%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : LCL733^5 : TPTP v9.3.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n018.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 11:23:43 AM UTC 2026 % Result : Theorem 2.13s 2.48s % Output : Proof 2.13s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL733^5 : TPTP v9.3.1. Released v4.0.0. % 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.09/0.36 % Computer : n018.cluster.edu % 0.09/0.36 % Model : x86_64 x86_64 % 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.36 % Memory : 8046.5625MB % 0.09/0.36 % OS : Linux 6.8.0-71-generic % 0.09/0.36 % CPULimit : 300 % 0.09/0.36 % WCLimit : 300 % 0.09/0.36 % DateTime : Sat Sep 5 21:20:19 UTC 2026 % 0.09/0.36 % CPUTime : % 0.09/0.42 %----Proving TH0 % 2.13/2.48 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 2.13/2.48 % SZS status Theorem % 2.13/2.48 % SZS output start Proof % 2.13/2.48 ( % 2.13/2.48 (declare-sort tptp.b 0) % 2.13/2.48 (define @t1 () (@var "Xp" (-> tptp.b Bool))) % 2.13/2.48 (define @t2 () (@var "Xj" (-> (-> tptp.b Bool) tptp.b))) % 2.13/2.48 (define @t3 () (_ @t2 @t1)) % 2.13/2.48 (define @t4 () (_ @t1 @t3)) % 2.13/2.48 (define @t5 () (@var "Xz" tptp.b)) % 2.13/2.48 (define @t6 () (_ @t1 @t5)) % 2.13/2.48 (define @t7 () (@list @t5)) % 2.13/2.48 (define @t8 () (exists @t7 @t6)) % 2.13/2.48 (define @t9 () (=> @t8 @t4)) % 2.13/2.48 (define @t10 () (@list @t1)) % 2.13/2.48 (define @t11 () (forall @t10 @t9)) % 2.13/2.48 (define @t12 () (@list @t2)) % 2.13/2.48 (define @t13 () (exists @t12 @t11)) % 2.13/2.48 (define @t14 () (@var "Xx" (-> tptp.b Bool))) % 2.13/2.48 (define @t15 () (@var "Xf" (-> (-> tptp.b Bool) tptp.b))) % 2.13/2.48 (define @t16 () (_ @t15 @t14)) % 2.13/2.48 (define @t17 () (_ @t14 @t16)) % 2.13/2.48 (define @t18 () (@var "Xx0" tptp.b)) % 2.13/2.48 (define @t19 () (_ @t14 @t18)) % 2.13/2.48 (define @t20 () (@list @t18)) % 2.13/2.48 (define @t21 () (exists @t20 @t19)) % 2.13/2.48 (define @t22 () (=> @t21 @t17)) % 2.13/2.48 (define @t23 () (@list @t14)) % 2.13/2.48 (define @t24 () (forall @t23 @t22)) % 2.13/2.48 (define @t25 () (@list @t15)) % 2.13/2.48 (define @t26 () (exists @t25 @t24)) % 2.13/2.48 (define @t27 () (@var "Xy" tptp.b)) % 2.13/2.48 (define @t28 () (_ @t14 @t27)) % 2.13/2.48 (define @t29 () (=> @t21 @t28)) % 2.13/2.48 (define @t30 () (@list @t27)) % 2.13/2.48 (define @t31 () (exists @t30 @t29)) % 2.13/2.48 (define @t32 () (forall @t23 @t31)) % 2.13/2.48 (define @t33 () (=> @t32 @t26)) % 2.13/2.48 (define @t34 () (@list (@var "Xr" (-> (-> tptp.b Bool) tptp.b Bool)))) % 2.13/2.48 (define @t35 () (forall @t34 @t33)) % 2.13/2.48 (define @t36 () (=> @t35 @t13)) % 