%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : LCL614^1 : TPTP v9.3.1. Released v3.6.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n013.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Sep 7 11:23:10 AM UTC 2026 % Result : Theorem 0.19s 0.51s % Output : Proof 0.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL614^1 : TPTP v9.3.1. Released v3.6.0. % 0.00/0.05 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.11/0.36 % Computer : n013.cluster.edu % 0.11/0.36 % Model : x86_64 x86_64 % 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.36 % Memory : 8046.5625MB % 0.11/0.36 % OS : Linux 6.8.0-71-generic % 0.11/0.36 % CPULimit : 300 % 0.11/0.36 % WCLimit : 300 % 0.11/0.36 % DateTime : Sat Sep 5 11:36:05 UTC 2026 % 0.11/0.37 % CPUTime : % 0.11/0.44 %----Proving TH0 % 0.19/0.51 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.19/0.51 % SZS status Theorem % 0.19/0.51 % SZS output start Proof % 0.19/0.51 ( % 0.19/0.51 (declare-sort $$unsorted 0) % 0.19/0.51 (declare-sort tptp.individuals 0) % 0.19/0.51 (define tptp.mfalse () (lambda (@list (@var "X" $$unsorted)) false)) % 0.19/0.51 (define tptp.mtrue () (lambda (@list (@var "X" $$unsorted)) true)) % 0.19/0.51 (define tptp.mnot () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.19/0.51 (define tptp.mor () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.19/0.51 (define tptp.mand () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.19/0.51 (define tptp.mimpl () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "V" (-> $$unsorted Bool)))) (let ((_let_3 (@var "U" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.19/0.51 (define tptp.miff () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "U" (-> $$unsorted Bool)))) (let ((_let_3 (@var "V" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimpl _let_2) _let_3)) (_ (_ tptp.mimpl _let_3) _let_2)) _let_1)))))) % 0.19/0.51 (define tptp.mbox () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" $$unsorted))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (forall (@list _let_1) (=> (_ (_ _let_4 _let_3) _let_1) (_ _let_2 _let_1))))))))) % 0.19/0.51 (define tptp.mdia () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" $$unsorted))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (exists (@list _let_1) (and (_ (_ _let_4 _let_3) _let_1) (_ _let_2 _let_1))))))))) % 0.19/0.51 (define tptp.mall () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.individuals))) (let ((_let_3 (@var "P" (-> tptp.individuals $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.19/0.51 (define tptp.mexists () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.individuals))) (let ((_let_3 (@var "P" (-> tptp.individuals $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (exists (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.19/0.51 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.19/0.51 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 0.19/0.51 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.19/0.51 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.19/0.51 (define @t1 () (@var "X" (-> $$unsorted Bool))) % 0.19/0.51 (define @t2 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.19/0.51 (define @t3 () (_ (_ tptp.mbox @t2) @t1)) % 0.19/0.51 (define @t4 () (@var "Y" (-> $$unsorted Bool))) % 0.19/0.51 (define @t5 () (=> (_ tptp.mvalid (_ (_ tptp.mimpl @t1) @t4)) (_ tptp.mvalid (_ (_ tptp.mimpl @t3) @t3)))) % 0.19/0.51 (define @t6 () (@list @t2 @t1 @t4)) % 0.19/0.51 (define @t7 () (forall @t6 @t5)) % 0.19/0.51 (define @t8 () (not @t7)) % 0.19/0.51 (define @t9 () (@var "X" $$unsorted)) % 0.19/0.51 (define @t10 () (@list @t9)) % 0.19/0.51 (define @t11 () (lambda @t10 false)) % 0.19/0.51 (define @t12 () (lambda @t10 true)) % 0.19/0.51 (define @t13 () (@var "U" $$unsorted)) % 0.19/0.51 (define @t14 () (_ @t1 @t13)) % 0.19/0.51 (define @t15 () (lambda (@list @t1 @t13) (not @t14))) % 0.19/0.51 (define @t16 () (_ @t4 @t13)) % 0.19/0.51 (define @t17 () (@list @t1 @t4 @t13)) % 0.19/0.51 (define @t18 () (lambda @t17 (or @t14 @t16))) % 0.19/0.51 (define @t19 () (lambda @t17 (and @t14 @t16))) % 0.19/0.51 (define @t20 () (@var "__flatten_var_0" $$unsorted)) % 0.19/0.51 (define @t21 () (@var "V" (-> $$unsorted Bool))) % 0.19/0.51 (define @t22 () (@var "U" (-> $$unsorted Bool))) % 0.19/0.51 (define @t23 () (@list @t22 @t21 @t20)) % 0.19/0.51 (define @t24 () (lambda @t23 (_ (_ (_ tptp.mor (_ tptp.mnot @t22)) @t21) @t20))) % 0.19/0.51 (define @t25 () (lambda @t23 (_ (_ (_ tptp.mand (_ (_ tptp.mimpl @t22) @t21)) (_ (_ tptp.mimpl @t21) @t22)) @t20))) % 0.19/0.51 (define @t26 () (@var "Y" $$unsorted)) % 0.19/0.51 (define @t27 () (@var "P" (-> $$unsorted Bool))) % 0.19/0.51 (define @t28 () (_ @t27 @t26)) % 0.19/0.51 (define @t29 () (_ (_ @t2 @t9) @t26)) % 0.19/0.51 (define @t30 () (@list @t26)) % 0.19/0.51 (define @t31 () (forall @t30 (=> @t29 @t28))) % 0.19/0.51 (define @t32 () (@list @t2 @t27 @t9)) % 0.19/0.51 (define @t33 () (lambda @t32 @t31)) % 0.19/0.51 (define @t34 () (lambda @t32 (exists @t30 (and @t29 @t28)))) % 0.19/0.51 (define @t35 () (@var "W" $$unsorted)) % 0.19/0.51 (define @t36 () (@var "X" tptp.individuals)) % 0.19/0.51 (define @t37 () (@var "P" (-> tptp.individuals $$unsorted Bool))) % 0.19/0.51 (define @t38 () (_ (_ @t37 @t36) @t35)) % 0.19/0.51 (define @t39 () (@list @t36)) % 0.19/0.51 (define @t40 () (@list @t37 @t35)) % 0.19/0.51 (define @t41 () (lambda @t40 (forall @t39 @t38))) % 0.19/0.51 (define @t42 () (lambda @t40 (exists @t39 @t38))) % 0.19/0.51 (define @t43 () (_ @t27 @t35)) % 0.19/0.51 (define @t44 () (@list @t35)) % 0.19/0.51 (define @t45 () (forall @t44 @t43)) % 0.19/0.51 (define @t46 () (@list @t27)) % 0.19/0.51 (define @t47 () (lambda @t46 @t45)) % 0.19/0.51 (define @t48 () (lambda @t46 (exists @t44 @t43))) % 0.19/0.51 (define @t49 () (not @t43)) % 0.19/0.51 (define @t50 () (lambda @t46 (exists @t44 @t49))) % 0.19/0.51 (define @t51 () (lambda @t46 (forall @t44 @t49))) % 0.19/0.51 (define @t52 () (_ @t4 @t35)) % 0.19/0.51 (define @t53 () (_ @t1 @t35)) % 0.19/0.51 (define @t54 () (_ @t1 @t26)) % 0.19/0.51 (define @t55 () (forall @t30 (or (not (_ @t2 @t35 @t26)) @t54))) % 0.19/0.51 (define @t56 () (or (not @t55) @t55)) % 0.19/0.51 (define @t57 () (forall @t30 (or (not (_ @t2 @t20 @t26)) @t54))) % 0.19/0.51 (define @t58 () (not @t57)) % 0.19/0.51 (define @t59 () (@list @t20)) % 0.19/0.51 (define @t60 () (lambda @t59 (or @t58 @t57))) % 0.19/0.51 (define @t61 () (_ @t60 @t35)) % 0.19/0.51 (define @t62 () (forall @t44 @t61)) % 0.19/0.51 (define @t63 () (_ @t27 @t35)) % 0.19/0.51 (define @t64 () (lambda @t46 (forall @t44 @t63))) % 0.19/0.51 (define @t65 () (_ @t2 @t9 @t26)) % 0.19/0.51 (define @t66 () (not @t65)) % 0.19/0.51 (define @t67 () (lambda @t10 (forall @t30 (or @t66 @t54)))) % 0.19/0.51 (define @t68 () (_ @t67 @t20)) % 0.19/0.51 (define @t69 () (or @t58 @t68)) % 0.19/0.51 (define @t70 () (lambda @t59 @t69)) % 0.19/0.51 (define @t71 () (_ @t21 @t20)) % 0.19/0.51 (define @t72 () (@list @t21 @t20)) % 0.19/0.51 (define @t73 () (_ @t27 @t26)) % 0.19/0.51 (define @t74 () (forall @t30 (or @t66 @t73))) % 0.19/0.51 (define @t75 () (lambda (@list @t27 @t9) @t74)) % 0.19/0.51 (define @t76 () (_ (lambda @t32 @t74) @t2)) % 0.19/0.51 (define @t77 () (not @t68)) % 0.19/0.51 (define @t78 () (or @t77 @t71)) % 0.19/0.51 (define @t79 () (lambda @t72 @t78)) % 0.19/0.51 (define @t80 () (or (not (_ @t22 @t20)) @t71)) % 0.19/0.51 (define @t81 () (lambda @t23 @t80)) % 0.19/0.51 (define @t82 () (_ @t4 @t35)) % 0.19/0.51 (define @t83 () (_ @t1 @t35)) % 0.19/0.51 (define @t84 () (not @t83)) % 0.19/0.51 (define @t85 () (or @t84 @t82)) % 0.19/0.51 (define @t86 () (not (_ @t1 @t20))) % 0.19/0.51 (define @t87 () (lambda @t59 (or @t86 (_ @t4 @t20)))) % 0.19/0.51 (define @t88 () (_ @t87 @t35)) % 0.19/0.51 (define @t89 () (forall @t44 @t88)) % 0.19/0.51 (define @t90 () (lambda @t72 (or @t86 @t71))) % 0.19/0.51 (define @t91 () (_ @t81 @t1)) % 0.19/0.51 (define @t92 () (_ @t76 @t1)) % 0.19/0.51 (define @t93 () (=> (_ @t64 (_ @t91 @t4)) (_ @t64 (_ (_ @t81 @t92) @t92)))) % 0.19/0.51 (define @t94 () (forall @t6 @t93)) % 0.19/0.51 (define @t95 () (not @t29)) % 0.19/0.51 (define @t96 () (or @t95 @t28)) % 0.19/0.51 (define @t97 () (not (_ @t22 @t13))) % 0.19/0.51 (define @t98 () (@list @t13)) % 0.19/0.51 (define @t99 () (lambda @t98 (or @t97 (_ @t21 @t13)))) % 0.19/0.51 (define @t100 () (@list @t4 @t13)) % 0.19/0.51 (define @t101 () (lambda @t98 @t97)) % 0.19/0.51 (define @t102 () (_ @t101 @t13)) % 0.19/0.51 (define @t103 () (or @t102 @t16)) % 0.19/0.51 (define @t104 () (lambda @t100 @t103)) % 0.19/0.51 (assume @p1 @t8) % 0.19/0.51 (assume @p2 true) % 0.19/0.51 (step @p3 (= tptp.mfalse @t11) :rule refl :args (@t11)) % 0.19/0.51 (step @p4 (= tptp.mtrue @t12) :rule refl :args (@t12)) % 0.19/0.51 (step @p5 (= tptp.mnot @t15) :rule refl :args (@t15)) % 0.19/0.51 (step @p6 (= tptp.mor @t18) :rule refl :args (@t18)) % 0.19/0.51 (step @p7 (= tptp.mand @t19) :rule refl :args (@t19)) % 0.19/0.51 (step @p8 (= tptp.mimpl @t24) :rule refl :args (@t24)) % 0.19/0.51 (step @p9 (= tptp.miff @t25) :rule refl :args (@t25)) % 0.19/0.51 (step @p10 (= tptp.mbox @t33) :rule refl :args (@t33)) % 0.19/0.51 (step @p11 (= tptp.mdia @t34) :rule refl :args (@t34)) % 0.19/0.51 (step @p12 (= tptp.mall @t41) :rule refl :args (@t41)) % 0.19/0.51 (step @p13 (= tptp.mexists @t42) :rule refl :args (@t42)) % 0.19/0.51 (step @p14 (= tptp.mvalid @t47) :rule refl :args (@t47)) % 0.19/0.51 (step @p15 (= tptp.msatisfiable @t48) :rule refl :args (@t48)) % 0.19/0.51 (step @p16 (= tptp.mcountersatisfiable @t50) :rule refl :args (@t50)) % 0.19/0.51 (step @p17 (= tptp.minvalid @t51) :rule refl :args (@t51)) % 0.19/0.51 (step @p18 :rule evaluate :args ((not true))) % 0.19/0.51 (step @p19 :rule quant-unused-vars :args ((= (forall @t6 true) true))) % 0.19/0.51 (step @p20 :rule bool-impl-true1 :args ((forall @t44 (or (not @t53) @t52)))) % 0.19/0.51 (step @p21 :rule quant-unused-vars :args ((= (forall @t44 true) true))) % 0.19/0.51 (step @p22 :rule bool-or-taut2 :args (false @t55 false false)) % 0.19/0.51 (step @p23 :rule cong :premises (@p22) :args ((forall @t44 @t56))) % 0.19/0.51 (step @p24 :rule trans :premises (@p23 @p21)) % 0.19/0.51 (step @p25 :rule beta-reduce :args ((= @t61 @t56))) % 0.19/0.51 (step @p26 :rule cong :premises (@p25) :args (@t62)) % 0.19/0.51 (step @p27 :rule trans :premises (@p26 @p24)) % 0.19/0.51 (step @p28 :rule beta-reduce :args ((= (_ @t64 @t60) @t62))) % 0.19/0.51 (step @p29 :rule trans :premises (@p28 @p27)) % 0.19/0.51 (step @p30 :rule beta-reduce :args ((= @t68 @t57))) % 0.19/0.51 (step @p31 :rule refl :args (@t58)) % 0.19/0.51 (step @p32 :rule nary_cong :premises (@p31 @p30) :args (@t69)) % 0.19/0.51 (step @p33 :rule cong :premises (@p32) :args (@t70)) % 0.19/0.51 (step @p34 :rule beta-reduce :args ((= (_ (lambda @t72 (or @t58 @t71)) @t67) @t70))) % 0.19/0.51 (step @p35 :rule trans :premises (@p34 @p33)) % 0.19/0.51 (step @p36 :rule beta-reduce :args ((= (_ @t75 @t1) @t67))) % 0.19/0.51 (step @p37 :rule refl :args (@t1)) % 0.19/0.51 (step @p38 :rule beta-reduce :args ((= @t76 @t75))) % 0.19/0.51 (step @p39 :rule ho_cong :premises (@p38 @p37)) % 0.19/0.51 (step @p40 :rule trans :premises (@p39 @p36)) % 0.19/0.51 (step @p41 :rule refl :args (@t71)) % 0.19/0.51 (step @p42 :rule cong :premises (@p30) :args (@t77)) % 0.19/0.51 (step @p43 :rule nary_cong :premises (@p42 @p41) :args (@t78)) % 0.19/0.51 (step @p44 :rule cong :premises (@p43) :args (@t79)) % 0.19/0.51 (step @p45 :rule beta-reduce :args ((= (_ @t81 @t67) @t79))) % 0.19/0.51 (step @p46 :rule trans :premises (@p45 @p44)) % 0.19/0.51 (step @p47 :rule refl :args (@t81)) % 0.19/0.51 (step @p48 :rule ho_cong :premises (@p47 @p40)) % 0.19/0.51 (step @p49 :rule trans :premises (@p48 @p46)) % 0.19/0.51 (step @p50 :rule ho_cong :premises (@p49 @p40)) % 0.19/0.51 (step @p51 :rule trans :premises (@p50 @p35)) % 0.19/0.51 (step @p52 :rule refl :args (@t64)) % 0.19/0.51 (step @p53 :rule ho_cong :premises (@p52 @p51)) % 0.19/0.51 (step @p54 :rule trans :premises (@p53 @p29)) % 0.19/0.51 (step @p55 :rule refl :args (@t52)) % 0.19/0.51 (step @p56 :rule refl :args (@t82)) % 0.19/0.51 (step @p57 :rule cong :premises (@p56 @p55) :args ((= @t82 @t52))) % 0.19/0.51 (step @p58 :rule symm :premises (@p57)) % 0.19/0.51 (step @p59 :rule eq_resolve :premises (@p56 @p58)) % 0.19/0.51 (step @p60 :rule refl :args (@t53)) % 0.19/0.51 (step @p61 :rule refl :args (@t83)) % 0.19/0.51 (step @p62 :rule cong :premises (@p61 @p60) :args ((= @t83 @t53))) % 0.19/0.51 (step @p63 :rule symm :premises (@p62)) % 0.19/0.51 (step @p64 :rule eq_resolve :premises (@p61 @p63)) % 0.19/0.51 (step @p65 :rule cong :premises (@p64) :args (@t84)) % 0.19/0.51 (step @p66 :rule nary_cong :premises (@p65 @p59) :args (@t85)) % 0.19/0.51 (step @p67 :rule cong :premises (@p66) :args ((forall @t44 @t85))) % 0.19/0.51 (step @p68 :rule beta-reduce :args ((= @t88 @t85))) % 0.19/0.51 (step @p69 :rule cong :premises (@p68) :args (@t89)) % 0.19/0.51 (step @p70 :rule trans :premises (@p69 @p67)) % 0.19/0.51 (step @p71 :rule beta-reduce :args ((= (_ @t64 @t87) @t89))) % 0.19/0.51 (step @p72 :rule trans :premises (@p71 @p70)) % 0.19/0.51 (step @p73 :rule beta-reduce :args ((= (_ @t90 @t4) @t87))) % 0.19/0.51 (step @p74 :rule refl :args (@t4)) % 0.19/0.51 (step @p75 :rule beta-reduce :args ((= @t91 @t90))) % 0.19/0.51 (step @p76 :rule ho_cong :premises (@p75 @p74)) % 0.19/0.51 (step @p77 :rule trans :premises (@p76 @p73)) % 0.19/0.51 (step @p78 :rule ho_cong :premises (@p52 @p77)) % 0.19/0.51 (step @p79 :rule trans :premises (@p78 @p72)) % 0.19/0.51 (step @p80 :rule cong :premises (@p79 @p54) :args (@t93)) % 0.19/0.51 (step @p81 :rule trans :premises (@p80 @p20)) % 0.19/0.51 (step @p82 :rule cong :premises (@p81) :args (@t94)) % 0.19/0.51 (step @p83 :rule trans :premises (@p82 @p19)) % 0.19/0.51 (step @p84 :rule cong :premises (@p83) :args ((not @t94))) % 0.19/0.51 (step @p85 :rule trans :premises (@p84 @p18)) % 0.19/0.51 (step @p86 :rule refl :args (@t2)) % 0.19/0.51 (step @p87 :rule refl :args (@t73)) % 0.19/0.51 (step @p88 :rule refl :args (@t28)) % 0.19/0.51 (step @p89 :rule cong :premises (@p88 @p87) :args ((= @t28 @t73))) % 0.19/0.51 (step @p90 :rule symm :premises (@p89)) % 0.19/0.51 (step @p91 :rule eq_resolve :premises (@p88 @p90)) % 0.19/0.51 (step @p92 :rule refl :args (@t65)) % 0.19/0.51 (step @p93 :rule refl :args (@t29)) % 0.19/0.51 (step @p94 :rule cong :premises (@p93 @p92) :args ((= @t29 @t65))) % 0.19/0.51 (step @p95 :rule symm :premises (@p94)) % 0.19/0.51 (step @p96 :rule eq_resolve :premises (@p93 @p95)) % 0.19/0.51 (step @p97 :rule cong :premises (@p96) :args (@t95)) % 0.19/0.51 (step @p98 :rule nary_cong :premises (@p97 @p91) :args (@t96)) % 0.19/0.51 (step @p99 :rule cong :premises (@p98) :args ((forall @t30 @t96))) % 0.19/0.51 (step @p100 :rule bool-impl-elim :args (@t29 @t28)) % 0.19/0.51 (step @p101 :rule cong :premises (@p100) :args (@t31)) % 0.19/0.51 (step @p102 :rule trans :premises (@p101 @p99)) % 0.19/0.51 (step @p103 :rule cong :premises (@p102) :args (@t33)) % 0.19/0.51 (step @p104 :rule trans :premises (@p10 @p103)) % 0.19/0.51 (step @p105 :rule ho_cong :premises (@p104 @p86)) % 0.19/0.51 (step @p106 :rule ho_cong :premises (@p105 @p37)) % 0.19/0.51 (step @p107 :rule beta-reduce :args ((= (_ @t99 @t20) @t80))) % 0.19/0.51 (step @p108 :rule refl :args (@t20)) % 0.19/0.51 (step @p109 :rule beta-reduce :args ((= (_ (lambda @t100 (or @t97 @t16)) @t21) @t99))) % 0.19/0.51 (step @p110 :rule refl :args (@t21)) % 0.19/0.51 (step @p111 :rule refl :args (@t16)) % 0.19/0.51 (step @p112 :rule beta-reduce :args ((= @t102 @t97))) % 0.19/0.51 (step @p113 :rule nary_cong :premises (@p112 @p111) :args (@t103)) % 0.19/0.51 (step @p114 :rule cong :premises (@p113) :args (@t104)) % 0.19/0.51 (step @p115 :rule beta-reduce :args ((= (_ @t18 @t101) @t104))) % 0.19/0.51 (step @p116 :rule trans :premises (@p115 @p114)) % 0.19/0.51 (step @p117 :rule beta-reduce :args ((= (_ @t15 @t22) @t101))) % 0.19/0.51 (step @p118 :rule refl :args (@t18)) % 0.19/0.51 (step @p119 :rule ho_cong :premises (@p118 @p117)) % 0.19/0.51 (step @p120 :rule trans :premises (@p119 @p116)) % 0.19/0.51 (step @p121 :rule ho_cong :premises (@p120 @p110)) % 0.19/0.51 (step @p122 :rule trans :premises (@p121 @p109)) % 0.19/0.51 (step @p123 :rule ho_cong :premises (@p122 @p108)) % 0.19/0.51 (step @p124 :rule trans :premises (@p123 @p107)) % 0.19/0.51 (step @p125 :rule refl :args (@t22)) % 0.19/0.51 (step @p126 :rule ho_cong :premises (@p5 @p125)) % 0.19/0.51 (step @p127 :rule ho_cong :premises (@p6 @p126)) % 0.19/0.51 (step @p128 :rule ho_cong :premises (@p127 @p110)) % 0.19/0.51 (step @p129 :rule ho_cong :premises (@p128 @p108)) % 0.19/0.51 (step @p130 :rule trans :premises (@p129 @p124)) % 0.19/0.51 (step @p131 :rule cong :premises (@p130) :args (@t24)) % 0.19/0.51 (step @p132 :rule trans :premises (@p8 @p131)) % 0.19/0.51 (step @p133 :rule ho_cong :premises (@p132 @p106)) % 0.19/0.51 (step @p134 :rule ho_cong :premises (@p133 @p106)) % 0.19/0.51 (step @p135 :rule refl :args (@t63)) % 0.19/0.51 (step @p136 :rule refl :args (@t43)) % 0.19/0.51 (step @p137 :rule cong :premises (@p136 @p135) :args ((= @t43 @t63))) % 0.19/0.51 (step @p138 :rule symm :premises (@p137)) % 0.19/0.51 (step @p139 :rule eq_resolve :premises (@p136 @p138)) % 0.19/0.51 (step @p140 :rule cong :premises (@p139) :args (@t45)) % 0.19/0.51 (step @p141 :rule cong :premises (@p140) :args (@t47)) % 0.19/0.51 (step @p142 :rule trans :premises (@p14 @p141)) % 0.19/0.51 (step @p143 :rule ho_cong :premises (@p142 @p134)) % 0.19/0.51 (step @p144 :rule ho_cong :premises (@p132 @p37)) % 0.19/0.51 (step @p145 :rule ho_cong :premises (@p144 @p74)) % 0.19/0.51 (step @p146 :rule ho_cong :premises (@p142 @p145)) % 0.19/0.51 (step @p147 :rule cong :premises (@p146 @p143) :args (@t5)) % 0.19/0.51 (step @p148 :rule cong :premises (@p147) :args (@t7)) % 0.19/0.51 (step @p149 :rule cong :premises (@p148) :args (@t8)) % 0.19/0.51 (step @p150 :rule trans :premises (@p149 @p85)) % 0.19/0.51 (step @p151 false :rule eq_resolve :premises (@p1 @p150)) % 0.19/0.51 ) % 0.19/0.51 % SZS output end Proof % 0.19/0.51 % cvc5 exiting %------------------------------------------------------------------------------