%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : KLE143+2 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n004.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 08:28:23 AM UTC 2026 % Result : Theorem 33.86s 34.06s % Output : Proof 33.86s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : KLE143+2 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n004.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Tue Jun 2 05:20:07 EDT 2026 % 0.17/0.34 % CPUTime : % 0.28/0.49 %----Proving TF0_NAR, FOF, or CNF % 33.86/34.06 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 33.86/34.06 --- Run --no-e-matching --full-saturate-quant at 6... % 33.86/34.06 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 6... % 33.86/34.06 --- Run --finite-model-find --uf-ss=no-minimal at 6... % 33.86/34.06 --- Run --multi-trigger-when-single --full-saturate-quant at 30... % 33.86/34.06 % SZS status Theorem % 33.86/34.06 % SZS output start Proof % 33.86/34.06 ( % 33.86/34.06 (declare-sort $$unsorted 0) % 33.86/34.06 (declare-const tptp.strong_iteration (-> $$unsorted $$unsorted)) % 33.86/34.06 (declare-const tptp.star (-> $$unsorted $$unsorted)) % 33.86/34.06 (declare-const tptp.leq (-> $$unsorted $$unsorted Bool)) % 33.86/34.06 (declare-const tptp.multiplication (-> $$unsorted $$unsorted $$unsorted)) % 33.86/34.06 (declare-const tptp.zero $$unsorted) % 33.86/34.06 (declare-const tptp.one $$unsorted) % 33.86/34.06 (declare-const tptp.addition (-> $$unsorted $$unsorted $$unsorted)) % 33.86/34.06 (define @t1 () (@var "A" $$unsorted)) % 33.86/34.06 (define @t2 () (@var "B" $$unsorted)) % 33.86/34.06 (define @t3 () (tptp.addition @t1 @t2)) % 33.86/34.06 (define @t4 () (@list @t1 @t2)) % 33.86/34.06 (define @t5 () (@var "C" $$unsorted)) % 33.86/34.06 (define @t6 () (tptp.addition @t2 @t5)) % 33.86/34.06 (define @t7 () (tptp.addition @t1 tptp.zero)) % 33.86/34.06 (define @t8 () (@list @t1)) % 33.86/34.06 (define @t9 () (forall @t8 (= @t7 @t1))) % 33.86/34.06 (define @t10 () (tptp.addition @t1 @t1)) % 33.86/34.06 (define @t11 () (forall @t8 (= @t10 @t1))) % 33.86/34.06 (define @t12 () (tptp.multiplication @t1 @t2)) % 33.86/34.06 (define @t13 () (tptp.multiplication @t2 @t5)) % 33.86/34.06 (define @t14 () (@list @t1 @t2 @t5)) % 33.86/34.06 (define @t15 () (forall @t14 (= (tptp.multiplication @t1 @t13) (tptp.multiplication @t12 @t5)))) % 33.86/34.06 (define @t16 () (tptp.multiplication @t1 tptp.one)) % 33.86/34.06 (define @t17 () (forall @t8 (= @t16 @t1))) % 33.86/34.06 (define @t18 () (tptp.multiplication tptp.one @t1)) % 33.86/34.06 (define @t19 () (forall @t8 (= @t18 @t1))) % 33.86/34.06 (define @t20 () (tptp.multiplication @t1 @t5)) % 33.86/34.06 (define @t21 () (tptp.multiplication tptp.zero @t1)) % 33.86/34.06 (define @t22 () (forall @t8 (= @t21 tptp.zero))) % 33.86/34.06 (define @t23 () (tptp.star @t1)) % 33.86/34.06 (define @t24 () (tptp.addition tptp.one (tptp.multiplication @t1 @t23))) % 33.86/34.06 (define @t25 () (forall @t8 (= @t24 @t23))) % 33.86/34.06 (define @t26 () (tptp.addition tptp.one (tptp.multiplication @t23 @t1))) % 33.86/34.06 (define @t27 () (forall @t8 (= @t26 @t23))) % 33.86/34.06 (define @t28 () (tptp.leq (tptp.multiplication @t23 @t2) @t5)) % 33.86/34.06 (define @t29 () (tptp.addition @t20 @t2)) % 33.86/34.06 (define @t30 () (tptp.leq @t29 @t5)) % 33.86/34.06 (define @t31 () (forall @t14 (=> @t30 @t28))) % 33.86/34.06 (define @t32 () (tptp.strong_iteration @t1)) % 33.86/34.06 (define @t33 () (tptp.leq @t5 (tptp.multiplication @t32 @t2))) % 33.86/34.06 (define @t34 () (tptp.leq @t5 @t29)) % 33.86/34.06 (define @t35 () (forall @t14 (=> @t34 @t33))) % 33.86/34.06 (define @t36 () (tptp.leq @t1 @t2)) % 33.86/34.06 (define @t37 () (= @t36 (= @t3 @t2))) % 33.86/34.06 (define @t38 () (forall @t4 @t37)) % 33.86/34.06 (define @t39 () (@var "X0" $$unsorted)) % 33.86/34.06 (define @t40 () (tptp.strong_iteration @t39)) % 33.86/34.06 (define @t41 () (tptp.multiplication @t40 @t40)) % 