2.13/2.48 (define @t37 () (not @t36)) % 2.13/2.48 (define @t38 () (@var "BOUND_VARIABLE_7463" tptp.b)) % 2.13/2.48 (define @t39 () (_ @t14 @t38)) % 2.13/2.48 (define @t40 () (@list @t38)) % 2.13/2.48 (define @t41 () (forall @t40 (not @t39))) % 2.13/2.48 (define @t42 () (not @t41)) % 2.13/2.48 (define @t43 () (@var "BOUND_VARIABLE_7479" tptp.b)) % 2.13/2.48 (define @t44 () (not (_ @t14 @t43))) % 2.13/2.48 (define @t45 () (or @t44 @t42)) % 2.13/2.48 (define @t46 () (forall (@list @t14 @t43) @t45)) % 2.13/2.48 (define @t47 () (@quantifiers_skolemize @t46 0)) % 2.13/2.48 (define @t48 () (forall @t40 (not (_ @t47 @t38)))) % 2.13/2.48 (define @t49 () (@quantifiers_skolemize @t46 1)) % 2.13/2.48 (define @t50 () (not (_ @t47 @t49))) % 2.13/2.48 (define @t51 () (or @t50 (not @t48))) % 2.13/2.48 (define @t52 () (not @t51)) % 2.13/2.48 (define @t53 () (not @t46)) % 2.13/2.48 (define @t54 () (@list false)) % 2.13/2.48 (define @t55 () (_ @t2 @t1)) % 2.13/2.48 (define @t56 () (_ @t1 @t55)) % 2.13/2.48 (define @t57 () (@var "BOUND_VARIABLE_7527" tptp.b)) % 2.13/2.48 (define @t58 () (not (_ @t1 @t57))) % 2.13/2.48 (define @t59 () (or @t58 @t56)) % 2.13/2.48 (define @t60 () (@list @t1 @t57)) % 2.13/2.48 (define @t61 () (forall @t60 @t59)) % 2.13/2.48 (define @t62 () (forall @t12 (not @t61))) % 2.13/2.48 (define @t63 () (@list @t57)) % 2.13/2.48 (define @t64 () (forall @t63 @t59)) % 2.13/2.48 (define @t65 () (forall @t63 @t58)) % 2.13/2.48 (define @t66 () (or @t65 @t56)) % 2.13/2.48 (define @t67 () (_ @t1 @t5)) % 2.13/2.48 (define @t68 () (forall @t7 (not @t67))) % 2.13/2.48 (define @t69 () (or @t68 @t4)) % 2.13/2.48 (define @t70 () (not @t68)) % 2.13/2.48 (define @t71 () (not @t6)) % 2.13/2.48 (define @t72 () (forall @t7 @t71)) % 2.13/2.48 (define @t73 () (not @t72)) % 2.13/2.48 (define @t74 () (_ @t15 @t14)) % 2.13/2.48 (define @t75 () (_ @t14 @t74)) % 2.13/2.48 (define @t76 () (@var "BOUND_VARIABLE_7495" tptp.b)) % 2.13/2.48 (define @t77 () (not (_ @t14 @t76))) % 2.13/2.48 (define @t78 () (or @t77 @t75)) % 2.13/2.48 (define @t79 () (@list @t14 @t76)) % 2.13/2.48 (define @t80 () (forall @t79 @t78)) % 2.13/2.48 (define @t81 () (forall @t25 (not @t80))) % 2.13/2.48 (define @t82 () (not @t81)) % 2.13/2.48 (define @t83 () (or @t53 @t82)) % 2.13/2.48 (define @t84 () (@list @t76)) % 2.13/2.48 (define @t85 () (forall @t84 @t78)) % 2.13/2.48 (define @t86 () (forall @t84 @t77)) % 2.13/2.48 (define @t87 () (@list @t18)) % 2.13/2.48 (define @t88 () (or @t86 @t75)) % 2.13/2.48 (define @t89 () (_ @t14 @t18)) % 2.13/2.48 (define @t90 () (forall @t20 (not @t89))) % 2.13/2.48 (define @t91 () (or @t90 @t17)) % 2.13/2.48 (define @t92 () (not @t90)) % 2.13/2.48 (define @t93 () (not @t92)) % 2.13/2.48 (define @t94 () (not @t19)) % 2.13/2.48 (define @t95 () (forall @t20 @t94)) % 2.13/2.48 (define @t96 () (not @t95)) % 2.13/2.48 (define @t97 () (@list @t43)) % 2.13/2.48 (define @t98 () (forall @t97 @t45)) % 2.13/2.48 (define @t99 () (forall @t97 @t44)) % 2.13/2.48 (define @t100 () (or @t99 @t42)) % 2.13/2.48 (define @t101 () (_ @t14 @t38)) % 2.13/2.48 (define @t102 () (not @t101)) % 2.13/2.48 (define @t103 () (forall @t40 @t102)) % 2.13/2.48 (define @t104 () (not @t28)) % 2.13/2.48 (define @t105 () (forall @t30 @t104)) % 2.13/2.48 (define @t106 () (forall @t30 @t92)) % 2.13/2.48 (define @t107 () (and @t106 @t105)) % 2.13/2.48 (define @t108 () (=> @t92 @t28)) % 2.13/2.48 (define @t109 () (forall @t30 (not @t108))) % 2.13/2.48 (define @t110 () (not @t109)) % 2.13/2.48 (define @t111 () (@quantifiers_skolemize @t81 0)) % 2.13/2.48 (define @t112 () (forall @t79 (or @t77 (_ @t14 (_ @t111 @t14))))) % 2.13/2.48 (define @t113 () (not (not @t112))) % 2.13/2.48 (define @t114 () (_ @t111 @t1)) % 2.13/2.48 (define @t115 () (@var "BOUND_VARIABLE_21918" (-> tptp.b Bool))) % 2.13/2.48 (define @t116 () (lambda (@list @t115) (_ @t111 @t115))) % 2.13/2.48 (define @t117 () (_ @t116 @t1)) % 2.13/2.48 (define @t118 () (_ @t1 @t117)) % 2.13/2.48 (define @t119 () (or @t58 @t118)) % 2.13/2.48 (define @t120 () (forall @t60 @t119)) % 2.13/2.48 (define @t121 () (not @t120)) % 2.13/2.48 (define @t122 () (forall @t60 (or @t58 (_ @t1 @t114)))) % 2.13/2.48 (define @t123 () (@quantifiers_skolemize @t122 1)) % 2.13/2.48 (define @t124 () (@quantifiers_skolemize @t122 0)) % 2.13/2.48 (define @t125 () (or (not (_ @t124 @t123)) (_ @t124 (_ @t111 @t124)))) % 2.13/2.48 (assume @p1 @t37) % 2.13/2.48 (assume @p2 true) % 2.13/2.48 (assume-push @p215 @t48) % 2.13/2.48 (step @p4 :rule instantiate :premises (@p215) :args ((@list @t49))) % 2.13/2.48 (step-pop @p216 :rule scope :premises (@p4)) % 2.13/2.48 (step @p5 :rule process_scope :premises (@p216) :args (@t50)) % 2.13/2.48 (step @p7 :rule implies_elim :premises (@p5)) % 2.13/2.48 (step @p8 :rule reordering :premises (@p7) :args (@t51)) % 2.13/2.48 (step @p9 :rule refl :args (@t52)) % 2.13/2.48 (step @p10 :rule bool-double-not-elim :args (@t46)) % 2.13/2.48 (step @p11 :rule nary_cong :premises (@p10 @p9) :args ((or (not @t53) @t52))) % 2.13/2.48 (assume-push @p217 @t53) % 2.13/2.48 (step @p13 :rule skolemize :premises (@p217)) % 2.13/2.48 (step-pop @p218 :rule scope :premises (@p13)) % 2.13/2.48 (step @p14 :rule process_scope :premises (@p218) :args (@t52)) % 2.13/2.48 (step @p16 :rule implies_elim :premises (@p14)) % 2.13/2.48 (step @p17 :rule eq_resolve :premises (@p16 @p11)) % 2.13/2.48 (step @p18 :rule chain_m_resolution :premises (@p17 @p8) :args (@t46 @t54 (@list @t51))) % 2.13/2.48 (step @p19 :rule exists-elim :args ((= (exists @t12 @t61) (not @t62)))) % 2.13/2.48 (step @p20 :rule quant-merge-prenex :args ((= (forall @t10 @t64) @t61))) % 2.13/2.48 (step @p21 :rule refl :args (@t56)) % 2.13/2.48 (step @p22 :rule alpha_equiv :args (@t65 (@list @t57) (@list @t5))) % 2.13/2.48 (step @p23 :rule nary_cong :premises (@p22 @p21) :args (@t66)) % 2.13/2.48 (step @p24 :rule quant-miniscope-or :args ((= @t64 @t66))) % 2.13/2.48 (step @p25 :rule trans :premises (@p24 @p23)) % 2.13/2.48 (step @p26 :rule symm :premises (@p25)) % 2.13/2.48 (step @p27 :rule cong :premises (@p26) :args ((forall @t10 (or @t68 @t56)))) % 2.13/2.48 (step @p28 :rule trans :premises (@p27 @p20)) % 2.13/2.48 (step @p29 :rule refl :args ((_ @t1 @t3))) % 2.13/2.48 (step @p30 :rule refl :args (@t55)) % 2.13/2.48 (step @p31 :rule cong :premises (@p30) :args (@t56)) % 2.13/2.48 (step @p32 :rule trans :premises (@p31 @p29)) % 2.13/2.48 (step @p33 :rule refl :args (@t1)) % 2.13/2.48 (step @p34 :rule ho_cong :premises (@p33 @p30)) % 2.13/2.48 (step @p35 :rule cong :premises (@p34 @p32) :args ((= (_ @t1 @t55) @t56))) % 2.13/2.48 (step @p36 :rule symm :premises (@p35)) % 2.13/2.48 (step @p37 :rule refl :args (@t4)) % 2.13/2.48 (step @p38 :rule eq_resolve :premises (@p37 @p36)) % 2.13/2.48 (step @p39 :rule refl :args (@t3)) % 2.13/2.48 (step @p40 :rule cong :premises (@p39 @p30) :args ((= @t3 @t55))) % 2.13/2.48 (step @p41 :rule symm :premises (@p40)) % 2.13/2.48 (step @p42 :rule eq_resolve :premises (@p39 @p41)) % 2.13/2.48 (step @p43 :rule ho_cong :premises (@p33 @p42)) % 2.13/2.48 (step @p44 :rule trans :premises (@p43 @p38)) % 2.13/2.48 (step @p45 :rule refl :args (@t68)) % 2.13/2.48 (step @p46 :rule nary_cong :premises (@p45 @p44) :args (@t69)) % 2.13/2.48 (step @p47 :rule cong :premises (@p46) :args ((forall @t10 @t69))) % 2.13/2.48 (step @p48 :rule trans :premises (@p47 @p28)) % 2.13/2.48 (step @p49 :rule bool-double-not-elim :args (@t68)) % 2.13/2.48 (step @p50 :rule nary_cong :premises (@p49 @p37) :args ((or (not @t70) @t4))) % 2.13/2.48 (step @p51 :rule bool-impl-elim :args (@t70 @t4)) % 2.13/2.48 (step @p52 :rule trans :premises (@p51 @p50)) % 2.13/2.48 (step @p53 :rule cong :premises (@p52) :args ((forall @t10 (=> @t70 @t4)))) % 2.13/2.48 (step @p54 :rule trans :premises (@p53 @p48)) % 2.13/2.48 (step @p55 :rule refl :args (@t4)) % 2.13/2.48 (step @p56 :rule refl :args (@t67)) % 2.13/2.48 (step @p57 :rule refl :args (@t6)) % 2.13/2.48 (step @p58 :rule cong :premises (@p57 @p56) :args ((= @t6 @t67))) % 2.13/2.48 (step @p59 :rule symm :premises (@p58)) % 2.13/2.48 (step @p60 :rule eq_resolve :premises (@p57 @p59)) % 2.13/2.48 (step @p61 :rule cong :premises (@p60) :args (@t71)) % 2.13/2.48 (step @p62 :rule cong :premises (@p61) :args (@t72)) % 2.13/2.48 (step @p63 :rule cong :premises (@p62) :args (@t73)) % 2.13/2.48 (step @p64 :rule exists-elim :args ((= @t8 @t73))) % 2.13/2.48 (step @p65 :rule trans :premises (@p64 @p63)) % 2.13/2.48 (step @p66 :rule cong :premises (@p65 @p55) :args (@t9)) % 2.13/2.48 (step @p67 :rule cong :premises (@p66) :args (@t11)) % 2.13/2.48 (step @p68 :rule trans :premises (@p67 @p54)) % 2.13/2.48 (step @p69 :rule cong :premises (@p68) :args (@t13)) % 2.13/2.48 (step @p70 :rule trans :premises (@p69 @p19)) % 2.13/2.48 (step @p71 :rule quant-unused-vars :args ((= (forall @t34 @t83) @t83))) % 2.13/2.48 (step @p72 :rule bool-impl-elim :args (@t46 @t82)) % 2.13/2.48 (step @p73 :rule cong :premises (@p72) :args ((forall @t34 (=> @t46 @t82)))) % 2.13/2.48 (step @p74 :rule trans :premises (@p73 @p71)) % 2.13/2.48 (step @p75 :rule exists-elim :args ((= (exists @t25 @t80) @t82))) % 2.13/2.48 (step @p76 :rule quant-merge-prenex :args ((= (forall @t23 @t85) @t80))) % 2.13/2.48 (step @p77 :rule refl :args (@t75)) % 2.13/2.48 (step @p78 :rule alpha_equiv :args (@t86 (@list @t76) @t87)) % 2.13/2.48 (step @p79 :rule nary_cong :premises (@p78 @p77) :args (@t88)) % 2.13/2.48 (step @p80 :rule quant-miniscope-or :args ((= @t85 @t88))) % 2.13/2.48 (step @p81 :rule trans :premises (@p80 @p79)) % 2.13/2.48 (step @p82 :rule symm :premises (@p81)) % 2.13/2.48 (step @p83 :rule cong :premises (@p82) :args ((forall @t23 (or @t90 @t75)))) % 2.13/2.48 (step @p84 :rule trans :premises (@p83 @p76)) % 2.13/2.48 (step @p85 :rule refl :args ((_ @t14 @t16))) % 2.13/2.48 (step @p86 :rule refl :args (@t74)) % 2.13/2.48 (step @p87 :rule cong :premises (@p86) :args (@t75)) % 2.13/2.48 (step @p88 :rule trans :premises (@p87 @p85)) % 2.13/2.48 (step @p89 :rule refl :args (@t14)) % 2.13/2.48 (step @p90 :rule ho_cong :premises (@p89 @p86)) % 2.13/2.48 (step @p91 :rule cong :premises (@p90 @p88) :args ((= (_ @t14 @t74) @t75))) % 2.13/2.48 (step @p92 :rule symm :premises (@p91)) % 2.13/2.48 (step @p93 :rule refl :args (@t17)) % 2.13/2.48 (step @p94 :rule eq_resolve :premises (@p93 @p92)) % 2.13/2.48 (step @p95 :rule refl :args (@t16)) % 2.13/2.48 (step @p96 :rule cong :premises (@p95 @p86) :args ((= @t16 @t74))) % 2.13/2.48 (step @p97 :rule symm :premises (@p96)) % 2.13/2.48 (step @p98 :rule eq_resolve :premises (@p95 @p97)) % 2.13/2.48 (step @p99 :rule ho_cong :premises (@p89 @p98)) % 2.13/2.48 (step @p100 :rule trans :premises (@p99 @p94)) % 2.13/2.48 (step @p101 :rule refl :args (@t90)) % 2.13/2.48 (step @p102 :rule nary_cong :premises (@p101 @p100) :args (@t91)) % 2.13/2.48 (step @p103 :rule cong :premises (@p102) :args ((forall @t23 @t91))) % 2.13/2.48 (step @p104 :rule trans :premises (@p103 @p84)) % 2.13/2.48 (step @p105 :rule bool-double-not-elim :args (@t90)) % 2.13/2.48 (step @p106 :rule nary_cong :premises (@p105 @p93) :args ((or @t93 @t17))) % 2.13/2.48 (step @p107 :rule bool-impl-elim :args (@t92 @t17)) % 2.13/2.48 (step @p108 :rule trans :premises (@p107 @p106)) % 2.13/2.48 (step @p109 :rule cong :premises (@p108) :args ((forall @t23 (=> @t92 @t17)))) % 2.13/2.48 (step @p110 :rule trans :premises (@p109 @p104)) % 2.13/2.48 (step @p111 :rule refl :args (@t17)) % 2.13/2.48 (step @p112 :rule refl :args (@t89)) % 2.13/2.48 (step @p113 :rule refl :args (@t19)) % 2.13/2.48 (step @p114 :rule cong :premises (@p113 @p112) :args ((= @t19 @t89))) % 2.13/2.48 (step @p115 :rule symm :premises (@p114)) % 2.13/2.48 (step @p116 :rule eq_resolve :premises (@p113 @p115)) % 2.13/2.48 (step @p117 :rule cong :premises (@p116) :args (@t94)) % 2.13/2.48 (step @p118 :rule cong :premises (@p117) :args (@t95)) % 2.13/2.48 (step @p119 :rule cong :premises (@p118) :args (@t96)) % 2.13/2.48 (step @p120 :rule exists-elim :args ((= @t21 @t96))) % 2.13/2.48 (step @p121 :rule trans :premises (@p120 @p119)) % 2.13/2.48 (step @p122 :rule cong :premises (@p121 @p111) :args (@t22)) % 2.13/2.48 (step @p123 :rule cong :premises (@p122) :args (@t24)) % 2.13/2.48 (step @p124 :rule trans :premises (@p123 @p110)) % 2.13/2.48 (step @p125 :rule cong :premises (@p124) :args (@t26)) % 2.13/2.48 (step @p126 :rule trans :premises (@p125 @p75)) % 2.13/2.48 (step @p127 :rule quant-merge-prenex :args ((= (forall @t23 @t98) @t46))) % 2.13/2.48 (step @p128 :rule refl :args (@t42)) % 2.13/2.48 (step @p129 :rule alpha_equiv :args (@t99 (@list @t43) @t87)) % 2.13/2.48 (step @p130 :rule nary_cong :premises (@p129 @p128) :args (@t100)) % 2.13/2.48 (step @p131 :rule quant-miniscope-or :args ((= @t98 @t100))) % 2.13/2.48 (step @p132 :rule trans :premises (@p131 @p130)) % 2.13/2.48 (step @p133 :rule symm :premises (@p132)) % 2.13/2.48 (step @p134 :rule cong :premises (@p133) :args ((forall @t23 (or @t90 @t42)))) % 2.13/2.48 (step @p135 :rule trans :premises (@p134 @p127)) % 2.13/2.48 (step @p136 :rule nary_cong :premises (@p105 @p128) :args ((or @t93 @t42))) % 2.13/2.48 (step @p137 :rule bool-and-de-morgan :args (@t92 @t41 true)) % 2.13/2.48 (step @p138 :rule trans :premises (@p137 @p136)) % 2.13/2.48 (step @p139 :rule cong :premises (@p138) :args ((forall @t23 (not (and @t92 @t41))))) % 