%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : LCL612^1 : 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 : n019.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 11:23:09 AM UTC 2026 % Result : Theorem 0.20s 0.53s % Output : Proof 0.20s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL612^1 : TPTP v9.3.1. Released v3.6.0. % 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.10/0.37 % Computer : n019.cluster.edu % 0.10/0.37 % Model : x86_64 x86_64 % 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.37 % Memory : 8046.5625MB % 0.10/0.37 % OS : Linux 6.8.0-71-generic % 0.10/0.37 % CPULimit : 300 % 0.10/0.37 % WCLimit : 300 % 0.10/0.37 % DateTime : Sun Sep 6 02:03:38 UTC 2026 % 0.10/0.38 % CPUTime : % 0.10/0.45 %----Proving TH0 % 0.20/0.53 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.20/0.53 % SZS status Theorem % 0.20/0.53 % SZS output start Proof % 0.20/0.53 ( % 0.20/0.53 (declare-sort $$unsorted 0) % 0.20/0.53 (declare-sort tptp.individuals 0) % 0.20/0.53 (define tptp.mfalse () (lambda (@list (@var "X" $$unsorted)) false)) % 0.20/0.53 (define tptp.mtrue () (lambda (@list (@var "X" $$unsorted)) true)) % 0.20/0.53 (define tptp.mnot () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.20/0.53 (define tptp.mor () (let ((_let_1 (@var "U" $$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))))))) % 0.20/0.53 (define tptp.mand () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.20/0.53 (define tptp.mimpl () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.20/0.53 (define tptp.miff () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "U" (-> $$unsorted Bool)))) (let ((_let_3 (@var "V" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimpl _let_2) _let_3)) (_ (_ tptp.mimpl _let_3) _let_2)) _let_1)))))) % 0.20/0.53 (define tptp.mbox () (let ((_let_1 (@var "Y" $$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))))))))) % 0.20/0.53 (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 $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (exists (@list _let_1) (and (_ (_ _let_4 _let_3) _let_1) (_ _let_2 _let_1))))))))) % 0.20/0.53 (define tptp.mall () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.individuals))) (let ((_let_3 (@var "P" (-> tptp.individuals $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.20/0.53 (define tptp.mexists () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.individuals))) (let ((_let_3 (@var "P" (-> tptp.individuals $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (exists (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.20/0.53 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.20/0.53 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 0.20/0.53 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.20/0.53 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.20/0.53 (define @t1 () (@var "Y" (-> $$unsorted Bool))) % 0.20/0.53 (define @t2 () (@var "X" (-> $$unsorted Bool))) % 0.20/0.53 (define @t3 () (and (_ tptp.mvalid @t2) (_ tptp.mvalid (_ (_ tptp.mimpl @t2) @t1)))) % 0.20/0.53 (define @t4 () (=> @t3 (_ tptp.mvalid @t1))) % 0.20/0.53 (define @t5 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.20/0.53 (define @t6 () (@list @t5 @t2 @t1)) % 0.20/0.53 (define @t7 () (forall @t6 @t4)) % 0.20/0.53 (define @t8 () (not @t7)) % 0.20/0.53 (define @t9 () (@var "X" $$unsorted)) % 0.20/0.53 (define @t10 () (@list @t9)) % 0.20/0.53 (define @t11 () (lambda @t10 false)) % 0.20/0.53 (define @t12 () (lambda @t10 true)) % 0.20/0.53 (define @t13 () (@var "U" $$unsorted)) % 0.20/0.53 (define @t14 () (_ @t2 @t13)) % 0.20/0.53 (define @t15 () (lambda (@list @t2 @t13) (not @t14))) % 0.20/0.53 (define @t16 () (_ @t1 @t13)) % 0.20/0.53 (define @t17 () (@list @t2 @t1 @t13)) % 0.20/0.53 (define @t18 () (lambda @t17 (or @t14 @t16))) % 0.20/0.53 (define @t19 () (lambda @t17 (and @t14 @t16))) % 0.20/0.53 (define @t20 () (@var "__flatten_var_0" $$unsorted)) % 0.20/0.53 (define @t21 () (@var "V" (-> $$unsorted Bool))) % 0.20/0.53 (define @t22 () (@var "U" (-> $$unsorted Bool))) % 0.20/0.53 (define @t23 () (@list @t22 @t21 @t20)) % 0.20/0.53 (define @t24 () (lambda @t23 (_ (_ (_ tptp.mor (_ tptp.mnot @t22)) @t21) @t20))) % 0.20/0.53 (define @t25 () (lambda @t23 (_ (_ (_ tptp.mand (_ (_ tptp.mimpl @t22) @t21)) (_ (_ tptp.mimpl @t21) @t22)) @t20))) % 0.20/0.53 (define @t26 () (@var "Y" $$unsorted)) % 0.20/0.53 (define @t27 () (@var "P" (-> $$unsorted Bool))) % 0.20/0.53 (define @t28 () (_ @t27 @t26)) % 0.20/0.53 (define @t29 () (_ (_ @t5 @t9) @t26)) % 0.20/0.53 (define @t30 () (@list @t26)) % 0.20/0.53 (define @t31 () (@list @t5 @t27 @t9)) % 0.20/0.53 (define @t32 () (lambda @t31 (forall @t30 (=> @t29 @t28)))) % 0.20/0.53 (define @t33 () (lambda @t31 (exists @t30 (and @t29 @t28)))) % 0.20/0.53 (define @t34 () (@var "W" $$unsorted)) % 0.20/0.53 (define @t35 () (@var "X" tptp.individuals)) % 0.20/0.53 (define @t36 () (@var "P" (-> tptp.individuals $$unsorted Bool))) % 0.20/0.53 (define @t37 () (_ (_ @t36 @t35) @t34)) % 0.20/0.53 (define @t38 () (@list @t35)) % 0.20/0.53 (define @t39 () (@list @t36 @t34)) % 0.20/0.53 (define @t40 () (lambda @t39 (forall @t38 @t37))) % 0.20/0.53 (define @t41 () (lambda @t39 (exists @t38 @t37))) % 0.20/0.53 (define @t42 () (_ @t27 @t34)) % 0.20/0.53 (define @t43 () (@list @t34)) % 0.20/0.53 (define @t44 () (forall @t43 @t42)) % 0.20/0.53 (define @t45 () (@list @t27)) % 0.20/0.53 (define @t46 () (lambda @t45 @t44)) % 0.20/0.53 (define @t47 () (lambda @t45 (exists @t43 @t42))) % 0.20/0.53 (define @t48 () (not @t42)) % 0.20/0.53 (define @t49 () (lambda @t45 (exists @t43 @t48))) % 0.20/0.53 (define @t50 () (lambda @t45 (forall @t43 @t48))) % 0.20/0.53 (define @t51 () (@var "BOUND_VARIABLE_7806" $$unsorted)) % 0.20/0.53 (define @t52 () (_ @t1 @t51)) % 0.20/0.53 (define @t53 () (_ @t1 @t34)) % 0.20/0.53 (define @t54 () (_ @t2 @t34)) % 0.20/0.53 (define @t55 () (forall @t43 (or (not @t54) @t53))) % 0.20/0.53 (define @t56 () (not @t55)) % 0.20/0.53 (define @t57 () (forall @t43 @t54)) % 0.20/0.53 (define @t58 () (not @t57)) % 0.20/0.53 (define @t59 () (or @t58 @t56 @t52)) % 0.20/0.53 (define @t60 () (forall (@list @t2 @t1 @t51) @t59)) % 0.20/0.53 (define @t61 () (@list @t51)) % 0.20/0.53 (define @t62 () (forall @t61 @t59)) % 0.20/0.53 (define @t63 () (@list @t2 @t1)) % 0.20/0.53 (define @t64 () (forall @t61 @t52)) % 0.20/0.53 (define @t65 () (or @t58 @t56 @t64)) % 0.20/0.53 (define @t66 () (forall @t43 @t53)) % 0.20/0.53 (define @t67 () (or @t58 @t56 @t66)) % 0.20/0.53 (define @t68 () (forall @t63 @t67)) % 0.20/0.53 (define @t69 () (and @t57 @t55)) % 0.20/0.53 (define @t70 () (_ @t27 @t34)) % 0.20/0.53 (define @t71 () (lambda @t45 (forall @t43 @t70))) % 0.20/0.53 (define @t72 () (_ @t71 @t1)) % 0.20/0.53 (define @t73 () (_ @t1 @t34)) % 0.20/0.53 (define @t74 () (_ @t2 @t34)) % 0.20/0.53 (define @t75 () (not @t74)) % 0.20/0.53 (define @t76 () (or @t75 @t73)) % 0.20/0.53 (define @t77 () (not (_ @t2 @t20))) % 0.20/0.53 (define @t78 () (lambda (@list @t20) (or @t77 (_ @t1 @t20)))) % 0.20/0.53 (define @t79 () (_ @t78 @t34)) % 0.20/0.53 (define @t80 () (forall @t43 @t79)) % 0.20/0.53 (define @t81 () (_ @t21 @t20)) % 0.20/0.53 (define @t82 () (lambda (@list @t21 @t20) (or @t77 @t81))) % 0.20/0.53 (define @t83 () (or (not (_ @t22 @t20)) @t81)) % 0.20/0.53 (define @t84 () (_ (lambda @t23 @t83) @t2)) % 0.20/0.53 (define @t85 () (_ @t71 @t2)) % 0.20/0.53 (define @t86 () (and @t85 (_ @t71 (_ @t84 @t1)))) % 0.20/0.53 (define @t87 () (=> @t86 @t72)) % 0.20/0.53 (define @t88 () (forall @t6 @t87)) % 0.20/0.53 (define @t89 () (not (_ @t22 @t13))) % 0.20/0.53 (define @t90 () (@list @t13)) % 0.20/0.53 (define @t91 () (lambda @t90 (or @t89 (_ @t21 @t13)))) % 0.20/0.53 (define @t92 () (@list @t1 @t13)) % 0.20/0.53 (define @t93 () (lambda @t90 @t89)) % 0.20/0.53 (define @t94 () (_ @t93 @t13)) % 0.20/0.53 (define @t95 () (or @t94 @t16)) % 0.20/0.53 (define @t96 () (lambda @t92 @t95)) % 0.20/0.53 (define @t97 () (@quantifiers_skolemize @t60 0)) % 0.20/0.53 (define @t98 () (_ @t97 @t34)) % 0.20/0.53 (define @t99 () (forall @t43 @t98)) % 0.20/0.53 (define @t100 () (@quantifiers_skolemize @t60 2)) % 0.20/0.53 (define @t101 () (@quantifiers_skolemize @t60 1)) % 0.20/0.53 (define @t102 () (_ @t101 @t100)) % 0.20/0.53 (define @t103 () (forall @t43 (or (not @t98) (_ @t101 @t34)))) % 0.20/0.53 (define @t104 () (not @t103)) % 0.20/0.53 (define @t105 () (not @t99)) % 0.20/0.53 (define @t106 () (or @t105 @t104 @t102)) % 0.20/0.53 (define @t107 () (@list true)) % 0.20/0.53 (define @t108 () (@list @t106)) % 0.20/0.53 (define @t109 () (@list @t100)) % 0.20/0.53 (define @t110 () (_ @t97 @t100)) % 0.20/0.53 (define @t111 () (not @t110)) % 0.20/0.53 (define @t112 () (or @t111 @t102)) % 0.20/0.53 (define @t113 () (@list true false)) % 0.20/0.53 (assume @p1 @t8) % 0.20/0.53 (assume @p2 true) % 0.20/0.53 (step @p3 (= tptp.mfalse @t11) :rule refl :args (@t11)) % 0.20/0.53 (step @p4 (= tptp.mtrue @t12) :rule refl :args (@t12)) % 0.20/0.53 (step @p5 (= tptp.mnot @t15) :rule refl :args (@t15)) % 0.20/0.53 (step @p6 (= tptp.mor @t18) :rule refl :args (@t18)) % 0.20/0.53 (step @p7 (= tptp.mand @t19) :rule refl :args (@t19)) % 