33.86/34.06 (define @t42 () (tptp.leq @t40 @t41)) % 33.86/34.06 (define @t43 () (tptp.leq @t41 @t40)) % 33.86/34.06 (define @t44 () (@list @t39)) % 33.86/34.06 (define @t45 () (forall @t44 (and @t43 @t42))) % 33.86/34.06 (define @t46 () (not @t45)) % 33.86/34.06 (define @t47 () (@var "BOUND_VARIABLE_7556" $$unsorted)) % 33.86/34.06 (define @t48 () (tptp.strong_iteration @t47)) % 33.86/34.06 (define @t49 () (forall (@list @t47) (tptp.leq @t48 (tptp.multiplication @t48 @t48)))) % 33.86/34.06 (define @t50 () (@quantifiers_skolemize @t49 0)) % 33.86/34.06 (define @t51 () (tptp.strong_iteration @t50)) % 33.86/34.06 (define @t52 () (tptp.multiplication @t50 @t51)) % 33.86/34.06 (define @t53 () (tptp.addition @t52 @t51)) % 33.86/34.06 (define @t54 () (@var "BOUND_VARIABLE_7549" $$unsorted)) % 33.86/34.06 (define @t55 () (tptp.strong_iteration @t54)) % 33.86/34.06 (define @t56 () (forall (@list @t54) (tptp.leq (tptp.multiplication @t55 @t55) @t55))) % 33.86/34.06 (define @t57 () (@quantifiers_skolemize @t56 0)) % 33.86/34.06 (define @t58 () (tptp.strong_iteration @t57)) % 33.86/34.06 (define @t59 () (@list @t57 @t58 @t58)) % 33.86/34.06 (define @t60 () (tptp.multiplication @t58 tptp.one)) % 33.86/34.06 (define @t61 () (@list @t58)) % 33.86/34.06 (define @t62 () (tptp.addition @t58 @t60)) % 33.86/34.06 (define @t63 () (= @t60 @t62)) % 33.86/34.06 (define @t64 () (tptp.leq @t58 @t60)) % 33.86/34.06 (define @t65 () (= @t64 @t63)) % 33.86/34.06 (define @t66 () (@list false false)) % 33.86/34.06 (define @t67 () (@list @t57)) % 33.86/34.06 (define @t68 () (tptp.multiplication @t57 @t58)) % 33.86/34.06 (define @t69 () (tptp.multiplication @t58 tptp.zero)) % 33.86/34.06 (define @t70 () (tptp.star @t57)) % 33.86/34.06 (define @t71 () (@list @t70)) % 33.86/34.06 (define @t72 () (tptp.multiplication tptp.one @t58)) % 33.86/34.06 (define @t73 () (tptp.addition @t72 @t70)) % 33.86/34.06 (define @t74 () (tptp.multiplication @t57 @t70)) % 33.86/34.06 (define @t75 () (tptp.addition @t68 @t74)) % 33.86/34.06 (define @t76 () (tptp.multiplication @t70 @t57)) % 33.86/34.06 (define @t77 () (tptp.addition tptp.one @t76)) % 33.86/34.06 (define @t78 () (tptp.addition @t72 @t76)) % 33.86/34.06 (define @t79 () (tptp.addition @t58 @t68)) % 33.86/34.06 (define @t80 () (tptp.addition @t68 @t58)) % 33.86/34.06 (define @t81 () (tptp.leq @t80 @t58)) % 33.86/34.06 (define @t82 () (tptp.multiplication @t70 @t58)) % 33.86/34.06 (define @t83 () (tptp.leq @t82 @t58)) % 33.86/34.06 (define @t84 () (not @t81)) % 33.86/34.06 (define @t85 () (or @t84 @t83)) % 33.86/34.06 (define @t86 () (tptp.multiplication @t76 @t58)) % 33.86/34.06 (define @t87 () (tptp.multiplication @t58 (tptp.multiplication tptp.zero @t58))) % 33.86/34.06 (define @t88 () (tptp.multiplication @t69 @t58)) % 33.86/34.06 (define @t89 () (= @t87 @t88)) % 33.86/34.06 (define @t90 () (@list false)) % 33.86/34.06 (define @t91 () (tptp.addition @t70 @t88)) % 33.86/34.06 (define @t92 () (tptp.addition @t91 @t72)) % 33.86/34.06 (define @t93 () (tptp.multiplication @t58 @t58)) % 33.86/34.06 (define @t94 () (= @t80 (tptp.addition @t58 @t80))) % 33.86/34.06 (define @t95 () (tptp.leq @t58 @t80)) % 33.86/34.06 (define @t96 () (= @t95 @t94)) % 33.86/34.06 (define @t97 () (tptp.leq @t58 @t93)) % 33.86/34.06 (define @t98 () (not @t95)) % 33.86/34.06 (define @t99 () (or @t98 @t97)) % 33.86/34.06 (define @t100 () (= @t93 (tptp.addition @t58 @t93))) % 33.86/34.06 (define @t101 () (= @t97 @t100)) % 33.86/34.06 (define @t102 () (tptp.leq @t93 @t58)) % 33.86/34.06 (define @t103 () (not @t102)) % 33.86/34.06 (define @t104 () (not @t56)) % 33.86/34.06 (define @t105 () (forall @t44 @t42)) % 33.86/34.06 (define @t106 () (@list @t39)) % 33.86/34.06 (define @t107 () (forall @t44 @t43)) % 33.86/34.06 (define @t108 () (and @t107 @t105)) % 33.86/34.06 (define @t109 () (not @t49)) % 33.86/34.06 (define @t110 () (tptp.leq @t51 (tptp.multiplication @t51 @t51))) % 33.86/34.06 (define @t111 () (not @t110)) % 33.86/34.06 (define @t112 () (tptp.leq @t51 @t53)) % 33.86/34.06 (define @t113 () (not @t112)) % 33.86/34.06 (define @t114 () (or @t113 @t110)) % 33.86/34.06 (define @t115 () (@list true false)) % 33.86/34.06 (define @t116 () (= @t53 (tptp.addition @t51 @t53))) % 33.86/34.06 (define @t117 () (= @t112 @t116)) % 33.86/34.06 (define @t118 () (not @t116)) % 33.86/34.06 (define @t119 () (tptp.addition @t51 @t51)) % 33.86/34.06 (define @t120 () (tptp.addition @t119 @t52)) % 33.86/34.06 (define @t121 () (tptp.addition @t51 @t52)) % 33.86/34.06 (define @t122 () (tptp.addition @t51 @t121)) % 33.86/34.06 (define @t123 () (= @t122 @t120)) % 33.86/34.06 (define @t124 () (not @t123)) % 33.86/34.06 (define @t125 () (= @t51 @t119)) % 33.86/34.06 (define @t126 () (not @t125)) % 33.86/34.06 (define @t127 () (= @t53 @t121)) % 33.86/34.06 (define @t128 () (not @t127)) % 33.86/34.06 (define @t129 () (= @t120 @t122)) % 33.86/34.06 (define @t130 () (and @t123 @t124)) % 33.86/34.06 (assume @p1 (forall @t4 (= @t3 (tptp.addition @t2 @t1)))) % 33.86/34.06 (assume @p2 (forall (@list @t5 @t2 @t1) (= (tptp.addition @t1 @t6) (tptp.addition @t3 @t5)))) % 33.86/34.06 (assume @p3 @t9) % 33.86/34.06 (assume @p4 @t11) % 33.86/34.06 (assume @p5 @t15) % 33.86/34.06 (assume @p6 @t17) % 33.86/34.06 (assume @p7 @t19) % 33.86/34.06 (assume @p8 (forall @t14 (= (tptp.multiplication @t1 @t6) (tptp.addition @t12 @t20)))) % 33.86/34.06 (assume @p9 (forall @t14 (= (tptp.multiplication @t3 @t5) (tptp.addition @t20 @t13)))) % 33.86/34.06 (assume @p10 @t22) % 33.86/34.06 (assume @p11 @t25) % 33.86/34.06 (assume @p12 @t27) % 33.86/34.06 (assume @p13 @t31) % 33.86/34.06 (assume @p14 (forall @t14 (=> (tptp.leq (tptp.addition (tptp.multiplication @t5 @t1) @t2) @t5) (tptp.leq (tptp.multiplication @t2 @t23) @t5)))) % 33.86/34.06 (assume @p15 (forall @t8 (= @t32 (tptp.addition (tptp.multiplication @t1 @t32) tptp.one)))) % 33.86/34.06 (assume @p16 @t35) % 33.86/34.06 (assume @p17 (forall @t8 (= @t32 (tptp.addition @t23 (tptp.multiplication @t32 tptp.zero))))) % 33.86/34.06 (assume @p18 @t38) % 33.86/34.06 (assume @p19 @t46) % 33.86/34.06 (assume @p20 true) % 33.86/34.06 (step @p21 :rule instantiate :premises (@p1) :args ((@list @t52 @t51))) % 33.86/34.06 (step @p22 :rule eq-symm :args (@t3 @t2)) % 33.86/34.06 (step @p23 :rule refl :args (@t36)) % 33.86/34.06 (step @p24 :rule cong :premises (@p23 @p22) :args (@t37)) % 33.86/34.06 (step @p25 :rule cong :premises (@p24) :args (@t38)) % 33.86/34.06 (step @p26 :rule eq_resolve :premises (@p18 @p25)) % 33.86/34.06 (step @p27 :rule instantiate :premises (@p26) :args ((@list @t51 @t53))) % 33.86/34.06 (step @p28 :rule bool-impl-elim :args (@t34 @t33)) % 33.86/34.06 (step @p29 :rule cong :premises (@p28) :args (@t35)) % 33.86/34.06 (step @p30 :rule eq_resolve :premises (@p16 @p29)) % 33.86/34.06 (step @p31 :rule instantiate :premises (@p30) :args ((@list @t50 @t51 @t51))) % 33.86/34.06 (step @p32 :rule bool-impl-elim :args (@t30 @t28)) % 33.86/34.06 (step @p33 :rule cong :premises (@p32) :args (@t31)) % 33.86/34.06 (step @p34 :rule eq_resolve :premises (@p13 @p33)) % 33.86/34.06 (step @p35 :rule instantiate :premises (@p34) :args (@t59)) % 33.86/34.06 (step @p36 :rule instantiate :premises (@p26) :args ((@list @t58 @t60))) % 33.86/34.06 (step @p37 :rule eq-symm :args (@t16 @t1)) % 33.86/34.06 (step @p38 :rule cong :premises (@p37) :args (@t17)) % 33.86/34.06 (step @p39 :rule eq_resolve :premises (@p6 @p38)) % 33.86/34.06 (step @p40 :rule instantiate :premises (@p39) :args (@t61)) % 33.86/34.06 (step @p41 :rule refl :args (@t58)) % 33.86/34.06 (step @p42 :rule cong :premises (@p41 @p40) :args ((tptp.addition @t58 @t58))) % 33.86/34.06 (step @p43 :rule eq-symm :args (@t10 @t1)) % 33.86/34.06 (step @p44 :rule cong :premises (@p43) :args (@t11)) % 33.86/34.06 (step @p45 :rule eq_resolve :premises (@p4 @p44)) % 33.86/34.06 (step @p46 :rule instantiate :premises (@p45) :args (@t61)) % 33.86/34.06 (step @p47 :rule symm :premises (@p40)) % 33.86/34.06 (step @p48 :rule trans :premises (@p47 @p46 @p42)) % 33.86/34.06 (step @p49 :rule cnf_equiv_pos2 :args (@t65)) % 33.86/34.06 (step @p50 :rule reordering :premises (@p49) :args ((or @t64 (not @t63) (not @t65)))) % 33.86/34.06 (step @p51 :rule chain_m_resolution :premises (@p50 @p48 @p36) :args (@t64 @t66 (@list @t63 @t65))) % 33.86/34.06 (step @p52 :rule true_intro :premises (@p51)) % 33.86/34.06 (step @p53 :rule instantiate :premises (@p15) :args (@t67)) % 33.86/34.06 (step @p54 :rule symm :premises (@p53)) % 33.86/34.06 (step @p55 :rule trans :premises (@p54 @p40)) % 33.86/34.06 (step @p56 :rule cong :premises (@p41 @p55) :args ((tptp.leq @t58 (tptp.addition @t68 tptp.one)))) % 33.86/34.06 (step @p57 :rule symm :premises (@p46)) % 33.86/34.06 (step @p58 :rule cong :premises (@p41 @p47) :args (@t62)) % 33.86/34.06 (step @p59 :rule instantiate :premises (@p1) :args ((@list @t68 tptp.one))) % 33.86/34.06 (step @p60 :rule symm :premises (@p59)) % 33.86/34.06 (step @p61 :rule trans :premises (@p60 @p54 @p40)) % 33.86/34.06 (step @p62 :rule cong :premises (@p41 @p61) :args ((tptp.addition @t58 (tptp.addition tptp.one @t68)))) % 33.86/34.06 (step @p63 :rule instantiate :premises (@p2) :args ((@list @t68 tptp.one @t58))) % 33.86/34.06 (step @p64 :rule symm :premises (@p63)) % 33.86/34.06 (step @p65 :rule refl :args (@t68)) % 33.86/34.06 (step @p66 :rule refl :args (tptp.one)) % 33.86/34.06 (step @p67 :rule instantiate :premises (@p17) :args (@t67)) % 33.86/34.06 (step @p68 :rule symm :premises (@p67)) % 33.86/34.06 (step @p69 :rule instantiate :premises (@p1) :args ((@list @t70 @t69))) % 33.86/34.06 (step @p70 :rule symm :premises (@p69)) % 33.86/34.06 (step @p71 :rule instantiate :premises (@p45) :args (@t71)) % 33.86/34.06 (step @p72 :rule symm :premises (@p71)) % 33.86/34.06 (step @p73 :rule refl :args (@t69)) % 33.86/34.06 (step @p74 :rule cong :premises (@p73 @p72) :args ((tptp.addition @t69 (tptp.addition @t70 @t70)))) % 33.86/34.06 (step @p75 :rule instantiate :premises (@p2) :args ((@list @t70 @t70 @t69))) % 33.86/34.06 (step @p76 :rule symm :premises (@p75)) % 33.86/34.06 (step @p77 :rule refl :args (@t70)) % 33.86/34.06 (step @p78 :rule trans :premises (@p67 @p69)) % 33.86/34.06 (step @p79 :rule eq-symm :args (@t18 @t1)) % 33.86/34.06 (step @p80 :rule cong :premises (@p79) :args (@t19)) % 33.86/34.06 (step @p81 :rule eq_resolve :premises (@p7 @p80)) % 33.86/34.06 (step @p82 :rule instantiate :premises (@p81) :args (@t61)) % 33.86/34.06 (step @p83 :rule symm :premises (@p82)) % 33.86/34.06 (step @p84 :rule trans :premises (@p83 @p78)) % 33.86/34.06 (step @p85 :rule cong :premises (@p84 @p77) :args (@t73)) % 33.86/34.06 (step @p86 :rule trans :premises (@p85 @p76 @p74 @p70 @p68)) % 33.86/34.06 (step @p87 :rule refl :args (@t57)) % 33.86/34.06 (step @p88 :rule cong :premises (@p87 @p86) :args ((tptp.multiplication @t57 @t73))) % 33.86/34.06 (step @p89 :rule instantiate :premises (@p8) :args ((@list @t57 @t72 @t70))) % 33.86/34.06 (step @p90 :rule symm :premises (@p89)) % 33.86/34.06 (step @p91 :rule refl :args (@t74)) % 33.86/34.06 (step @p92 :rule cong :premises (@p87 @p82) :args (@t68)) % 33.86/34.06 (step @p93 :rule cong :premises (@p92 @p91) :args (@t75)) % 33.86/34.06 (step @p94 :rule trans :premises (@p93 @p90 @p88)) % 33.86/34.06 (step @p95 :rule cong :premises (@p94 @p66) :args ((tptp.addition @t75 tptp.one))) % 33.86/34.06 (step @p96 :rule instantiate :premises (@p2) :args ((@list tptp.one @t74 @t68))) % 33.86/34.06 (step @p97 :rule instantiate :premises (@p1) :args ((@list tptp.one @t74))) % 33.86/34.06 (step @p98 :rule eq-symm :args (@t24 @t23)) % 33.86/34.06 (step @p99 :rule cong :premises (@p98) :args (@t25)) % 33.86/34.06 (step @p100 :rule eq_resolve :premises (@p11 @p99)) % 33.86/34.06 (step @p101 :rule instantiate :premises (@p100) :args (@t67)) % 33.86/34.06 (step @p102 :rule trans :premises (@p101 @p97)) % 33.86/34.06 (step @p103 :rule cong :premises (@p65 @p102) :args ((tptp.addition @t68 @t70))) % 33.86/34.06 (step @p104 :rule eq-symm :args (@t26 @t23)) % 33.86/34.06 (step @p105 :rule cong :premises (@p104) :args (@t27)) % 33.86/34.06 (step @p106 :rule eq_resolve :premises (@p12 @p105)) % 33.86/34.06 (step @p107 :rule instantiate :premises (@p106) :args (@t67)) % 33.86/34.06 (step @p108 :rule symm :premises (@p107)) % 33.86/34.06 (step @p109 :rule cong :premises (@p65 @p108) :args ((tptp.addition @t68 @t77))) % 33.86/34.06 (step @p110 :rule instantiate :premises (@p2) :args ((@list @t76 tptp.one @t68))) % 33.86/34.06 (step @p111 :rule symm :premises (@p110)) % 33.86/34.06 (step @p112 :rule refl :args (@t76)) % 33.86/34.06 (step @p113 :rule trans :premises (@p83 @p53)) % 33.86/34.06 (step @p114 :rule cong :premises (@p113 @p112) :args (@t78)) % 33.86/34.06 (step @p115 :rule trans :premises (@p114 @p111 @p109 @p103 @p96 @p95 @p54)) % 33.86/34.06 (step @p116 :rule cong :premises (@p115 @p66) :args ((tptp.addition @t78 tptp.one))) % 33.86/34.06 (step @p117 :rule symm :premises (@p114)) % 33.86/34.06 (step @p118 :rule symm :premises (@p109)) % 33.86/34.06 (step @p119 :rule instantiate :premises (@p1) :args ((@list @t68 @t70))) % 33.86/34.06 (step @p120 :rule symm :premises (@p119)) % 33.86/34.06 (step @p121 :rule trans :premises (@p120 @p118 @p110 @p117)) % 33.86/34.06 (step @p122 :rule cong :premises (@p121 @p66) :args ((tptp.addition (tptp.addition @t70 @t68) tptp.one))) % 33.86/34.06 (step @p123 :rule instantiate :premises (@p2) :args ((@list tptp.one @t68 @t70))) % 33.86/34.06 (step @p124 :rule cong :premises (@p77 @p53) :args ((tptp.addition @t70 @t58))) % 33.86/34.06 (step @p125 :rule cong :premises (@p77 @p83) :args ((tptp.addition @t70 @t72))) % 33.86/34.06 (step @p126 :rule instantiate :premises (@p1) :args ((@list @t72 @t70))) % 33.86/34.06 (step @p127 :rule symm :premises (@p85)) % 33.86/34.06 (step @p128 :rule symm :premises (@p74)) % 33.86/34.06 (step @p129 :rule trans :premises (@p67 @p69 @p128 @p75 @p127 @p126 @p125 @p124 @p123 @p122 @p116)) % 33.86/34.06 (step @p130 :rule cong :premises (@p129 @p65) :args (@t79)) % 33.86/34.06 (step @p131 :rule instantiate :premises (@p1) :args ((@list @t68 @t58))) % 33.86/34.06 (step @p132 :rule trans :premises (@p131 @p130 @p64 @p62 @p58 @p57)) % 33.86/34.06 (step @p133 :rule cong :premises (@p132 @p53) :args (@t81)) % 33.86/34.06 (step @p134 :rule trans :premises (@p133 @p56 @p52)) % 33.86/34.06 (step @p135 :rule true_elim :premises (@p134)) % 33.86/34.06 (step @p136 :rule cnf_or_pos :args (@t85)) % 33.86/34.06 (step @p137 :rule reordering :premises (@p136) :args ((or @t84 @t83 (not @t85)))) % 33.86/34.06 (step @p138 :rule chain_m_resolution :premises (@p137 @p135 @p35) :args (@t83 @t66 (@list @t81 @t85))) % 33.86/34.06 (step @p139 :rule true_intro :premises (@p138)) % 33.86/34.06 (step @p140 :rule cong :premises (@p108 @p41) :args ((tptp.multiplication @t77 @t58))) % 33.86/34.06 (step @p141 :rule instantiate :premises (@p9) :args ((@list tptp.one @t76 @t58))) % 33.86/34.06 (step @p142 :rule symm :premises (@p141)) % 33.86/34.06 (step @p143 :rule refl :args (@t86)) % 33.86/34.06 (step @p144 :rule trans :premises (@p83 @p40)) % 33.86/34.06 (step @p145 :rule instantiate :premises (@p81) :args (@t71)) % 33.86/34.06 (step @p146 :rule symm :premises (@p145)) % 33.86/34.06 (step @p147 :rule cong :premises (@p146 @p73) :args ((tptp.addition (tptp.multiplication tptp.one @t70) @t69))) % 33.86/34.06 (step @p148 :rule eq-symm :args (@t21 tptp.zero)) % 33.86/34.06 (step @p149 :rule cong :premises (@p148) :args (@t22)) % 33.86/34.06 (step @p150 :rule eq_resolve :premises (@p10 @p149)) % 33.86/34.06 (step @p151 :rule instantiate :premises (@p150) :args (@t61)) % 33.86/34.06 (step @p152 :rule symm :premises (@p151)) % 33.86/34.06 (step @p153 :rule cong :premises (@p41 @p152) :args (@t87)) % 33.86/34.06 (step @p154 :rule eq-symm :args (@t87 @t88)) % 33.86/34.06 (step @p155 :rule refl :args (@t15)) % 