2.13/2.48 (step @p140 :rule trans :premises (@p139 @p135)) % 2.13/2.48 (step @p141 :rule refl :args (@t39)) % 2.13/2.48 (step @p142 :rule refl :args (@t101)) % 2.13/2.48 (step @p143 :rule cong :premises (@p142 @p141) :args ((= @t101 @t39))) % 2.13/2.48 (step @p144 :rule symm :premises (@p143)) % 2.13/2.49 (step @p145 :rule eq_resolve :premises (@p142 @p144)) % 2.13/2.49 (step @p146 :rule cong :premises (@p145) :args (@t102)) % 2.13/2.49 (step @p147 :rule cong :premises (@p146) :args (@t103)) % 2.13/2.49 (step @p148 :rule refl :args (@t92)) % 2.13/2.49 (step @p149 :rule nary_cong :premises (@p148 @p147) :args ((and @t92 @t103))) % 2.13/2.49 (step @p150 :rule alpha_equiv :args (@t105 (@list @t27) (@list @t38))) % 2.13/2.49 (step @p151 :rule quant-unused-vars :args ((= @t106 @t92))) % 2.13/2.49 (step @p152 :rule nary_cong :premises (@p151 @p150) :args (@t107)) % 2.13/2.49 (step @p153 :rule quant-miniscope-and :args ((= (forall @t30 (and @t92 @t104)) @t107))) % 2.13/2.49 (step @p154 :rule trans :premises (@p153 @p152)) % 2.13/2.49 (step @p155 :rule trans :premises (@p154 @p149)) % 2.13/2.49 (step @p156 :rule bool-implies-de-morgan :args (@t92 @t28)) % 2.13/2.49 (step @p157 :rule cong :premises (@p156) :args (@t109)) % 2.13/2.49 (step @p158 :rule trans :premises (@p157 @p155)) % 2.13/2.49 (step @p159 :rule cong :premises (@p158) :args (@t110)) % 2.13/2.49 (step @p160 :rule exists-elim :args ((= (exists @t30 @t108) @t110))) % 2.13/2.49 (step @p161 :rule trans :premises (@p160 @p159)) % 2.13/2.49 (step @p162 :rule refl :args (@t28)) % 2.13/2.49 (step @p163 :rule cong :premises (@p121 @p162) :args (@t29)) % 2.13/2.49 (step @p164 :rule cong :premises (@p163) :args (@t31)) % 2.13/2.49 (step @p165 :rule trans :premises (@p164 @p161)) % 2.13/2.49 (step @p166 :rule cong :premises (@p165) :args (@t32)) % 2.13/2.49 (step @p167 :rule trans :premises (@p166 @p140)) % 2.13/2.49 (step @p168 :rule cong :premises (@p167 @p126) :args (@t33)) % 2.13/2.49 (step @p169 :rule cong :premises (@p168) :args (@t35)) % 2.13/2.49 (step @p170 :rule trans :premises (@p169 @p74)) % 2.13/2.49 (step @p171 :rule cong :premises (@p170 @p70) :args (@t36)) % 2.13/2.49 (step @p172 :rule cong :premises (@p171) :args (@t37)) % 2.13/2.49 (step @p173 :rule eq_resolve :premises (@p1 @p172)) % 2.13/2.49 (step @p174 :rule not_implies_elim1 :premises (@p173)) % 2.13/2.49 (step @p175 :rule reordering :premises (@p174) :args ((or @t82 @t53))) % 2.13/2.49 (step @p176 :rule chain_m_resolution :premises (@p175 @p18) :args (@t82 @t54 (@list @t46))) % 2.13/2.49 (step @p177 :rule refl :args (@t112)) % 2.13/2.49 (step @p178 :rule bool-double-not-elim :args (@t81)) % 