :premises (@p3) :args ((@list @t50 @t31 tptp.a))) % 160.17/160.45 (step @p70 :rule symm :premises (@p69)) % 160.17/160.45 (step @p71 :rule refl :args (@t50)) % 160.17/160.45 (step @p72 :rule cong :premises (@p71 @p57) :args (@t52)) % 160.17/160.45 (step @p73 :rule trans :premises (@p72 @p70 @p68 @p39)) % 160.17/160.45 (step @p74 :rule cong :premises (@p73 @p55) :args ((tptp.multiply @t52 @t31))) % 160.17/160.45 (step @p75 :rule instantiate :premises (@p3) :args ((@list @t50 tptp.identity @t31))) % 160.17/160.45 (step @p76 :rule symm :premises (@p75)) % 160.17/160.45 (step @p77 :rule cong :premises (@p71 @p60) :args (@t51)) % 160.17/160.45 (step @p78 :rule trans :premises (@p66 @p77 @p76 @p74)) % 160.17/160.45 (step @p79 :rule cong :premises (@p55 @p78) :args (@t53)) % 160.17/160.45 (step @p80 :rule instantiate :premises (@p33) :args (@t54)) % 160.17/160.45 (step @p81 :rule symm :premises (@p80)) % 160.17/160.45 (step @p82 :rule cong :premises (@p55 @p81) :args ((tptp.multiply @t31 (tptp.multiply @t55 @t32)))) % 160.17/160.45 (step @p83 :rule instantiate :premises (@p3) :args ((@list @t31 @t55 @t32))) % 160.17/160.45 (step @p84 :rule trans :premises (@p83 @p82 @p79 @p64 @p62 @p61)) % 160.17/160.45 (step @p85 :rule symm :premises (@p83)) % 160.17/160.45 (step @p86 :rule symm :premises (@p82)) % 160.17/160.45 (step @p87 :rule cong :premises (@p55 @p58) :args ((tptp.multiply @t31 @t49))) % 160.17/160.45 (step @p88 :rule trans :premises (@p87 @p86 @p85)) % 160.17/160.45 (step @p89 :rule symm :premises (@p87)) % 160.17/160.45 (step @p90 :rule trans :premises (@p89 @p88 @p84)) % 160.17/160.45 (step @p91 :rule cong :premises (@p90 @p59) :args ((tptp.least_upper_bound @t53 @t49))) % 160.17/160.45 (step @p92 :rule trans :premises (@p41 @p57)) % 160.17/160.45 (step @p93 :rule refl :args (@t53)) % 160.17/160.45 (step @p94 :rule cong :premises (@p93 @p92) :args ((tptp.least_upper_bound @t53 @t46))) % 160.17/160.45 (step @p95 :rule instantiate :premises (@p14) :args ((@list @t31 tptp.identity tptp.identity))) % 160.17/160.45 (step @p96 :rule instantiate :premises (@p33) :args (@t41)) % 160.17/160.45 (step @p97 :rule symm :premises (@p96)) % 160.17/160.45 (step @p98 :rule refl :args (@t56)) % 160.17/160.45 (step @p99 :rule cong :premises (@p98 @p29) :args ((tptp.multiply @t56 (tptp.multiply tptp.identity @t30)))) % 160.17/160.45 (step @p100 :rule instantiate :premises (@p3) :args ((@list @t56 tptp.identity @t30))) % 160.17/160.45 (step @p101 :rule cong :premises (@p98 @p47) :args ((tptp.multiply @t56 @t37))) % 160.17/160.45 (step @p102 :rule instantiate :premises (@p3) :args ((@list @t56 @t35 @t33))) % 160.17/160.45 (step @p103 :rule refl :args (@t33)) % 160.17/160.45 (step @p104 :rule instantiate :premises (@p3) :args ((@list @t56 @t30 tptp.identity))) % 160.17/160.45 (step @p105 :rule refl :args (tptp.identity)) % 160.17/160.45 (step @p106 :rule cong :premises (@p96 @p105) :args (@t46)) % 160.17/160.45 (step @p107 :rule trans :premises (@p40 @p106 @p104)) % 160.17/160.45 (step @p108 :rule cong :premises (@p107 @p103) :args (@t47)) % 160.17/160.45 (step @p109 :rule symm :premises (@p43)) % 160.17/160.45 (step @p110 :rule symm :premises (@p42)) % 160.17/160.45 (step @p111 :rule trans :premises (@p36 @p110 @p109 @p108 @p102 @p101)) % 160.17/160.45 (step @p112 :rule cong :premises (@p111 @p30) :args ((tptp.multiply @t29 @t30))) % 160.17/160.45 (step @p113 :rule cong :premises (@p37 @p30) :args (@t34)) % 160.17/160.45 (step @p114 :rule trans :premises (@p113 @p112 @p100 @p99 @p97)) % 160.17/160.45 (step @p115 :rule instantiate :premises (@p27) :args (@t54)) % 160.17/160.45 (step @p116 :rule symm :premises (@p115)) % 160.17/160.45 (step @p117 :rule refl :args (@t32)) % 160.17/160.45 (step @p118 :rule cong :premises (@p35 @p117) :args ((tptp.multiply (tptp.multiply @t30 @t29) @t32))) % 160.17/160.45 (step @p119 :rule instantiate :premises (@p3) :args ((@list @t30 @t29 @t32))) % 160.17/160.45 (step @p120 :rule symm :premises (@p119)) % 160.17/160.45 (step @p121 :rule instantiate :premises (@p12) :args ((@list @t29 @t31 tptp.identity))) % 160.17/160.45 (step @p122 :rule symm :premises (@p121)) % 160.17/160.45 (step @p123 :rule cong :premises (@p37 @p105) :args ((tptp.multiply @t33 tptp.identity))) % 160.17/160.45 (step @p124 :rule instantiate :premises (@p15) :args ((@list tptp.identity tptp.a tptp.identity))) % 160.17/160.45 (step @p125 :rule symm :premises (@p124)) % 160.17/160.45 (step @p126 :rule cong :premises (@p39 @p105) :args ((tptp.multiply @t45 tptp.identity))) % 160.17/160.45 (step @p127 :rule trans :premises (@p70 @p68 @p39)) % 160.17/160.45 (step @p128 :rule trans :premises (@p127 @p38)) % 160.17/160.45 (step @p129 :rule cong :premises (@p128 @p105) :args ((tptp.multiply @t57 tptp.identity))) % 160.17/160.45 (step @p130 :rule instantiate :premises (@p3) :args ((@list @t50 @t49 tptp.identity))) % 160.17/160.45 (step @p131 :rule symm :premises (@p130)) % 160.17/160.45 (step @p132 :rule cong :premises (@p57 @p105) :args (@t46)) % 160.17/160.45 (step @p133 :rule trans :premises (@p58 @p40 @p132)) % 160.17/160.45 (step @p134 :rule cong :premises (@p71 @p133) :args (@t57)) % 160.17/160.45 (step @p135 :rule symm :premises (@p68)) % 160.17/160.45 (step @p136 :rule trans :premises (@p38 @p135 @p69 @p134 @p131 @p129 @p126)) % 160.17/160.45 (step @p137 :rule cong :premises (@p40 @p136) :args (@t33)) % 160.17/160.45 (step @p138 :rule trans :premises (@p137 @p125 @p123)) % 160.17/160.45 (step @p139 :rule eq-symm :args (@t19 @t1)) % 160.17/160.45 (step @p140 :rule cong :premises (@p139) :args (@t20)) % 160.17/160.45 (step @p141 :rule eq_resolve :premises (@p9 @p140)) % 160.17/160.45 (step @p142 :rule instantiate :premises (@p141) :args (@t44)) % 160.17/160.45 (step @p143 :rule symm :premises (@p142)) % 160.17/160.45 (step @p144 :rule cong :premises (@p65 @p143) :args ((tptp.greatest_lower_bound tptp.a (tptp.greatest_lower_bound tptp.identity tptp.identity)))) % 160.17/160.45 (step @p145 :rule trans :premises (@p58 @p142)) % 160.17/160.45 (step @p146 :rule cong :premises (@p39 @p145) :args ((tptp.greatest_lower_bound @t45 @t49))) % 160.17/160.45 (step @p147 :rule instantiate :premises (@p15) :args ((@list tptp.identity @t31 tptp.a))) % 160.17/160.45 (step @p148 :rule trans :premises (@p147 @p146 @p144)) % 160.17/160.45 (step @p149 :rule cong :premises (@p148 @p55) :args ((tptp.multiply (tptp.multiply @t58 tptp.a) @t31))) % 160.17/160.45 (step @p150 :rule instantiate :premises (@p3) :args ((@list @t58 tptp.a @t31))) % 160.17/160.45 (step @p151 :rule symm :premises (@p150)) % 160.17/160.45 (step @p152 :rule instantiate :premises (@p4) :args (@t59)) % 160.17/160.45 (step @p153 :rule symm :premises (@p152)) % 160.17/160.45 (step @p154 :rule cong :premises (@p153 @p78) :args ((tptp.multiply (tptp.greatest_lower_bound @t31 tptp.identity) tptp.identity))) % 160.17/160.45 (step @p155 :rule cong :premises (@p61 @p105) :args ((tptp.multiply @t60 tptp.identity))) % 160.17/160.45 (step @p156 :rule instantiate :premises (@p3) :args ((@list tptp.identity @t31 tptp.identity))) % 160.17/160.45 (step @p157 :rule symm :premises (@p156)) % 160.17/160.45 (step @p158 :rule trans :premises (@p157 @p155 @p79 @p64 @p62 @p61)) % 160.17/160.45 (step @p159 :rule cong :premises (@p105 @p58) :args (@t61)) % 160.17/160.45 (step @p160 :rule trans :premises (@p159 @p41)) % 160.17/160.45 (step @p161 :rule cong :premises (@p160 @p158) :args ((tptp.greatest_lower_bound @t61 (tptp.multiply tptp.identity @t53)))) % 160.17/160.45 (step @p162 :rule symm :premises (@p155)) % 160.17/160.45 (step @p163 :rule trans :premises (@p162 @p156)) % 160.17/160.45 (step @p164 :rule symm :premises (@p160)) % 160.17/160.45 (step @p165 :rule trans :premises (@p58 @p164)) % 160.17/160.45 (step @p166 :rule cong :premises (@p165 @p163) :args (@t62)) % 160.17/160.45 (step @p167 :rule instantiate :premises (@p13) :args ((@list @t31 tptp.a tptp.identity))) % 160.17/160.45 (step @p168 :rule cong :premises (@p55 @p37) :args ((tptp.multiply @t31 @t33))) % 160.17/160.45 (step @p169 :rule trans :premises (@p168 @p167 @p166 @p161)) % 160.17/160.45 (step @p170 :rule symm :premises (@p168)) % 160.17/160.45 (step @p171 :rule symm :premises (@p167)) % 160.17/160.45 (step @p172 :rule trans :premises (@p171 @p170 @p169 @p152)) % 160.17/160.45 (step @p173 :rule cong :premises (@p172 @p105) :args ((tptp.multiply @t62 tptp.identity))) % 160.17/160.45 (step @p174 :rule cong :premises (@p167 @p105) :args ((tptp.multiply @t63 tptp.identity))) % 160.17/160.45 (step @p175 :rule instantiate :premises (@p3) :args ((@list @t31 @t29 tptp.identity))) % 160.17/160.45 (step @p176 :rule symm :premises (@p175)) % 160.17/160.45 (step @p177 :rule trans :premises (@p36 @p137 @p125 @p123)) % 160.17/160.45 (step @p178 :rule cong :premises (@p55 @p177) :args (@t63)) % 160.17/160.45 (step @p179 :rule symm :premises (@p166)) % 160.17/160.45 (step @p180 :rule symm :premises (@p161)) % 160.17/160.45 (step @p181 :rule trans :premises (@p153 @p180 @p179 @p171 @p178 @p176 @p174 @p173 @p154 @p151 @p149)) % 160.17/160.45 (step @p182 :rule refl :args (@t29)) % 160.17/160.45 (step @p183 :rule cong :premises (@p61 @p182) :args (@t64)) % 160.17/160.45 (step @p184 :rule eq-symm :args (@t64 @t65)) % 160.17/160.45 (step @p185 :rule refl :args (@t11)) % 160.17/160.45 (step @p186 :rule cong :premises (@p185 @p184) :args ((=> @t11 @t66))) % 160.17/160.45 (assume-push @p266 @t11) % 160.17/160.45 (step @p188 :rule instantiate :premises (@p3) :args (@t67)) % 160.17/160.45 (step-pop @p267 :rule scope :premises (@p188)) % 160.17/160.45 (step @p189 :rule process_scope :premises (@p267) :args (@t66)) % 160.17/160.45 (step @p191 :rule eq_resolve :premises (@p189 @p186)) % 160.17/160.45 (step @p192 :rule implies_elim :premises (@p191)) % 160.17/160.45 (step @p193 :rule chain_m_resolution :premises (@p192 @p3) :args ((= @t65 @t64) (@list false) (@list @t11))) % 160.17/160.45 (step @p194 :rule refl :args (@t63)) % 160.17/160.45 (step @p195 :rule cong :premises (@p58 @p194) :args ((tptp.multiply @t49 @t63))) % 160.17/160.45 (step @p196 :rule trans :premises (@p195 @p193 @p183 @p167 @p166 @p161 @p152)) % 160.17/160.45 (step @p197 :rule symm :premises (@p195)) % 160.17/160.45 (step @p188 :rule instantiate :premises (@p3) :args (@t67)) % 160.17/160.45 (step @p198 :rule symm :premises (@p183)) % 160.17/160.45 (step @p199 :rule trans :premises (@p198 @p188 @p197)) % 160.17/160.45 (step @p200 :rule trans :premises (@p199 @p196 @p181)) % 160.17/160.45 (step @p201 :rule cong :premises (@p200 @p138) :args (@t68)) % 160.17/160.45 (step @p202 :rule cong :premises (@p105 @p36) :args (@t69)) % 160.17/160.45 (step @p203 :rule trans :premises (@p202 @p43 @p42)) % 160.17/160.45 (step @p204 :rule cong :premises (@p194 @p203) :args ((tptp.least_upper_bound @t63 @t69))) % 160.17/160.45 (step @p205 :rule instantiate :premises (@p14) :args ((@list @t31 tptp.identity @t29))) % 160.17/160.45 (step @p206 :rule eq-symm :args (@t23 @t1)) % 160.17/160.45 (step @p207 :rule cong :premises (@p206) :args (@t24)) % 160.17/160.45 (step @p208 :rule eq_resolve :premises (@p11 @p207)) % 160.17/160.45 (step @p209 :rule instantiate :premises (@p208) :args ((@list @t70 @t49))) % 160.17/160.45 (step @p210 :rule symm :premises (@p209)) % 160.17/160.45 (step @p211 :rule refl :args (@t49)) % 160.17/160.45 (step @p212 :rule symm :premises (@p205)) % 160.17/160.45 (step @p213 :rule symm :premises (@p204)) % 160.17/160.45 (step @p214 :rule trans :premises (@p213 @p212)) % 160.17/160.45 (step @p215 :rule cong :premises (@p214 @p211) :args ((tptp.least_upper_bound @t68 @t49))) % 160.17/160.45 (step @p216 :rule instantiate :premises (@p5) :args ((@list @t49 @t68))) % 160.17/160.45 (step @p217 :rule instantiate :premises (@p7) :args ((@list @t49 @t63 @t33))) % 160.17/160.45 (step @p218 :rule symm :premises (@p217)) % 160.17/160.45 (step @p219 :rule instantiate :premises (@p12) :args ((@list @t31 tptp.a @t29))) % 160.17/160.45 (step @p220 :rule eq-symm :args (@t21 @t1)) % 160.17/160.45 (step @p221 :rule cong :premises (@p220) :args (@t22)) % 160.17/160.45 (step @p222 :rule eq_resolve :premises (@p10 @p221)) % 160.17/160.45 (step @p223 :rule instantiate :premises (@p222) :args (@t42)) % 160.17/160.45 (step @p224 :rule cong :premises (@p55 @p223) :args (@t49)) % 160.17/160.45 (step @p225 :rule trans :premises (@p57 @p224 @p219)) % 160.17/160.45 (step @p226 :rule cong :premises (@p225 @p103) :args ((tptp.least_upper_bound tptp.identity @t33))) % 160.17/160.45 (step @p227 :rule instantiate :premises (@p222) :args ((@list tptp.identity tptp.a))) % 160.17/160.45 (step @p228 :rule trans :premises (@p58 @p227 @p226 @p218 @p216 @p215)) % 160.17/160.45 (step @p229 :rule refl :args (@t70)) % 160.17/160.45 (step @p230 :rule cong :premises (@p229 @p228) :args ((tptp.greatest_lower_bound @t70 @t49))) % 160.17/160.45 (step @p231 :rule instantiate :premises (@p13) :args ((@list @t32 tptp.a tptp.identity))) % 160.17/160.45 (step @p232 :rule symm :premises (@p231)) % 160.17/160.45 (step @p233 :rule cong :premises (@p232 @p92) :args ((tptp.greatest_lower_bound (tptp.greatest_lower_bound @t72 @t71) @t46))) % 160.17/160.45 (step @p234 :rule instantiate :premises (@p6) :args ((@list @t72 @t71 @t46))) % 160.17/160.45 (step @p235 :rule instantiate :premises (@p15) :args ((@list @t32 tptp.identity tptp.identity))) % 160.17/160.45 (step @p236 :rule instantiate :premises (@p5) :args (@t73)) % 160.17/160.45 (step @p237 :rule symm :premises (@p236)) % 160.17/160.45 (step @p238 :rule cong :premises (@p237 @p105) :args ((tptp.greatest_lower_bound @t74 tptp.identity))) % 160.17/160.45 (step @p239 :rule instantiate :premises (@p4) :args ((@list tptp.identity @t74))) % 160.17/160.45 (step @p240 :rule instantiate :premises (@p208) :args (@t59)) % 160.17/160.45 (step @p241 :rule trans :premises (@p240 @p239 @p238)) % 160.17/160.45 (step @p242 :rule cong :premises (@p241 @p105) :args (@t46)) % 160.17/160.45 (step @p243 :rule trans :premises (@p58 @p40 @p242 @p235)) % 160.17/160.45 (step @p244 :rule refl :args (@t72)) % 160.17/160.45 (step @p245 :rule cong :premises (@p244 @p243) :args ((tptp.greatest_lower_bound @t72 @t49))) % 160.17/160.45 (step @p246 :rule instantiate :premises (@p15) :args ((@list @t32 @t31 tptp.a))) % 160.17/160.45 (step @p247 :rule instantiate :premises (@p4) :args ((@list @t31 @t32))) % 160.17/160.45 (step @p248 :rule instantiate :premises (@p208) :args (@t73)) % 160.17/160.45 (step @p249 :rule trans :premises (@p248 @p247)) % 160.17/160.45 (step @p250 :rule cong :premises (@p249 @p65) :args (@t49)) % 160.17/160.45 (step @p251 :rule trans :premises (@p57 @p250 @p246 @p245 @p234 @p233 @p230 @p210 @p205 @p204 @p201 @p122)) % 160.17/160.45 (step @p252 :rule cong :premises (@p30 @p251) :args (@t35)) % 160.17/160.45 (step @p253 :rule trans :premises (@p252 @p120 @p118 @p116)) % 160.17/160.45 (step @p254 :rule cong :premises (@p253 @p114) :args (@t36)) % 160.17/160.45 (step @p255 :rule trans :premises (@p254 @p95 @p94 @p91 @p56)) % 160.17/160.45 (step @p256 :rule cong :premises (@p255 @p49) :args (@t40)) % 160.17/160.45 (step @p257 :rule trans :premises (@p256 @p24)) % 160.17/160.45 (step @p258 :rule eq_resolve :premises (@p257 @p23)) % 160.17/160.45 (step @p259 :rule false_elim :premises (@p258)) % 160.17/160.45 (assume-push @p268 @t11) % 160.17/160.45 (step @p261 :rule instantiate :premises (@p3) :args ((@list @t35 @t33 @t30))) % 160.17/160.45 (step-pop @p269 :rule scope :premises (@p261)) % 160.17/160.45 (step @p262 :rule process_scope :premises (@p269) :args (@t39)) % 160.17/160.45 (step @p264 :rule implies_elim :premises (@p262)) % 160.17/160.45 (step @p265 false :rule chain_m_resolution :premises (@p264 @p259 @p3) :args (false (@list true false) (@list @t39 @t11))) % 160.17/160.45 ) % 160.17/160.46 % SZS output end Proof % 160.17/160.46 % cvc5 exiting %------------------------------------------------------------------------------