0.20/0.53 (step @p8 (= tptp.mimpl @t24) :rule refl :args (@t24)) % 0.20/0.53 (step @p9 (= tptp.miff @t25) :rule refl :args (@t25)) % 0.20/0.53 (step @p10 (= tptp.mbox @t32) :rule refl :args (@t32)) % 0.20/0.53 (step @p11 (= tptp.mdia @t33) :rule refl :args (@t33)) % 0.20/0.53 (step @p12 (= tptp.mall @t40) :rule refl :args (@t40)) % 0.20/0.53 (step @p13 (= tptp.mexists @t41) :rule refl :args (@t41)) % 0.20/0.53 (step @p14 (= tptp.mvalid @t46) :rule refl :args (@t46)) % 0.20/0.53 (step @p15 (= tptp.msatisfiable @t47) :rule refl :args (@t47)) % 0.20/0.53 (step @p16 (= tptp.mcountersatisfiable @t49) :rule refl :args (@t49)) % 0.20/0.53 (step @p17 (= tptp.minvalid @t50) :rule refl :args (@t50)) % 0.20/0.53 (step @p18 :rule quant-merge-prenex :args ((= (forall @t63 @t62) @t60))) % 0.20/0.53 (step @p19 :rule alpha_equiv :args (@t64 (@list @t51) (@list @t34))) % 0.20/0.53 (step @p20 :rule refl :args (@t56)) % 0.20/0.53 (step @p21 :rule refl :args (@t58)) % 0.20/0.53 (step @p22 :rule nary_cong :premises (@p21 @p20 @p19) :args (@t65)) % 0.20/0.53 (step @p23 :rule quant-miniscope-or :args ((= @t62 @t65))) % 0.20/0.53 (step @p24 :rule trans :premises (@p23 @p22)) % 0.20/0.53 (step @p25 :rule symm :premises (@p24)) % 0.20/0.53 (step @p26 :rule cong :premises (@p25) :args (@t68)) % 0.20/0.53 (step @p27 :rule trans :premises (@p26 @p18)) % 0.20/0.53 (step @p28 :rule quant-unused-vars :args ((= (forall @t6 @t67) @t68))) % 0.20/0.53 (step @p29 :rule trans :premises (@p28 @p27)) % 0.20/0.53 (step @p30 :rule aci_norm :args ((= (or (or @t58 @t56) @t66) @t67))) % 0.20/0.53 (step @p31 :rule refl :args (@t66)) % 0.20/0.53 (step @p32 :rule bool-and-de-morgan :args (@t57 @t55 true)) % 0.20/0.53 (step @p33 :rule nary_cong :premises (@p32 @p31) :args ((or (not @t69) @t66))) % 0.20/0.53 (step @p34 :rule trans :premises (@p33 @p30)) % 0.20/0.53 (step @p35 :rule bool-impl-elim :args (@t69 @t66)) % 0.20/0.53 (step @p36 :rule trans :premises (@p35 @p34)) % 0.20/0.53 (step @p37 :rule cong :premises (@p36) :args ((forall @t6 (=> @t69 @t66)))) % 0.20/0.53 (step @p38 :rule trans :premises (@p37 @p29)) % 0.20/0.53 (step @p39 :rule beta-reduce :args ((= @t72 @t66))) % 0.20/0.53 (step @p40 :rule refl :args (@t53)) % 0.20/0.53 (step @p41 :rule refl :args (@t73)) % 0.20/0.53 (step @p42 :rule cong :premises (@p41 @p40) :args ((= @t73 @t53))) % 0.20/0.53 (step @p43 :rule symm :premises (@p42)) % 0.20/0.53 (step @p44 :rule eq_resolve :premises (@p41 @p43)) % 0.20/0.53 (step @p45 :rule refl :args (@t54)) % 0.20/0.53 (step @p46 :rule refl :args (@t74)) % 0.20/0.53 (step @p47 :rule cong :premises (@p46 @p45) :args ((= @t74 @t54))) % 0.20/0.53 (step @p48 :rule symm :premises (@p47)) % 0.20/0.53 (step @p49 :rule eq_resolve :premises (@p46 @p48)) % 0.20/0.53 (step @p50 :rule cong :premises (@p49) :args (@t75)) % 0.20/0.53 (step @p51 :rule nary_cong :premises (@p50 @p44) :args (@t76)) % 0.20/0.53 (step @p52 :rule cong :premises (@p51) :args ((forall @t43 @t76))) % 0.20/0.53 (step @p53 :rule beta-reduce :args ((= @t79 @t76))) % 0.20/0.53 (step @p54 :rule cong :premises (@p53) :args (@t80)) % 0.20/0.53 (step @p55 :rule trans :premises (@p54 @p52)) % 0.20/0.53 (step @p56 :rule beta-reduce :args ((= (_ @t71 @t78) @t80))) % 0.20/0.53 (step @p57 :rule trans :premises (@p56 @p55)) % 0.20/0.53 (step @p58 :rule beta-reduce :args ((= (_ @t82 @t1) @t78))) % 0.20/0.53 (step @p59 :rule refl :args (@t1)) % 0.20/0.53 (step @p60 :rule beta-reduce :args ((= @t84 @t82))) % 0.20/0.53 (step @p61 :rule ho_cong :premises (@p60 @p59)) % 0.20/0.53 (step @p62 :rule trans :premises (@p61 @p58)) % 0.20/0.53 (step @p63 :rule refl :args (@t71)) % 0.20/0.53 (step @p64 :rule ho_cong :premises (@p63 @p62)) % 0.20/0.53 (step @p65 :rule trans :premises (@p64 @p57)) % 0.20/0.53 (step @p66 :rule beta-reduce :args ((= @t85 @t57))) % 0.20/0.53 (step @p67 :rule nary_cong :premises (@p66 @p65) :args (@t86)) % 0.20/0.53 (step @p68 :rule cong :premises (@p67 @p39) :args (@t87)) % 0.20/0.53 (step @p69 :rule cong :premises (@p68) :args (@t88)) % 0.20/0.53 (step @p70 :rule trans :premises (@p69 @p38)) % 0.20/0.53 (step @p71 :rule cong :premises (@p70) :args ((not @t88))) % 0.20/0.53 (step @p72 :rule refl :args (@t70)) % 0.20/0.53 (step @p73 :rule refl :args (@t42)) % 0.20/0.53 (step @p74 :rule cong :premises (@p73 @p72) :args ((= @t42 @t70))) % 0.20/0.53 (step @p75 :rule symm :premises (@p74)) % 0.20/0.53 (step @p76 :rule eq_resolve :premises (@p73 @p75)) % 0.20/0.53 (step @p77 :rule cong :premises (@p76) :args (@t44)) % 0.20/0.53 (step @p78 :rule cong :premises (@p77) :args (@t46)) % 0.20/0.53 (step @p79 :rule trans :premises (@p14 @p78)) % 0.20/0.53 (step @p80 :rule ho_cong :premises (@p79 @p59)) % 0.20/0.53 (step @p81 :rule refl :args (@t2)) % 0.20/0.53 (step @p82 :rule beta-reduce :args ((= (_ @t91 @t20) @t83))) % 0.20/0.53 (step @p83 :rule refl :args (@t20)) % 0.20/0.53 (step @p84 :rule beta-reduce :args ((= (_ (lambda @t92 (or @t89 @t16)) @t21) @t91))) % 0.20/0.53 (step @p85 :rule refl :args (@t21)) % 0.20/0.53 (step @p86 :rule refl :args (@t16)) % 0.20/0.53 (step @p87 :rule beta-reduce :args ((= @t94 @t89))) % 0.20/0.53 (step @p88 :rule nary_cong :premises (@p87 @p86) :args (@t95)) % 0.20/0.53 (step @p89 :rule cong :premises (@p88) :args (@t96)) % 0.20/0.53 (step @p90 :rule beta-reduce :args ((= (_ @t18 @t93) @t96))) % 0.20/0.53 (step @p91 :rule trans :premises (@p90 @p89)) % 0.20/0.53 (step @p92 :rule beta-reduce :args ((= (_ @t15 @t22) @t93))) % 0.20/0.53 (step @p93 :rule refl :args (@t18)) % 0.20/0.53 (step @p94 :rule ho_cong :premises (@p93 @p92)) % 0.20/0.53 (step @p95 :rule trans :premises (@p94 @p91)) % 0.20/0.53 (step @p96 :rule ho_cong :premises (@p95 @p85)) % 0.20/0.53 (step @p97 :rule trans :premises (@p96 @p84)) % 0.20/0.53 (step @p98 :rule ho_cong :premises (@p97 @p83)) % 0.20/0.53 (step @p99 :rule trans :premises (@p98 @p82)) % 0.20/0.53 (step @p100 :rule refl :args (@t22)) % 0.20/0.53 (step @p101 :rule ho_cong :premises (@p5 @p100)) % 0.20/0.53 (step @p102 :rule ho_cong :premises (@p6 @p101)) % 0.20/0.53 (step @p103 :rule ho_cong :premises (@p102 @p85)) % 