33.86/34.06 (step @p156 :rule cong :premises (@p155 @p154) :args ((=> @t15 @t89))) % 33.86/34.06 (assume-push @p317 @t15) % 33.86/34.06 (step @p158 :rule instantiate :premises (@p5) :args ((@list @t58 tptp.zero @t58))) % 33.86/34.06 (step-pop @p318 :rule scope :premises (@p158)) % 33.86/34.06 (step @p159 :rule process_scope :premises (@p318) :args (@t89)) % 33.86/34.06 (step @p161 :rule eq_resolve :premises (@p159 @p156)) % 33.86/34.06 (step @p162 :rule implies_elim :premises (@p161)) % 33.86/34.06 (step @p163 :rule chain_m_resolution :premises (@p162 @p5) :args ((= @t88 @t87) @t90 (@list @t15))) % 33.86/34.06 (step @p164 :rule trans :premises (@p163 @p153)) % 33.86/34.06 (step @p165 :rule cong :premises (@p145 @p164) :args (@t91)) % 33.86/34.06 (step @p166 :rule trans :premises (@p165 @p147 @p68)) % 33.86/34.06 (step @p167 :rule cong :premises (@p166 @p144) :args (@t92)) % 33.86/34.06 (step @p168 :rule trans :premises (@p167 @p58 @p57)) % 33.86/34.06 (step @p169 :rule trans :premises (@p168 @p82)) % 33.86/34.06 (step @p170 :rule cong :premises (@p169 @p143) :args ((tptp.addition @t92 @t86))) % 33.86/34.06 (step @p171 :rule instantiate :premises (@p2) :args ((@list @t86 @t72 @t91))) % 33.86/34.06 (step @p172 :rule symm :premises (@p140)) % 33.86/34.06 (step @p173 :rule trans :premises (@p172 @p141)) % 33.86/34.06 (step @p174 :rule refl :args (@t91)) % 33.86/34.06 (step @p175 :rule cong :premises (@p174 @p173) :args ((tptp.addition @t91 @t82))) % 33.86/34.06 (step @p176 :rule instantiate :premises (@p2) :args ((@list @t82 @t88 @t70))) % 33.86/34.06 (step @p177 :rule instantiate :premises (@p1) :args ((@list @t82 @t88))) % 33.86/34.06 (step @p178 :rule instantiate :premises (@p9) :args ((@list @t70 @t69 @t58))) % 33.86/34.06 (step @p179 :rule cong :premises (@p67 @p41) :args (@t93)) % 33.86/34.06 (step @p180 :rule trans :premises (@p179 @p178 @p177)) % 33.86/34.06 (step @p181 :rule cong :premises (@p77 @p180) :args ((tptp.addition @t70 @t93))) % 33.86/34.06 (step @p182 :rule instantiate :premises (@p1) :args ((@list @t93 @t70))) % 33.86/34.06 (step @p183 :rule eq-symm :args (@t7 @t1)) % 33.86/34.06 (step @p184 :rule cong :premises (@p183) :args (@t9)) % 33.86/34.06 (step @p185 :rule eq_resolve :premises (@p3 @p184)) % 33.86/34.06 (step @p186 :rule instantiate :premises (@p185) :args (@t61)) % 33.86/34.06 (step @p187 :rule symm :premises (@p186)) % 33.86/34.06 (step @p188 :rule cong :premises (@p41 @p187) :args ((tptp.multiplication @t58 (tptp.addition @t58 tptp.zero)))) % 33.86/34.06 (step @p189 :rule instantiate :premises (@p8) :args ((@list @t58 @t58 tptp.zero))) % 33.86/34.06 (step @p190 :rule symm :premises (@p189)) % 33.86/34.06 (step @p191 :rule trans :premises (@p190 @p188)) % 33.86/34.06 (step @p192 :rule cong :premises (@p191 @p77) :args ((tptp.addition (tptp.addition @t93 @t69) @t70))) % 33.86/34.06 (step @p193 :rule instantiate :premises (@p2) :args ((@list @t70 @t69 @t93))) % 33.86/34.06 (step @p194 :rule refl :args (@t93)) % 33.86/34.06 (step @p195 :rule cong :premises (@p194 @p78) :args ((tptp.addition @t93 @t58))) % 33.86/34.06 (step @p196 :rule instantiate :premises (@p1) :args ((@list @t93 @t58))) % 33.86/34.06 (step @p197 :rule symm :premises (@p196)) % 33.86/34.06 (step @p198 :rule instantiate :premises (@p26) :args ((@list @t58 @t93))) % 33.86/34.06 (step @p199 :rule instantiate :premises (@p30) :args (@t59)) % 33.86/34.06 (step @p200 :rule instantiate :premises (@p26) :args ((@list @t58 @t80))) % 33.86/34.06 (step @p201 :rule symm :premises (@p131)) % 33.86/34.06 (step @p202 :rule cong :premises (@p41 @p201) :args ((tptp.addition @t58 @t79))) % 33.86/34.06 (step @p203 :rule instantiate :premises (@p2) :args ((@list @t68 @t58 @t58))) % 33.86/34.06 (step @p204 :rule symm :premises (@p203)) % 33.86/34.06 (step @p205 :rule cong :premises (@p46 @p65) :args (@t79)) % 33.86/34.06 (step @p206 :rule trans :premises (@p131 @p205 @p204 @p202)) % 33.86/34.06 (step @p207 :rule cnf_equiv_pos2 :args (@t96)) % 33.86/34.06 (step @p208 :rule reordering :premises (@p207) :args ((or @t95 (not @t94) (not @t96)))) % 33.86/34.06 (step @p209 :rule chain_m_resolution :premises (@p208 @p206 @p200) :args (@t95 @t66 (@list @t94 @t96))) % 33.86/34.06 (step @p210 :rule cnf_or_pos :args (@t99)) % 33.86/34.06 (step @p211 :rule reordering :premises (@p210) :args ((or @t98 @t97 (not @t99)))) % 33.86/34.06 (step @p212 :rule chain_m_resolution :premises (@p211 @p209 @p199) :args (@t97 @t66 (@list @t95 @t99))) % 33.86/34.06 (step @p213 :rule cnf_equiv_pos1 :args (@t101)) % 33.86/34.06 (step @p214 :rule reordering :premises (@p213) :args ((or (not @t97) @t100 (not @t101)))) % 33.86/34.06 (step @p215 :rule chain_m_resolution :premises (@p214 @p212 @p198) :args (@t100 @t66 (@list @t97 @t101))) % 33.86/34.06 (step @p216 :rule trans :premises (@p215 @p197 @p195 @p193 @p192 @p182 @p181 @p176 @p175 @p171 @p170 @p142 @p140)) % 33.86/34.06 (step @p217 :rule cong :premises (@p216 @p41) :args (@t102)) % 33.86/34.06 (step @p218 :rule trans :premises (@p217 @p139)) % 33.86/34.06 (step @p219 :rule true_elim :premises (@p218)) % 33.86/34.06 (step @p220 :rule refl :args (@t103)) % 33.86/34.06 (step @p221 :rule bool-double-not-elim :args (@t56)) % 33.86/34.06 (step @p222 :rule nary_cong :premises (@p221 @p220) :args ((or (not @t104) @t103))) % 33.86/34.06 (assume-push @p319 @t104) % 33.86/34.06 (step @p224 :rule skolemize :premises (@p319)) % 33.86/34.06 (step-pop @p320 :rule scope :premises (@p224)) % 33.86/34.06 (step @p225 :rule process_scope :premises (@p320) :args (@t103)) % 33.86/34.06 (step @p227 :rule implies_elim :premises (@p225)) % 33.86/34.06 (step @p228 :rule eq_resolve :premises (@p227 @p222)) % 33.86/34.06 (step @p229 :rule chain_m_resolution :premises (@p228 @p219) :args (@t56 @t90 (@list @t102))) % 33.86/34.06 (step @p230 :rule alpha_equiv :args (@t105 @t106 (@list @t47))) % 33.86/34.06 (step @p231 :rule alpha_equiv :args (@t107 @t106 (@list @t54))) % 33.86/34.06 (step @p232 :rule nary_cong :premises (@p231 @p230) :args (@t108)) % 33.86/34.06 (step @p233 :rule quant-miniscope-and :args ((= @t45 @t108))) % 33.86/34.06 (step @p234 :rule trans :premises (@p233 @p232)) % 33.86/34.06 (step @p235 :rule cong :premises (@p234) :args (@t46)) % 33.86/34.06 (step @p236 :rule eq_resolve :premises (@p19 @p235)) % 33.86/34.06 (step @p237 :rule not_and :premises (@p236)) % 33.86/34.06 (step @p238 :rule chain_m_resolution :premises (@p237 @p229) :args (@t109 @t90 (@list @t56))) % 33.86/34.06 (step @p239 :rule refl :args (@t111)) % 33.86/34.06 (step @p240 :rule bool-double-not-elim :args (@t49)) % 33.86/34.06 (step @p241 :rule nary_cong :premises (@p240 @p239) :args ((or (not @t109) @t111))) % 33.86/34.06 (assume-push @p321 @t109) % 33.86/34.06 (step @p243 :rule skolemize :premises (@p321)) % 33.86/34.06 (step-pop @p322 :rule scope :premises (@p243)) % 33.86/34.06 (step @p244 :rule process_scope :premises (@p322) :args (@t111)) % 33.86/34.06 (step @p246 :rule implies_elim :premises (@p244)) % 33.86/34.06 (step @p247 :rule eq_resolve :premises (@p246 @p241)) % 33.86/34.06 (step @p248 :rule chain_m_resolution :premises (@p247 @p238) :args (@t111 (@list true) (@list @t49))) % 33.86/34.06 (step @p249 :rule cnf_or_pos :args (@t114)) % 33.86/34.06 (step @p250 :rule reordering :premises (@p249) :args ((or @t110 @t113 (not @t114)))) % 33.86/34.06 (step @p251 :rule chain_m_resolution :premises (@p250 @p248 @p31) :args (@t113 @t115 (@list @t110 @t114))) % 33.86/34.06 (step @p252 :rule cnf_equiv_pos2 :args (@t117)) % 33.86/34.06 (step @p253 :rule reordering :premises (@p252) :args ((or @t112 @t118 (not @t117)))) % 33.86/34.06 (step @p254 :rule chain_m_resolution :premises (@p253 @p251 @p27) :args (@t118 @t115 (@list @t112 @t117))) % 33.86/34.06 (step @p255 :rule instantiate :premises (@p45) :args ((@list @t51))) % 33.86/34.06 (step @p256 :rule instantiate :premises (@p2) :args ((@list @t52 @t51 @t51))) % 33.86/34.06 (step @p257 :rule