%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : LCL620^1 : 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 : n003.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 0.18s 0.50s % Output : Proof 0.18s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL620^1 : 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 % 0.09/0.35 % Computer : n003.cluster.edu % 0.09/0.35 % Model : x86_64 x86_64 % 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.35 % Memory : 8046.5625MB % 0.09/0.35 % OS : Linux 6.8.0-71-generic % 0.09/0.35 % CPULimit : 300 % 0.09/0.35 % WCLimit : 300 % 0.09/0.35 % DateTime : Sun Sep 6 00:14:51 UTC 2026 % 0.09/0.36 % CPUTime : % 0.14/0.42 %----Proving TH0 % 0.18/0.50 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.18/0.50 % SZS status Theorem % 0.18/0.50 % SZS output start Proof % 0.18/0.50 ( % 0.18/0.50 (declare-sort $$unsorted 0) % 0.18/0.50 (declare-sort tptp.individuals 0) % 0.18/0.50 (define tptp.mfalse () (lambda (@list (@var "X" $$unsorted)) false)) % 0.18/0.50 (define tptp.mtrue () (lambda (@list (@var "X" $$unsorted)) true)) % 0.18/0.50 (define tptp.mnot () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.18/0.50 (define tptp.mor () (let ((_let_1 (@var "U" $$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))))))) % 0.18/0.50 (define tptp.mand () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.18/0.50 (define tptp.mimpl () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.18/0.50 (define tptp.miff () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "U" (-> $$unsorted Bool)))) (let ((_let_3 (@var "V" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimpl _let_2) _let_3)) (_ (_ tptp.mimpl _let_3) _let_2)) _let_1)))))) % 0.18/0.50 (define tptp.mbox () (let ((_let_1 (@var "Y" $$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))))))))) % 0.18/0.50 (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 $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (exists (@list _let_1) (and (_ (_ _let_4 _let_3) _let_1) (_ _let_2 _let_1))))))))) % 0.18/0.50 (define tptp.mall () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.individuals))) (let ((_let_3 (@var "P" (-> tptp.individuals $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.18/0.50 (define tptp.mexists () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.individuals))) (let ((_let_3 (@var "P" (-> tptp.individuals $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (exists (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.18/0.50 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.18/0.50 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 0.18/0.50 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.18/0.50 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.18/0.50 (define @t1 () (@var "Y" (-> $$unsorted Bool))) % 0.18/0.50 (define @t2 () (@var "X" (-> $$unsorted