0.20/0.53 (step @p104 :rule ho_cong :premises (@p103 @p83)) % 0.20/0.53 (step @p105 :rule trans :premises (@p104 @p99)) % 0.20/0.53 (step @p106 :rule cong :premises (@p105) :args (@t24)) % 0.20/0.53 (step @p107 :rule trans :premises (@p8 @p106)) % 0.20/0.53 (step @p108 :rule ho_cong :premises (@p107 @p81)) % 0.20/0.53 (step @p109 :rule ho_cong :premises (@p108 @p59)) % 0.20/0.53 (step @p110 :rule ho_cong :premises (@p79 @p109)) % 0.20/0.53 (step @p111 :rule ho_cong :premises (@p79 @p81)) % 0.20/0.53 (step @p112 :rule nary_cong :premises (@p111 @p110) :args (@t3)) % 0.20/0.53 (step @p113 :rule cong :premises (@p112 @p80) :args (@t4)) % 0.20/0.53 (step @p114 :rule cong :premises (@p113) :args (@t7)) % 0.20/0.53 (step @p115 :rule cong :premises (@p114) :args (@t8)) % 0.20/0.53 (step @p116 :rule trans :premises (@p115 @p71)) % 0.20/0.53 (step @p117 :rule eq_resolve :premises (@p1 @p116)) % 0.20/0.53 (step @p118 :rule skolemize :premises (@p117)) % 0.20/0.53 (step @p119 :rule bool-double-not-elim :args (@t99)) % 0.20/0.53 (step @p120 :rule refl :args (@t106)) % 0.20/0.53 (step @p121 :rule nary_cong :premises (@p120 @p119) :args ((or @t106 (not @t105)))) % 0.20/0.53 (step @p122 :rule cnf_or_neg :args (@t106 0)) % 0.20/0.53 (step @p123 :rule eq_resolve :premises (@p122 @p121)) % 0.20/0.53 (step @p124 :rule reordering :premises (@p123) :args ((or @t99 @t106))) % 0.20/0.53 (step @p125 :rule chain_m_resolution :premises (@p124 @p118) :args (@t99 @t107 @t108)) % 0.20/0.53 (step @p126 :rule bool-double-not-elim :args (@t103)) % 0.20/0.53 (step @p127 :rule nary_cong :premises (@p120 @p126) :args ((or @t106 (not @t104)))) % 0.20/0.53 (step @p128 :rule cnf_or_neg :args (@t106 1)) % 0.20/0.53 (step @p129 :rule eq_resolve :premises (@p128 @p127)) % 0.20/0.53 (step @p130 :rule reordering :premises (@p129) :args ((or @t103 @t106))) % 0.20/0.53 (step @p131 :rule chain_m_resolution :premises (@p130 @p118) :args (@t103 @t107 @t108)) % 0.20/0.53 (step @p132 :rule instantiate :premises (@p131) :args (@t109)) % 0.20/0.53 (step @p133 :rule cnf_or_neg :args (@t106 2)) % 0.20/0.53 (step @p134 :rule chain_m_resolution :premises (@p133 @p118) :args ((not @t102) @t107 @t108)) % 0.20/0.53 (step @p135 :rule cnf_or_pos :args (@t112)) % 0.20/0.53 (step @p136 :rule reordering :premises (@p135) :args ((or @t102 @t111 (not @t112)))) % 0.20/0.53 (step @p137 :rule chain_m_resolution :premises (@p136 @p134 @p132) :args (@t111 @t113 (@list @t102 @t112))) % 0.20/0.53 (assume-push @p144 @t99) % 0.20/0.53 (step @p139 :rule instantiate :premises (@p125) :args (@t109)) % 0.20/0.53 (step-pop @p145 :rule scope :premises (@p139)) % 0.20/0.53 (step @p140 :rule process_scope :premises (@p145) :args (@t110)) % 0.20/0.53 (step @p142 :rule implies_elim :premises (@p140)) % 0.20/0.53 (step @p143 false :rule chain_m_resolution :premises (@p142 @p137 @p125) :args (false @t113 (@list @t110 @t99))) % 0.20/0.53 ) % 0.20/0.53 % SZS output end Proof % 0.20/0.53 % cvc5 exiting %------------------------------------------------------------------------------