refl :args (@t124)) % 33.86/34.06 (step @p258 :rule refl :args (@t126)) % 33.86/34.06 (step @p259 :rule bool-double-not-elim :args (@t116)) % 33.86/34.06 (step @p260 :rule refl :args (@t128)) % 33.86/34.06 (step @p261 :rule nary_cong :premises (@p260 @p259 @p258 @p257) :args ((or @t128 (not @t118) @t126 @t124))) % 33.86/34.06 (assume-push @p323 @t123) % 33.86/34.06 (assume-push @p324 @t124) % 33.86/34.06 (step @p264 :rule evaluate :args ((= false true))) % 33.86/34.06 (step @p265 :rule true_intro :premises (@p256)) % 33.86/34.06 (step @p266 :rule false_intro :premises (@p324)) % 33.86/34.06 (step @p267 :rule symm :premises (@p266)) % 33.86/34.06 (step @p268 :rule trans :premises (@p267 @p265)) % 33.86/34.06 (step @p269 false :rule eq_resolve :premises (@p268 @p264)) % 33.86/34.06 (step-pop @p325 :rule scope :premises (@p269)) % 33.86/34.06 (step-pop @p326 :rule scope :premises (@p325)) % 33.86/34.06 (step @p270 :rule process_scope :premises (@p326) :args (false)) % 33.86/34.06 (assume-push @p327 @t127) % 33.86/34.06 (assume-push @p328 @t118) % 33.86/34.06 (assume-push @p329 @t125) % 33.86/34.06 (assume-push @p330 @t123) % 33.86/34.06 (assume-push @p331 @t127) % 33.86/34.06 (assume-push @p332 @t125) % 33.86/34.06 (assume-push @p333 @t118) % 33.86/34.06 (step @p280 :rule bool-eq-false :args (@t123)) % 33.86/34.06 (step @p281 :rule symm :premises (@p280)) % 33.86/34.06 (step @p282 :rule eq-symm :args (@t120 @t122)) % 33.86/34.06 (step @p283 :rule cong :premises (@p282) :args ((not @t129))) % 33.86/34.06 (step @p284 :rule bool-eq-false :args (@t129)) % 33.86/34.06 (step @p285 :rule trans :premises (@p284 @p283)) % 33.86/34.06 (step @p286 :rule trans :premises (@p285 @p281)) % 33.86/34.06 (step @p287 :rule false_intro :premises (@p328)) % 33.86/34.06 (step @p288 :rule symm :premises (@p21)) % 33.86/34.06 (step @p289 :rule refl :args (@t51)) % 33.86/34.06 (step @p290 :rule cong :premises (@p289 @p288) :args (@t122)) % 33.86/34.06 (step @p291 :rule refl :args (@t52)) % 33.86/34.06 (step @p292 :rule symm :premises (@p255)) % 33.86/34.06 (step @p293 :rule cong :premises (@p292 @p291) :args (@t120)) % 33.86/34.06 (step @p294 :rule trans :premises (@p293 @p288)) % 33.86/34.06 (step @p295 :rule cong :premises (@p294 @p290) :args (@t129)) % 33.86/34.06 (step @p296 :rule trans :premises (@p295 @p287)) % 33.86/34.06 (step @p297 :rule eq_resolve :premises (@p296 @p286)) % 33.86/34.06 (step @p298 :rule false_elim :premises (@p297)) % 33.86/34.06 (step-pop @p334 :rule scope :premises (@p298)) % 33.86/34.06 (step-pop @p335 :rule scope :premises (@p334)) % 33.86/34.06 (step-pop @p336 :rule scope :premises (@p335)) % 33.86/34.06 (step @p299 :rule process_scope :premises (@p336) :args (@t124)) % 33.86/34.06 (step @p303 :rule and_intro :premises (@p21 @p255 @p328)) % 33.86/34.06 (step @p304 :rule modus_ponens :premises (@p303 @p299)) % 33.86/34.06 (step @p305 :rule and_intro :premises (@p256 @p304)) % 33.86/34.06 (step-pop @p337 :rule scope :premises (@p305)) % 33.86/34.06 (step-pop @p338 :rule scope :premises (@p337)) % 33.86/34.06 (step-pop @p339 :rule scope :premises (@p338)) % 33.86/34.06 (step-pop @p340 :rule scope :premises (@p339)) % 33.86/34.06 (step @p306 :rule process_scope :premises (@p340) :args (@t130)) % 33.86/34.06 (step @p311 :rule implies_elim :premises (@p306)) % 33.86/34.06 (step @p312 :rule resolution :premises (@p311 @p270) :args (true @t130)) % 33.86/34.06 (step @p313 :rule not_and :premises (@p312)) % 33.86/34.06 (step @p314 :rule eq_resolve :premises (@p313 @p261)) % 33.86/34.06 (step @p315 :rule reordering :premises (@p314) :args ((or @t116 @t128 @t126 @t124))) % 33.86/34.06 (step @p316 false :rule chain_m_resolution :premises (@p315 @p256 @p255 @p254 @p21) :args (false (@list false false true false) (@list @t123 @t125 @t116 @t127))) % 33.86/34.06 ) % 33.86/34.06 % SZS output end Proof % 33.86/34.06 % cvc5 exiting %------------------------------------------------------------------------------