Bool))) % 0.18/0.50 (define @t3 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.18/0.50 (define @t4 () (@list @t3 @t2 @t1)) % 0.18/0.50 (define @t5 () (forall @t4 (_ tptp.mvalid (_ (_ tptp.mimpl (_ tptp.mnot (_ (_ tptp.mand @t2) @t1))) (_ (_ tptp.mor (_ tptp.mnot @t2)) (_ tptp.mnot @t1)))))) % 0.18/0.50 (define @t6 () (not @t5)) % 0.18/0.50 (define @t7 () (@var "X" $$unsorted)) % 0.18/0.50 (define @t8 () (@list @t7)) % 0.18/0.50 (define @t9 () (lambda @t8 false)) % 0.18/0.50 (define @t10 () (lambda @t8 true)) % 0.18/0.50 (define @t11 () (@var "U" $$unsorted)) % 0.18/0.50 (define @t12 () (_ @t2 @t11)) % 0.18/0.50 (define @t13 () (not @t12)) % 0.18/0.50 (define @t14 () (lambda (@list @t2 @t11) @t13)) % 0.18/0.50 (define @t15 () (_ @t1 @t11)) % 0.18/0.50 (define @t16 () (@list @t2 @t1 @t11)) % 0.18/0.50 (define @t17 () (lambda @t16 (or @t12 @t15))) % 0.18/0.50 (define @t18 () (and @t12 @t15)) % 0.18/0.50 (define @t19 () (lambda @t16 @t18)) % 0.18/0.50 (define @t20 () (@var "__flatten_var_0" $$unsorted)) % 0.18/0.50 (define @t21 () (@var "V" (-> $$unsorted Bool))) % 0.18/0.50 (define @t22 () (@var "U" (-> $$unsorted Bool))) % 0.18/0.50 (define @t23 () (@list @t22 @t21 @t20)) % 0.18/0.50 (define @t24 () (lambda @t23 (_ (_ (_ tptp.mor (_ tptp.mnot @t22)) @t21) @t20))) % 0.18/0.50 (define @t25 () (lambda @t23 (_ (_ (_ tptp.mand (_ (_ tptp.mimpl @t22) @t21)) (_ (_ tptp.mimpl @t21) @t22)) @t20))) % 0.18/0.50 (define @t26 () (@var "Y" $$unsorted)) % 0.18/0.50 (define @t27 () (@var "P" (-> $$unsorted Bool))) % 0.18/0.50 (define @t28 () (_ @t27 @t26)) % 0.18/0.50 (define @t29 () (_ (_ @t3 @t7) @t26)) % 0.18/0.50 (define @t30 () (@list @t26)) % 0.18/0.50 (define @t31 () (@list @t3 @t27 @t7)) % 0.18/0.50 (define @t32 () (lambda @t31 (forall @t30 (=> @t29 @t28)))) % 0.18/0.50 (define @t33 () (lambda @t31 (exists @t30 (and @t29 @t28)))) % 0.18/0.50 (define @t34 () (@var "W" $$unsorted)) % 0.18/0.50 (define @t35 () (@var "X" tptp.individuals)) % 0.18/0.50 (define @t36 () (@var "P" (-> tptp.individuals $$unsorted Bool))) % 0.18/0.50 (define @t37 () (_ (_ @t36 @t35) @t34)) % 0.18/0.50 (define @t38 () (@list @t35)) % 0.18/0.50 (define @t39 () (@list @t36 @t34)) % 0.18/0.50 (define @t40 () (lambda @t39 (forall @t38 @t37))) % 0.18/0.50 (define @t41 () (lambda @t39 (exists @t38 @t37))) % 0.18/0.50 (define @t42 () (_ @t27 @t34)) % 0.18/0.50 (define @t43 () (@list @t34)) % 0.18/0.50 (define @t44 () (forall @t43 @t42)) % 0.18/0.50 (define @t45 () (@list @t27)) % 0.18/0.50 (define @t46 () (lambda @t45 @t44)) % 0.18/0.50 (define @t47 () (lambda @t45 (exists @t43 @t42))) % 0.18/0.50 (define @t48 () (not @t42)) % 0.18/0.50 (define @t49 () (lambda @t45 (exists @t43 @t48))) % 0.18/0.50 (define @t50 () (lambda @t45 (forall @t43 @t48))) % 0.18/0.50 (define @t51 () (_ @t1 @t34)) % 0.18/0.50 (define @t52 () (_ @t2 @t34)) % 0.18/0.50 (define @t53 () (or (and @t52 @t51) (not @t52) (not @t51))) % 0.18/0.50 (define @t54 () (forall (@list @t2 @t1 @t34) @t53)) % 0.18/0.50 (define @t55 () (forall (@list @t3 @t2 @t1 @t34) @t53)) % 0.18/0.50 (define @t56 () (_ @t1 @t34)) % 0.18/0.50 (define @t57 () (not @t56)) % 0.18/0.50 (define @t58 () (_ @t2 @t34)) % 0.18/0.50 (define @t59 () (not @t58)) % 0.18/0.50 (define @t60 () (and @t58 @t56)) % 0.18/0.50 (define @t61 () (or @t60 @t59 @t57)) % 0.18/0.50 (define @t62 () (_ @t1 @t20)) % 0.18/0.50 (define @t63 () (not @t62)) % 0.18/0.50 (define @t64 () (_ @t2 @t20)) % 0.18/0.50 (define @t65 () (not @t64)) % 0.18/0.50 (define @t66 () (and @t64 @t62)) % 0.18/0.50 (define @t67 () (or @t66 @t65 @t63)) % 0.18/0.50 (define @t68 () (@list @t20)) % 0.18/0.50 (define @t69 () (lambda @t68 @t67)) % 0.18/0.50 (define @t70 () (_ @t69 @t34)) % 0.18/0.50 (define @t71 () (forall @t43 @t70)) % 0.18/0.50 (define @t72 () (_ @t27 @t34)) % 0.18/0.50 (define @t73 () (lambda @t45 (forall @t43 @t72))) % 0.18/0.50 (define @t74 () (or @t65 @t63)) % 0.18/0.50 (define @t75 () (not @t15)) % 0.18/0.50 (define @t76 () (@list @t11)) % 0.18/0.50 (define @t77 () (lambda @t76 (or @t13 @t75))) % 0.18/0.50 (define @t78 () (_ @t77 @t20)) % 0.18/0.50 (define @t79 () (or @t66 @t78)) % 0.18/0.50 (define @t80 () (lambda @t68 @t79)) % 0.18/0.50 (define @t81 () (_ @t21 @t20)) % 0.18/0.50 (define @t82 () (@list @t21 @t20)) % 0.18/0.50 (define @t83 () (lambda @t76 @t75)) % 0.18/0.50 (define @t84 () (_ @t83 @t11)) % 0.18/0.50 (define @t85 () (or @t13 @t84)) % 0.18/0.50 (define @t86 () (lambda @t76 @t85)) % 0.18/0.50 (define @t87 () (@list @t1 @t11)) % 0.18/0.50 (define @t88 () (_ @t14 @t1)) % 0.18/0.50 (define @t89 () (lambda @t76 @t13)) % 0.18/0.50 (define @t90 () (_ @t89 @t11)) % 0.18/0.50 (define @t91 () (or @t90 @t15)) % 0.18/0.50 (define @t92 () (lambda @t87 @t91)) % 0.18/0.50 (define @t93 () (_ @t14 @t2)) % 0.18/0.50 (define @t94 () (lambda @t76 (not @t18))) % 0.18/0.50 (define @t95 () (_ @t94 @t20)) % 0.18/0.50 (define @t96 () (not @t95)) % 0.18/0.50 (define @t97 () (or @t96 @t81)) % 0.18/0.50 (define @t98 () (lambda @t82 @t97)) % 0.18/0.50 (define @t99 () (or (not (_ @t22 @t20)) @t81)) % 0.18/0.50 (define @t100 () (lambda @t23 @t99)) % 0.18/0.50 (define @t101 () (lambda @t76 @t18)) % 0.18/0.50 (define @t102 () (_ @t101 @t11)) % 0.18/0.50 (define @t103 () (not @t102)) % 0.18/0.50 (define @t104 () (lambda @t76 @t103)) % 0.18/0.50 (define @t105 () (lambda @t87 @t18)) % 0.18/0.50 (define @t106 () (_ @t19 @t2)) % 0.18/0.50 (define @t107 () (forall @t4 (_ @t73 (_ (_ @t100 (_ @t14 (_ @t106 @t1))) (_ (_ @t17 @t93) @t88))))) % 0.18/0.50 (define @t108 () (not (_ @t22 @t11))) % 0.18/0.50 (define @t109 () (lambda @t76 (or @t108 (_ @t21 @t11)))) % 0.18/0.50 (define @t110 () (lambda @t76 @t108)) % 0.18/0.50 (define @t111 () (_ @t110 @t11)) % 0.18/0.50 (define @t112 () (or @t111 @t15)) % 0.18/0.50 (define @t113 () (lambda @t87 @t112)) % 0.18/0.50 (define @t114 () (@quantifiers_skolemize @t54 2)) % 0.18/0.50 (define @t115 () (_ (@quantifiers_skolemize @t54 1) @t114)) % 0.18/0.50 (define @t116 () (not @t115)) % 0.18/0.50 (define @t117 () (_ (@quantifiers_skolemize @t54 0) @t114)) % 0.18/0.50 (define @t118 () (not @t117)) % 0.18/0.50 (define @t119 () (and @t117 @t115)) % 0.18/0.50 (define @t120 () (or @t119 @t118 @t116)) % 0.18/0.50 (define @t121 () (@list true)) % 0.18/0.50 (define @t122 () (@list @t120)) % 0.18/0.50 (assume @p1 @t6) % 0.18/0.50 (assume @p2 true) % 0.18/0.50 (step @p3 (= tptp.mfalse @t9) :rule refl :args (@t9)) % 0.18/0.50 (step @p4 (= tptp.mtrue @t10) :rule refl :args (@t10)) % 0.18/0.50 (step @p5 (= tptp.mnot @t14) :rule refl :args (@t14)) % 0.18/0.50 (step @p6 (= tptp.mor @t17) :rule refl :args (@t17)) % 0.18/0.50 (step @p7 (= tptp.mand @t19) :rule refl :args (@t19)) % 0.18/0.50 (step @p8 (= tptp.mimpl @t24) :rule refl :args (@t24)) % 0.18/0.50 (step @p9 (= tptp.miff @t25) :rule refl :args (@t25)) % 0.18/0.50 (step @p10 (= tptp.mbox @t32) :rule refl :args (@t32)) % 0.18/0.50 (step @p11 (= tptp.mdia @t33) :rule refl :args (@t33)) % 0.18/0.50 (step @p12 (= tptp.mall @t40) :rule refl :args (@t40)) % 0.18/0.50 (step @p13 (= tptp.mexists @t41) :rule refl :args (@t41)) % 0.18/0.50 (step @p14 (= tptp.mvalid @t46) :rule refl :args (@t46)) % 0.18/0.50 (step @p15 (= tptp.msatisfiable @t47) :rule refl :args (@t47)) % 0.18/0.50 (step @p16 (= tptp.mcountersatisfiable @t49) :rule refl :args (@t49)) % 0.18/0.50 (step @p17 (= tptp.minvalid @t50) :rule refl :args (@t50)) % 0.18/0.50 (step @p18 :rule quant-unused-vars :args ((= @t55 @t54))) % 0.18/0.50 (step @p19 :rule quant-merge-prenex :args ((= (forall @t4 (forall @t43 @t53)) @t55))) % 0.18/0.50 (step @p20 :rule trans :premises (@p19 @p18)) % 0.18/0.50 (step @p21 :rule refl :args (@t51)) % 0.18/0.50 (step @p22 :rule refl :args (@t56)) % 0.18/0.50 (step @p23 :rule cong :premises (@p22 @p21) :args ((= @t56 @t51))) % 0.18/0.50 (step @p24 :rule symm :premises (@p23)) % 0.18/0.50 (step @p25 :rule eq_resolve :premises (@p22 @p24)) % 0.18/0.50 (step @p26 :rule cong :premises (@p25) :args (@t57)) % 0.18/0.50 (step @p27 :rule refl :args (@t52)) % 0.18/0.50 (step @p28 :rule refl :args (@t58)) % 0.18/0.50 (step @p29 :rule cong :premises (@p28 @p27) :args ((= @t58 @t52))) % 0.18/0.50 (step @p30 :rule symm :premises (@p29)) % 0.18/0.50 (step @p31 :rule eq_resolve :premises (@p28 @p30)) % 0.18/0.50 (step @p32 :rule cong :premises (@p31) :args (@t59)) % 0.18/0.50 (step @p33 :rule nary_cong :premises (@p31 @p25) :args (@t60)) % 0.18/0.50 (step @p34 :rule nary_cong :premises (@p33 @p32 @p26) :args (@t61)) % 0.18/0.50 (step @p35 :rule cong :premises (@p34) :args ((forall @t43 @t61))) % 0.18/0.50 (step @p36 :rule beta-reduce :args ((= @t70 @t61))) % 0.18/0.50 (step @p37 :rule cong :premises (@p36) :args (@t71)) % 0.18/0.50 (step @p38 :rule trans :premises (@p37 @p35)) % 0.18/0.50 (step @p39 :rule beta-reduce :args ((= (_ @t73 @t69) @t71))) % 0.18/0.50 (step @p40 :rule trans :premises (@p39 @p38)) % 0.18/0.50 (step @p41 :rule aci_norm :args ((= (or @t66 @t74) @t67))) % 0.18/0.50 (step @p42 :rule beta-reduce :args ((= @t78 @t74))) % 0.18/0.50 (step @p43 :rule refl :args (@t66)) % 0.18/0.50 (step @p44 :rule nary_cong :premises (@p43 @p42) :args (@t79)) % 0.18/0.50 (step @p45 :rule trans :premises (@p44 @p41)) % 0.18/0.50 (step @p46 :rule cong :premises (@p45) :args (@t80)) % 0.18/0.50 (step @p47 :rule beta-reduce :args ((= (_ (lambda @t82 (or @t66 @t81)) @t77) @t80))) % 0.18/0.50 (step @p48 :rule trans :premises (@p47 @p46)) % 0.18/0.50 (step @p49 :rule beta-reduce :args ((= @t84 @t75))) % 0.18/0.50 (step @p50 :rule refl :args (@t13)) % 0.18/0.50 (step @p51 :rule nary_cong :premises (@p50 @p49) :args (@t85)) % 0.18/0.50 (step @p52 :rule cong :premises (@p51) :args (@t86)) % 0.18/0.50 (step @p53 :rule beta-reduce :args ((= (_ (lambda @t87 (or @t13 @t15)) @t83) @t86))) % 0.18/0.50 (step @p54 :rule trans :premises (@p53 @p52)) % 0.18/0.50 (step @p55 :rule beta-reduce :args ((= @t88 @t83))) % 0.18/0.50 (step @p56 :rule refl :args (@t15)) % 0.18/0.50 (step @p57 :rule beta-reduce :args ((= @t90 @t13))) % 0.18/0.50 (step @p58 :rule nary_cong :premises (@p57 @p56) :args (@t91)) % 0.18/0.50 (step @p59 :rule cong :premises (@p58) :args (@t92)) % 0.18/0.50 (step @p60 :rule beta-reduce :args ((= (_ @t17 @t89) @t92))) % 0.18/0.50 (step @p61 :rule trans :premises (@p60 @p59)) % 0.18/0.50 (step @p62 :rule beta-reduce :args ((= @t93 @t89))) % 0.18/0.50 (step @p63 :rule refl :args (@t17)) % 0.18/0.50 (step @p64 :rule ho_cong :premises (@p63 @p62)) % 0.18/0.50 (step @p65 :rule trans :premises (@p64 @p61)) % 0.18/0.50 (step @p66 :rule ho_cong :premises (@p65 @p55)) % 0.18/0.50 (step @p67 :rule trans :premises (@p66 @p54)) % 0.18/0.50 (step @p68 :rule refl :args (@t81)) % 0.18/0.50 (step @p69 :rule bool-double-not-elim :args (@t66)) % 0.18/0.50 (step @p70 :rule beta-reduce :args ((= @t95 (not @t66)))) % 0.18/0.50 (step @p71 :rule cong :premises (@p70) :args (@t96)) % 0.18/0.50 (step @p72 :rule trans :premises (@p71 @p69)) % 0.18/0.50 (step @p73 :rule nary_cong :premises (@p72 @p68) :args (@t97)) % 0.18/0.50 (step @p74 :rule cong :premises (@p73) :args (@t98)) % 0.18/0.50 (step @p75 :rule beta-reduce :args ((= (_ @t100 @t94) @t98))) % 0.18/0.50 (step @p76 :rule trans :premises (@p75 @p74)) % 0.18/0.50 (step @p77 :rule beta-reduce :args ((= @t102 @t18))) % 0.18/0.50 (step @p78 :rule cong :premises (@p77) :args (@t103)) % 0.18/0.50 (step @p79 :rule cong :premises (@p78) :args (@t104)) % 0.18/0.50 (step @p80 :rule beta-reduce :args ((= (_ @t14 @t101) @t104))) % 0.18/0.50 (step @p81 :rule trans :premises (@p80 @p79)) % 0.18/0.50 (step @p82 :rule beta-reduce :args ((= (_ @t105 @t1) @t101))) % 0.18/0.50 (step @p83 :rule refl :args (@t1)) % 0.18/0.50 (step @p84 :rule beta-reduce :args ((= @t106 @t105))) % 0.18/0.50 (step @p85 :rule ho_cong :premises (@p84 @p83)) % 0.18/0.50 (step @p86 :rule trans :premises (@p85 @p82)) % 0.18/0.50 (step @p87 :rule refl :args (@t14)) % 0.18/0.50 (step @p88 :rule ho_cong :premises (@p87 @p86)) % 0.18/0.50 (step @p89 :rule trans :premises (@p88 @p81)) % 0.18/0.50 (step @p90 :rule refl :args (@t100)) % 0.18/0.50 (step @p91 :rule ho_cong :premises (@p90 @p89)) % 0.18/0.50 (step @p92 :rule trans :premises (@p91 @p76)) % 0.18/0.50 (step @p93 :rule ho_cong :premises (@p92 @p67)) % 0.18/0.50 (step @p94 :rule trans :premises (@p93 @p48)) % 0.18/0.50 (step @p95 :rule refl :args (@t73)) % 0.18/0.50 (step @p96 :rule ho_cong :premises (@p95 @p94)) % 0.18/0.50 (step @p97 :rule trans :premises (@p96 @p40)) % 0.18/0.50 (step @p98 :rule cong :premises (@p97) :args (@t107)) % 0.18/0.50 (step @p99 :rule trans :premises (@p98 @p20)) % 0.18/0.50 (step @p100 :rule cong :premises (@p99) :args ((not @t107))) % 0.18/0.50 (step @p101 :rule ho_cong :premises (@p5 @p83)) % 0.18/0.50 (step @p102 :rule refl :args (@t2)) % 0.18/0.50 (step @p103 :rule ho_cong :premises (@p5 @p102)) % 0.18/0.50 (step @p104 :rule ho_cong :premises (@p6 @p103)) % 0.18/0.50 (step @p105 :rule ho_cong :premises (@p104 @p101)) % 0.18/0.50 (step @p106 :rule ho_cong :premises (@p7 @p102)) % 0.18/0.50 (step @p107 :rule ho_cong :premises (@p106 @p83)) % 0.18/0.50 (step @p108 :rule ho_cong :premises (@p5 @p107)) % 0.18/0.50 (step @p109 :rule beta-reduce :args ((= (_ @t109 @t20) @t99))) % 0.18/0.50 (step @p110 :rule refl :args (@t20)) % 0.18/0.50 (step @p111 :rule beta-reduce :args ((= (_ (lambda @t87 (or @t108 @t15)) @t21) @t109))) % 0.18/0.50 (step @p112 :rule refl :args (@t21)) % 0.18/0.50 (step @p113 :rule beta-reduce :args ((= @t111 @t108))) % 0.18/0.50 (step @p114 :rule nary_cong :premises (@p113 @p56) :args (@t112)) % 0.18/0.50 (step @p115 :rule cong :premises (@p114) :args (@t113)) % 0.18/0.50 (step @p116 :rule beta-reduce :args ((= (_ @t17 @t110) @t113))) % 0.18/0.50 (step @p117 :rule trans :premises (@p116 @p115)) % 0.18/0.50 (step @p118 :rule beta-reduce :args ((= (_ @t14 @t22) @t110))) % 0.18/0.50 (step @p119 :rule ho_cong :premises (@p63 @p118)) % 0.18/0.50 (step @p120 :rule trans :premises (@p119 @p117)) % 0.18/0.50 (step @p121 :rule ho_cong :premises (@p120 @p112)) % 0.18/0.50 (step @p122 :rule trans :premises (@p121 @p111)) % 0.18/0.50 (step @p123 :rule ho_cong :premises (@p122 @p110)) % 0.18/0.50 (step @p124 :rule trans :premises (@p123 @p109)) % 0.18/0.50 (step @p125 :rule refl :args (@t22)) % 0.18/0.50 (step @p126 :rule ho_cong :premises (@p5 @p125)) % 0.18/0.50 (step @p127 :rule ho_cong :premises (@p6 @p126)) % 0.18/0.50 (step @p128 :rule ho_cong :premises (@p127 @p112)) % 0.18/0.50 (step @p129 :rule ho_cong :premises (@p128 @p110)) % 0.18/0.50 (step @p130 :rule trans :premises (@p129 @p124)) % 0.18/0.50 (step @p131 :rule cong :premises (@p130) :args (@t24)) % 0.18/0.50 (step @p132 :rule trans :premises (@p8 @p131)) % 0.18/0.50 (step @p133 :rule ho_cong :premises (@p132 @p108)) % 0.18/0.50 (step @p134 :rule ho_cong :premises (@p133 @p105)) % 0.18/0.50 (step @p135 :rule refl :args (@t72)) % 0.18/0.50 (step @p136 :rule refl :args (@t42)) % 0.18/0.50 (step @p137 :rule cong :premises (@p136 @p135) :args ((= @t42 @t72))) % 0.18/0.50 (step @p138 :rule symm :premises (@p137)) % 0.18/0.50 (step @p139 :rule eq_resolve :premises (@p136 @p138)) % 0.18/0.50 (step @p140 :rule cong :premises (@p139) :args (@t44)) % 0.18/0.50 (step @p141 :rule cong :premises (@p140) :args (@t46)) % 0.18/0.50 (step @p142 :rule trans :premises (@p14 @p141)) % 0.18/0.50 (step @p143 :rule ho_cong :premises (@p142 @p134)) % 0.18/0.50 (step @p144 :rule cong :premises (@p143) :args (@t5)) % 0.18/0.50 (step @p145 :rule cong :premises (@p144) :args (@t6)) % 0.18/0.50 (step @p146 :rule trans :premises (@p145 @p100)) % 0.18/0.50 (step @p147 :rule eq_resolve :premises (@p1 @p146)) % 0.18/0.50 (step @p148 :rule skolemize :premises (@p147)) % 0.18/0.50 (step @p149 :rule cnf_or_neg :args (@t120 0)) % 0.18/0.50 (step @p150 :rule chain_m_resolution :premises (@p149 @p148) :args ((not @t119) @t121 @t122)) % 0.18/0.50 (step @p151 :rule bool-double-not-elim :args (@t117)) % 0.18/0.50 (step @p152 :rule refl :args (@t120)) % 0.18/0.50 (step @p153 :rule nary_cong :premises (@p152 @p151) :args ((or @t120 (not @t118)))) % 0.18/0.50 (step @p154 :rule cnf_or_neg :args (@t120 1)) % 0.18/0.50 (step @p155 :rule eq_resolve :premises (@p154 @p153)) % 0.18/0.50 (step @p156 :rule reordering :premises (@p155) :args ((or @t117 @t120))) % 0.18/0.50 (step @p157 :rule chain_m_resolution :premises (@p156 @p148) :args (@t117 @t121 @t122)) % 0.18/0.50 (step @p158 :rule bool-double-not-elim :args (@t115)) % 0.18/0.50 (step @p159 :rule nary_cong :premises (@p152 @p158) :args ((or @t120 (not @t116)))) % 0.18/0.50 (step @p160 :rule cnf_or_neg :args (@t120 2)) % 0.18/0.50 (step @p161 :rule eq_resolve :premises (@p160 @p159)) % 0.18/0.50 (step @p162 :rule reordering :premises (@p161) :args ((or @t115 @t120))) % 0.18/0.50 (step @p163 :rule chain_m_resolution :premises (@p162 @p148) :args (@t115 @t121 @t122)) % 0.18/0.50 (step @p164 :rule cnf_and_neg :args (@t119)) % 0.18/0.50 (step @p165 false :rule chain_m_resolution :premises (@p164 @p163 @p157 @p150) :args (false (@list false false true) (@list @t115 @t117 @t119))) % 0.18/0.50 ) % 0.18/0.50 % SZS output end Proof % 0.18/0.50 % cvc5 exiting %------------------------------------------------------------------------------