2.13/2.49 (step @p179 :rule nary_cong :premises (@p178 @p177) :args ((or (not @t82) @t112))) % 2.13/2.49 (step @p180 :rule bool-double-not-elim :args (@t112)) % 2.13/2.49 (step @p181 :rule refl :args (@t82)) % 2.13/2.49 (step @p182 :rule cong :premises (@p181 @p180) :args ((=> @t82 @t113))) % 2.13/2.49 (assume-push @p219 @t82) % 2.13/2.49 (step @p184 :rule skolemize :premises (@p219)) % 2.13/2.49 (step-pop @p220 :rule scope :premises (@p184)) % 2.13/2.49 (step @p185 :rule process_scope :premises (@p220) :args (@t113)) % 2.13/2.49 (step @p187 :rule eq_resolve :premises (@p185 @p182)) % 2.13/2.49 (step @p188 :rule implies_elim :premises (@p187)) % 2.13/2.49 (step @p189 :rule eq_resolve :premises (@p188 @p179)) % 2.13/2.49 (step @p190 :rule chain_m_resolution :premises (@p189 @p176) :args (@t112 (@list true) (@list @t81))) % 2.13/2.49 (step @p191 :rule not_implies_elim2 :premises (@p173)) % 2.13/2.49 (step @p192 :rule not_not_elim :premises (@p191)) % 2.13/2.49 (step @p193 :rule beta-reduce :args ((= @t117 @t114))) % 2.13/2.49 (step @p194 :rule cong :premises (@p193) :args (@t118)) % 2.13/2.49 (step @p195 :rule refl :args (@t58)) % 2.13/2.49 (step @p196 :rule nary_cong :premises (@p195 @p194) :args (@t119)) % 2.13/2.49 (step @p197 :rule cong :premises (@p196) :args (@t120)) % 2.13/2.49 (step @p198 :rule cong :premises (@p197) :args (@t121)) % 2.13/2.49 (step @p199 :rule refl :args (@t62)) % 2.13/2.49 (step @p200 :rule cong :premises (@p199 @p198) :args ((=> @t62 @t121))) % 2.13/2.49 (assume-push @p221 @t62) % 2.13/2.49 (step @p202 :rule instantiate :premises (@p192) :args ((@list @t116))) % 2.13/2.49 (step-pop @p222 :rule scope :premises (@p202)) % 2.13/2.49 (step @p203 :rule process_scope :premises (@p222) :args (@t121)) % 2.13/2.49 (step @p205 :rule eq_resolve :premises (@p203 @p200)) % 2.13/2.49 (step @p206 :rule implies_elim :premises (@p205)) % 2.13/2.49 (step @p207 :rule chain_m_resolution :premises (@p206 @p192) :args ((not @t122) @t54 (@list @t62))) % 2.13/2.49 (step @p208 :rule skolemize :premises (@p207)) % 2.13/2.49 (assume-push @p223 @t112) % 2.13/2.49 (step @p210 :rule instantiate :premises (@p223) :args ((@list @t124 @t123))) % 2.13/2.49 (step-pop @p224 :rule scope :premises (@p210)) % 2.13/2.49 (step @p211 :rule process_scope :premises (@p224) :args (@t125)) % 2.13/2.49 (step @p213 :rule implies_elim :premises (@p211)) % 2.13/2.49 (step @p214 false :rule chain_m_resolution :premises (@p213 @p208 @p190) :args (false (@list true false) (@list @t125 @t112))) % 2.13/2.49 ) % 2.13/2.49 % SZS output end Proof % 2.13/2.49 % cvc5 exiting %------------------------------------------------------------------------------