%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : KLE040+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 : n015.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 08:28:11 AM UTC 2026 % Result : Theorem 0.59s 0.89s % Output : Proof 0.70s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : KLE040+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 % 0.16/0.34 % Computer : n015.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Tue Jun 2 05:11:19 EDT 2026 % 0.16/0.34 % CPUTime : % 0.28/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.59/0.89 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.59/0.89 % SZS status Theorem % 0.59/0.89 % SZS output start Proof % 0.59/0.89 ( % 0.59/0.89 (declare-sort $$unsorted 0) % 0.59/0.89 (declare-const tptp.star (-> $$unsorted $$unsorted)) % 0.59/0.89 (declare-const tptp.multiplication (-> $$unsorted $$unsorted $$unsorted)) % 0.59/0.89 (declare-const tptp.leq (-> $$unsorted $$unsorted Bool)) % 0.59/0.89 (declare-const tptp.zero $$unsorted) % 0.59/0.89 (declare-const tptp.one $$unsorted) % 0.59/0.89 (declare-const tptp.addition (-> $$unsorted $$unsorted $$unsorted)) % 0.59/0.89 (define @t1 () (@var "A" $$unsorted)) % 0.59/0.89 (define @t2 () (@var "B" $$unsorted)) % 0.59/0.89 (define @t3 () (tptp.addition @t1 @t2)) % 0.59/0.89 (define @t4 () (@list @t1 @t2)) % 0.59/0.89 (define @t5 () (@var "C" $$unsorted)) % 0.59/0.89 (define @t6 () (tptp.addition @t2 @t5)) % 0.59/0.89 (define @t7 () (forall (@list @t5 @t2 @t1) (= (tptp.addition @t1 @t6) (tptp.addition @t3 @t5)))) % 0.59/0.89 (define @t8 () (@list @t1)) % 0.59/0.89 (define @t9 () (tptp.addition @t1 @t1)) % 0.59/0.89 (define @t10 () (forall @t8 (= @t9 @t1))) % 0.59/0.89 (define @t11 () (tptp.multiplication @t1 @t2)) % 0.59/0.89 (define @t12 () (tptp.multiplication @t2 @t5)) % 0.59/0.89 (define @t13 () (@list @t1 @t2 @t5)) % 0.59/0.89 (define @t14 () (tptp.multiplication @t1 tptp.one)) % 0.59/0.89 (define @t15 () (forall @t8 (= @t14 @t1))) % 0.59/0.89 (define @t16 () (tptp.multiplication tptp.one @t1)) % 0.59/0.89 (define @t17 () (forall @t8 (= @t16 @t1))) % 0.59/0.89 (define @t18 () (tptp.multiplication @t1 @t5)) % 0.59/0.89 (define @t19 () (tptp.leq @t1 @t2)) % 0.59/0.89 (define @t20 () (= @t19 (= @t3 @t2))) % 0.59/0.89 (define @t21 () (forall @t4 @t20)) % 0.59/0.89 (define @t22 () (tptp.star @t1)) % 0.59/0.89 (define @t23 () (tptp.leq (tptp.multiplication @t22 @t5) @t2)) % 0.59/0.89 (define @t24 () (tptp.addition @t11 @t5)) % 0.59/0.89 (define @t25 () (tptp.leq @t24 @t2)) % 0.59/0.89 (define @t26 () (forall @t13 (=> @t25 @t23))) % 0.59/0.89 (define @t27 () (@var "X0" $$unsorted)) % 0.59/0.89 (define @t28 () (tptp.star @t27)) % 0.59/0.89 (define @t29 () (tptp.multiplication @t28 @t28)) % 0.59/0.89 (define @t30 () (tptp.leq @t28 @t29)) % 0.59/0.89 (define @t31 () (tptp.leq @t29 @t28)) % 0.59/0.89 (define @t32 () (@list @t27)) % 0.59/0.89 (define @t33 () (forall @t32 (and @t31 @t30))) % 0.59/0.89 (define @t34 () (not @t33)) % 0.59/0.89 (define @t35 () (@var "BOUND_VARIABLE_7536" $$unsorted)) % 0.59/0.89 (define @t36 () (tptp.star @t35)) % 0.59/0.89 (define @t37 () (forall (@list @t35) (tptp.leq @t36 (tptp.multiplication @t36 @t36)))) % 0.59/0.89 (define @t38 () (@quantifiers_skolemize @t37 0)) % 0.59/0.89 (define @t39 () (tptp.star @t38)) % 0.59/0.89 (define @t40 () (tptp.multiplication @t39 @t39)) % 0.59/0.89 (define @t41 () (tptp.addition tptp.one (tptp.multiplication @t39 @t38))) % 0.59/0.89 (define @t42 () (@list @t38)) % 0.59/0.89 (define @t43 () (tptp.addition @t41 @t39)) % 0.59/0.89 (define @t44 () (= @t39 @t43)) % 0.59/0.89 (define @t45 () (tptp.leq @t41 @t39)) % 0.59/0.89 (define @t46 () (= @t45 @t44)) % 0.59/0.89 (define @t47 () (@list false false)) % 0.59/0.89 (define @t48 () (tptp.multiplication @t38 @t39)) % 0.59/0.89 (define @t49 () (tptp.addition tptp.one @t48)) % 0.59/0.89 (define @t50 () (= @t39 (tptp.addition @t49 @t39))) % 0.59/0.89 (define @t51 () (tptp.leq @t49 @t39)) % 0.59/0.89 (define @t52 () (= @t51 @t50)) % 0.59/0.89 (define @t53 () (tptp.addition @t48 @t39)) % 0.59/0.89 (define @t54 () (tptp.multiplication @t53 @t39)) % 0.59/0.89 (define @t55 () (tptp.multiplication tptp.one @t39)) % 0.59/0.89 (define @t56 () (tptp.addition @t55 @t54)) % 0.59/0.89 (define @t57 () (@list @t39)) % 0.59/0.89 (define @t58 () (tptp.multiplication @t39 tptp.one)) % 0.59/0.89 (define @t59 () (tptp.addition @t58 @t39)) % 0.59/0.89 (define @t60 () (tptp.leq (tptp.addition @t48 tptp.one) @t39)) % 0.59/0.89 (define @t61 () (tptp.leq @t58 @t39)) % 0.59/0.89 (define @t62 () (not @t60)) % 0.59/0.89 (define @t63 () (or @t62 @t61)) % 0.59/0.89 (define @t64 () (= @t39 @t59)) % 0.59/0.89 (define @t65 () (= @t61 @t64)) % 0.59/0.89 (define @t66 () (= @t40 (tptp.addition @t39 @t40))) % 0.59/0.89 (define @t67 () (tptp.leq @t39 @t40)) % 0.59/0.89 (define @t68 () (= @t67 @t66)) % 0.59/0.89 (define @t69 () (not @t67)) % 0.59/0.89 (define @t70 () (not @t37)) % 0.59/0.89 (define @t71 () (@list false)) % 0.59/0.89 (define @t72 () (@var "BOUND_VARIABLE_7529" $$unsorted)) % 0.59/0.89 (define @t73 () (tptp.star @t72)) % 0.59/0.89 (define @t74 () (forall (@list @t72) (tptp.leq (tptp.multiplication @t73 @t73) @t73))) % 0.59/0.89 (define @t75 () (@quantifiers_skolemize @t74 0)) % 0.59/0.89 (define @t76 () (tptp.star @t75)) % 0.59/0.89 (define @t77 () (tptp.multiplication @t75 @t76)) % 0.59/0.89 (define @t78 () (tptp.addition @t77 @t76)) % 0.59/0.89 (define @t79 () (tptp.addition @t76 @t76)) % 0.59/0.89 (define @t80 () (tptp.multiplication @t76 @t75)) % 0.59/0.89 (define @t81 () (tptp.addition tptp.one @t80)) % 0.59/0.89 (define @t82 () (@list @t75)) % 0.59/0.89 (define @t83 () (tptp.addition @t81 @t76)) % 0.59/0.89 (define @t84 () (= @t76 @t83)) % 0.59/0.89 (define @t85 () (tptp.leq @t81 @t76)) % 0.59/0.89 (define @t86 () (= @t85 @t84)) % 0.59/0.89 (define @t87 () (tptp.addition (tptp.addition (tptp.multiplication @t75 @t81) @t77) @t79)) % 0.59/0.89 (define @t88 () (tptp.addition @t76 @t78)) % 0.59/0.89 (define @t89 () (= @t78 @t88)) % 0.59/0.89 (define @t90 () (tptp.leq @t76 @t78)) % 0.59/0.89 (define @t91 () (= @t90 @t89)) % 0.59/0.89 (define @t92 () (tptp.addition tptp.one @t78)) % 0.59/0.89 (define @t93 () (tptp.addition tptp.one @t77)) % 0.59/0.89 (define @t94 () (tptp.addition @t93 @t76)) % 0.59/0.89 (define @t95 () (= @t92 @t94)) % 0.59/0.89 (define @t96 () (@list @t7)) % 0.59/0.89 (define @t97 () (= @t76 @t94)) % 0.59/0.89 (define @t98 () (tptp.leq @t93 @t76)) % 0.59/0.89 (define @t99 () (= @t98 @t97)) % 0.59/0.89 (define @t100 () (tptp.addition @t80 @t76)) % 0.59/0.89 (define @t101 () (tptp.addition @t76 @t77)) % 0.59/0.89 (define @t102 () (tptp.addition @t76 @t80)) % 0.59/0.89 (define @t103 () (tptp.addition @t80 @t102)) % 0.59/0.89 (define @t104 () (tptp.addition @t77 @t79)) % 0.59/0.89 (define @t105 () (tptp.addition @t78 @t76)) % 0.59/0.89 (define @t106 () (= @t104 @t105)) % 0.59/0.89 (define @t107 () (tptp.addition tptp.one @t100)) % 0.59/0.89 (define @t108 () (= @t107 @t83)) % 0.59/0.89 (define @t109 () (@list @t76 @t80 tptp.one)) % 0.59/0.89 (define @t110 () (tptp.addition tptp.one (tptp.addition @t80 @t101))) % 0.59/0.89 (define @t111 () (tptp.addition @t81 @t101)) % 0.59/0.89 (define @t112 () (= @t110 @t111)) % 0.59/0.89 (define @t113 () (tptp.addition @t100 @t81)) % 0.59/0.89 (define @t114 () (tptp.leq @t78 @t76)) % 0.59/0.89 (define @t115 () (tptp.leq (tptp.multiplication @t76 @t76) @t76)) % 0.59/0.89 (define @t116 () (not @t114)) % 0.59/0.89 (define @t117 () (or @t116 @t115)) % 0.59/0.89 (define @t118 () (not @t115)) % 0.59/0.89 (define @t119 () (not @t74)) % 0.59/0.89 (define @t120 () (forall @t32 @t30)) % 0.59/0.89 (define @t121 () (@list @t27)) % 0.59/0.89 (define @t122 () (forall @t32 @t31)) % 0.59/0.89 (define @t123 () (and @t122 @t120)) % 0.59/0.89 (assume @p1 (forall @t4 (= @t3 (tptp.addition @t2 @t1)))) % 0.59/0.89 (assume @p2 @t7) % 0.59/0.89 (assume @p3 (forall @t8 (= (tptp.addition @t1 tptp.zero) @t1))) % 0.59/0.89 (assume @p4 @t10) % 0.59/0.89 (assume @p5 (forall @t13 (= (tptp.multiplication @t1 @t12) (tptp.multiplication @t11 @t5)))) % 0.59/0.89 (assume @p6 @t15) % 0.59/0.89 (assume @p7 @t17) % 0.59/0.89 (assume @p8 (forall @t13 (= (tptp.multiplication @t1 @t6) (tptp.addition @t11 @t18)))) % 0.59/0.89 (assume @p9 (forall @t13 (= (tptp.multiplication @t3 @t5) (tptp.addition @t18 @t12)))) % 0.59/0.89 (assume @p10 (forall @t8 (= (tptp.multiplication @t1 tptp.zero) tptp.zero))) % 0.59/0.89 (assume @p11 (forall @t8 (= (tptp.multiplication tptp.zero @t1) tptp.zero))) % 0.59/0.89 (assume @p12 @t21) % 0.59/0.89 (assume @p13 (forall @t8 (tptp.leq (tptp.addition tptp.one (tptp.multiplication @t1 @t22)) @t22))) % 0.59/0.89 (assume @p14 (forall @t8 (tptp.leq (tptp.addition tptp.one (tptp.multiplication @t22 @t1)) @t22))) % 0.59/0.89 (assume @p15 @t26) % 0.59/0.89 (assume @p16 (forall @t13 (=> (tptp.leq @t24 @t1) (tptp.leq (tptp.multiplication @t5 (tptp.star @t2)) @t1)))) % 0.59/0.89 (assume @p17 @t34) % 0.59/0.89 (assume @p18 true) % 0.59/0.89 (step @p19 :rule eq-symm :args (@t3 @t2)) % 0.59/0.89 (step @p20 :rule refl :args (@t19)) % 0.59/0.89 (step @p21 :rule cong :premises (@p20 @p19) :args (@t20)) % 0.59/0.89 (step @p22 :rule cong :premises (@p21) :args (@t21)) % 0.59/0.89 (step @p23 :rule eq_resolve :premises (@p12 @p22)) % 0.59/0.89 (step @p24 :rule instantiate :premises (@p23) :args ((@list @t39 @t40))) % 0.59/0.89 (step @p25 :rule refl :args (@t40)) % 0.59/0.89 (step @p26 :rule instantiate :premises (@p23) :args ((@list @t41 @t39))) % 0.59/0.89 (step @p27 :rule instantiate :premises (@p14) :args (@t42)) % 0.59/0.89 (step @p28 :rule cnf_equiv_pos1 :args (@t46)) % 0.59/0.89 (step @p29 :rule reordering :premises (@p28) :args ((or (not @t45) @t44 (not @t46)))) % 0.59/0.89 (step @p30 :rule chain_m_resolution :premises (@p29 @p27 @p26) :args (@t44 @t47 (@list @t45 @t46))) % 0.59/0.89 (step @p31 :rule symm :premises (@p30)) % 0.59/0.89 (step @p32 :rule cong :premises (@p31 @p25) :args ((tptp.addition @t43 @t40))) % 0.59/0.89 (step @p33 :rule refl :args (@t39)) % 0.59/0.89 (step @p34 :rule instantiate :premises (@p23) :args ((@list @t49 @t39))) % 0.59/0.89 (step @p35 :rule instantiate :premises (@p13) :args (@t42)) % 0.59/0.89 (step @p36 :rule cnf_equiv_pos1 :args (@t52)) % 0.59/0.89 (step @p37 :rule reordering :premises (@p36) :args ((or (not @t51) @t50 (not @t52)))) % 0.59/0.89 (step @p38 :rule chain_m_resolution :premises (@p37 @p35 @p34) :args (@t50 @t47 (@list @t51 @t52))) % 0.59/0.89 (step @p39 :rule symm :premises (@p38)) % 0.59/0.89 (step @p40 :rule instantiate :premises (@p2) :args ((@list @t39 @t48 tptp.one))) % 0.59/0.89 (step @p41 :rule trans :premises (@p40 @p39)) % 0.59/0.89 (step @p42 :rule cong :premises (@p41 @p33) :args ((tptp.multiplication (tptp.addition tptp.one @t53) @t39))) % 0.59/0.89 (step @p43 :rule instantiate :premises (@p9) :args ((@list tptp.one @t53 @t39))) % 0.59/0.89 (step @p44 :rule symm :premises (@p43)) % 0.59/0.89 (step @p45 :rule trans :premises (@p44 @p42)) % 0.59/0.89 (step @p46 :rule cong :premises (@p30 @p45) :args ((tptp.addition @t39 @t56))) % 0.59/0.89 (step @p47 :rule instantiate :premises (@p2) :args ((@list @t54 @t55 @t39))) % 0.59/0.89 (step @p48 :rule symm :premises (@p47)) % 0.59/0.89 (step @p49 :rule refl :args (@t54)) % 0.59/0.89 (step @p50 :rule eq-symm :args (@t16 @t1)) % 0.59/0.89 (step @p51 :rule cong :premises (@p50) :args (@t17)) % 0.59/0.89 (step @p52 :rule eq_resolve :premises (@p7 @p51)) % 0.59/0.89 (step @p53 :rule instantiate :premises (@p52) :args (@t57)) % 0.59/0.89 (step @p54 :rule eq-symm :args (@t14 @t1)) % 0.59/0.89 (step @p55 :rule cong :premises (@p54) :args (@t15)) % 0.59/0.89 (step @p56 :rule eq_resolve :premises (@p6 @p55)) % 0.59/0.89 (step @p57 :rule instantiate :premises (@p56) :args (@t57)) % 0.59/0.89 (step @p58 :rule symm :premises (@p57)) % 0.59/0.89 (step @p59 :rule cong :premises (@p58 @p53) :args (@t59)) % 0.59/0.89 (step @p60 :rule instantiate :premises (@p23) :args ((@list @t58 @t39))) % 0.59/0.89 (step @p61 :rule bool-impl-elim :args (@t25 @t23)) % 0.59/0.89 (step @p62 :rule cong :premises (@p61) :args (@t26)) % 0.59/0.89 (step @p63 :rule eq_resolve :premises (@p15 @p62)) % 0.59/0.89 (step @p64 :rule instantiate :premises (@p63) :args ((@list @t38 @t39 tptp.one))) % 0.59/0.89 (step @p65 :rule true_intro :premises (@p35)) % 0.59/0.89 (step @p66 :rule instantiate :premises (@p1) :args ((@list tptp.one @t48))) % 0.59/0.89 (step @p67 :rule symm :premises (@p66)) % 0.59/0.89 (step @p68 :rule cong :premises (@p67 @p33) :args (@t60)) % 0.59/0.89 (step @p69 :rule trans :premises (@p68 @p65)) % 0.59/0.89 (step @p70 :rule true_elim :premises (@p69)) % 0.59/0.89 (step @p71 :rule cnf_or_pos :args (@t63)) % 0.59/0.89 (step @p72 :rule reordering :premises (@p71) :args ((or @t62 @t61 (not @t63)))) % 0.59/0.89 (step @p73 :rule chain_m_resolution :premises (@p72 @p70 @p64) :args (@t61 @t47 (@list @t60 @t63))) % 0.59/0.89 (step @p74 :rule cnf_equiv_pos1 :args (@t65)) % 0.59/0.89 (step @p75 :rule reordering :premises (@p74) :args ((or (not @t61) @t64 (not @t65)))) % 0.59/0.89 (step @p76 :rule chain_m_resolution :premises (@p75 @p73 @p60) :args (@t64 @t47 (@list @t61 @t65))) % 0.59/0.89 (step @p77 :rule trans :premises (@p76 @p59)) % 0.59/0.89 (step @p78 :rule trans :premises (@p58 @p77)) % 0.59/0.89 (step @p79 :rule cong :premises (@p78 @p49) :args ((tptp.addition @t58 @t54))) % 0.59/0.89 (step @p80 :rule symm :premises (@p53)) % 0.59/0.89 (step @p81 :rule trans :premises (@p80 @p57)) % 0.59/0.89 (step @p82 :rule cong :premises (@p81 @p49) :args (@t56)) % 0.59/0.89 (step @p83 :rule symm :premises (@p42)) % 0.59/0.89 (step @p84 :rule trans :premises (@p83 @p43 @p82 @p79 @p48 @p46 @p32)) % 0.59/0.89 (step @p85 :rule cnf_equiv_pos2 :args (@t68)) % 0.59/0.89 (step @p86 :rule reordering :premises (@p85) :args ((or @t67 (not @t66) (not @t68)))) % 0.59/0.89 (step @p87 :rule chain_m_resolution :premises (@p86 @p84 @p24) :args (@t67 @t47 (@list @t66 @t68))) % 0.59/0.89 (step @p88 :rule refl :args (@t69)) % 0.59/0.89 (step @p89 :rule bool-double-not-elim :args (@t37)) % 0.59/0.89 (step @p90 :rule nary_cong :premises (@p89 @p88) :args ((or (not @t70) @t69))) % 0.59/0.89 (assume-push @p257 @t70) % 0.59/0.89 (step @p92 :rule skolemize :premises (@p257)) % 0.59/0.89 (step-pop @p258 :rule scope :premises (@p92)) % 0.59/0.89 (step @p93 :rule process_scope :premises (@p258) :args (@t69)) % 0.59/0.89 (step @p95 :rule implies_elim :premises (@p93)) % 0.59/0.89 (step @p96 :rule eq_resolve :premises (@p95 @p90)) % 0.59/0.89 (step @p97 :rule chain_m_resolution :premises (@p96 @p87) :args (@t37 @t71 (@list @t67))) % 0.59/0.89 (step @p98 :rule instantiate :premises (@p63) :args ((@list @t75 @t76 @t76))) % 0.59/0.89 (step @p99 :rule instantiate :premises (@p23) :args ((@list @t76 @t78))) % 0.59/0.89 (step @p100 :rule instantiate :premises (@p1) :args ((@list @t78 @t76))) % 0.59/0.89 (step @p101 :rule instantiate :premises (@p2) :args ((@list @t76 @t76 @t77))) % 0.59/0.89 (step @p102 :rule refl :args (@t79)) % 0.59/0.89 (step @p103 :rule instantiate :premises (@p23) :args ((@list @t81 @t76))) % 0.59/0.89 (step @p104 :rule instantiate :premises (@p14) :args (@t82)) % 0.59/0.89 (step @p105 :rule cnf_equiv_pos1 :args (@t86)) % 0.59/0.89 (step @p106 :rule reordering :premises (@p105) :args ((or (not @t85) @t84 (not @t86)))) % 0.59/0.89 (step @p107 :rule chain_m_resolution :premises (@p106 @p104 @p103) :args (@t84 @t47 (@list @t85 @t86))) % 0.59/0.89 (step @p108 :rule symm :premises (@p107)) % 0.59/0.89 (step @p109 :rule refl :args (@t75)) % 0.59/0.89 (step @p110 :rule cong :premises (@p109 @p108) :args ((tptp.multiplication @t75 @t83))) % 0.59/0.89 (step @p111 :rule instantiate :premises (@p8) :args ((@list @t75 @t81 @t76))) % 0.59/0.89 (step @p112 :rule symm :premises (@p111)) % 0.59/0.89 (step @p113 :rule trans :premises (@p112 @p110)) % 0.59/0.89 (step @p114 :rule cong :premises (@p113 @p102) :args (@t87)) % 0.59/0.89 (step @p115 :rule eq-symm :args (@t9 @t1)) % 0.59/0.89 (step @p116 :rule cong :premises (@p115) :args (@t10)) % 0.59/0.89 (step @p117 :rule eq_resolve :premises (@p4 @p116)) % 0.59/0.89 (step @p118 :rule instantiate :premises (@p117) :args ((@list @t76))) % 0.59/0.89 (step @p119 :rule symm :premises (@p113)) % 0.59/0.89 (step @p120 :rule cong :premises (@p119 @p118) :args (@t78)) % 0.59/0.89 (step @p121 :rule trans :premises (@p120 @p114 @p101 @p100)) % 0.59/0.89 (step @p122 :rule cnf_equiv_pos2 :args (@t91)) % 0.59/0.89 (step @p123 :rule reordering :premises (@p122) :args ((or @t90 (not @t89) (not @t91)))) % 0.59/0.89 (step @p124 :rule chain_m_resolution :premises (@p123 @p121 @p99) :args (@t90 @t47 (@list @t89 @t91))) % 0.59/0.89 (step @p125 :rule true_intro :premises (@p124)) % 0.59/0.89 (step @p126 :rule instantiate :premises (@p1) :args ((@list @t77 @t76))) % 0.59/0.89 (step @p127 :rule symm :premises (@p126)) % 0.59/0.89 (step @p128 :rule refl :args (@t77)) % 0.59/0.89 (step @p129 :rule cong :premises (@p108 @p128) :args ((tptp.addition @t83 @t77))) % 0.59/0.89 (step @p130 :rule instantiate :premises (@p2) :args ((@list @t77 @t76 @t81))) % 0.59/0.89 (step @p131 :rule instantiate :premises (@p1) :args ((@list tptp.one @t80))) % 0.59/0.89 (step @p132 :rule symm :premises (@p131)) % 0.59/0.89 (step @p133 :rule cong :premises (@p132 @p126) :args ((tptp.addition (tptp.addition @t80 tptp.one) @t78))) % 0.59/0.89 (step @p134 :rule instantiate :premises (@p2) :args ((@list @t78 tptp.one @t80))) % 0.59/0.89 (step @p135 :rule eq-symm :args (@t92 @t94)) % 0.59/0.89 (step @p136 :rule refl :args (@t7)) % 0.59/0.89 (step @p137 :rule cong :premises (@p136 @p135) :args ((=> @t7 @t95))) % 0.59/0.89 (assume-push @p259 @t7) % 0.59/0.89 (step @p139 :rule instantiate :premises (@p2) :args ((@list @t76 @t77 tptp.one))) % 0.59/0.89 (step-pop @p260 :rule scope :premises (@p139)) % 0.59/0.89 (step @p140 :rule process_scope :premises (@p260) :args (@t95)) % 0.59/0.89 (step @p142 :rule eq_resolve :premises (@p140 @p137)) % 0.59/0.89 (step @p143 :rule implies_elim :premises (@p142)) % 0.59/0.89 (step @p144 :rule chain_m_resolution :premises (@p143 @p2) :args ((= @t94 @t92) @t71 @t96)) % 0.59/0.89 (step @p145 :rule instantiate :premises (@p23) :args ((@list @t93 @t76))) % 0.59/0.89 (step @p146 :rule instantiate :premises (@p13) :args (@t82)) % 0.59/0.89 (step @p147 :rule cnf_equiv_pos1 :args (@t99)) % 0.59/0.89 (step @p148 :rule reordering :premises (@p147) :args ((or (not @t98) @t97 (not @t99)))) % 0.59/0.89 (step @p149 :rule chain_m_resolution :premises (@p148 @p146 @p145) :args (@t97 @t47 (@list @t98 @t99))) % 0.59/0.89 (step @p150 :rule trans :premises (@p149 @p144)) % 0.59/0.89 (step @p151 :rule refl :args (@t80)) % 0.59/0.89 (step @p152 :rule cong :premises (@p151 @p150) :args (@t100)) % 0.59/0.89 (step @p153 :rule trans :premises (@p152 @p134 @p133 @p130 @p129 @p127)) % 0.59/0.89 (step @p154 :rule refl :args (@t76)) % 0.59/0.89 (step @p155 :rule cong :premises (@p154 @p153) :args ((tptp.leq @t76 @t100))) % 0.59/0.89 (step @p156 :rule symm :premises (@p152)) % 0.59/0.89 (step @p157 :rule symm :premises (@p134)) % 0.59/0.89 (step @p158 :rule symm :premises (@p133)) % 0.59/0.89 (step @p159 :rule instantiate :premises (@p2) :args ((@list @t101 @t80 tptp.one))) % 0.59/0.89 (step @p160 :rule instantiate :premises (@p1) :args ((@list @t80 @t76))) % 0.59/0.89 (step @p161 :rule symm :premises (@p160)) % 0.59/0.89 (step @p162 :rule trans :premises (@p161 @p152 @p134 @p133 @p130 @p129)) % 0.59/0.89 (step @p163 :rule cong :premises (@p151 @p162) :args (@t103)) % 0.59/0.89 (step @p164 :rule symm :premises (@p130)) % 0.59/0.89 (step @p165 :rule symm :premises (@p129)) % 0.59/0.89 (step @p166 :rule symm :premises (@p118)) % 0.59/0.89 (step @p167 :rule cong :premises (@p113 @p166) :args (@t87)) % 0.59/0.89 (step @p168 :rule cong :premises (@p119 @p102) :args (@t104)) % 0.59/0.89 (step @p169 :rule eq-symm :args (@t104 @t105)) % 0.59/0.89 (step @p170 :rule cong :premises (@p136 @p169) :args ((=> @t7 @t106))) % 0.59/0.89 (assume-push @p261 @t7) % 0.59/0.89 (step-pop @p262 :rule scope :premises (@p101)) % 0.59/0.89 (step @p172 :rule process_scope :premises (@p262) :args (@t106)) % 0.59/0.89 (step @p174 :rule eq_resolve :premises (@p172 @p170)) % 0.59/0.89 (step @p175 :rule implies_elim :premises (@p174)) % 0.59/0.89 (step @p176 :rule chain_m_resolution :premises (@p175 @p2) :args ((= @t105 @t104) @t71 @t96)) % 0.59/0.89 (step @p177 :rule symm :premises (@p100)) % 0.59/0.89 (step @p178 :rule trans :premises (@p177 @p176 @p168 @p167 @p126 @p165 @p164 @p158 @p157 @p156 @p160)) % 0.59/0.89 (step @p179 :rule cong :premises (@p151 @p178) :args ((tptp.addition @t80 @t88))) % 0.59/0.89 (step @p180 :rule instantiate :premises (@p2) :args ((@list @t78 @t76 @t80))) % 0.59/0.89 (step @p181 :rule symm :premises (@p180)) % 0.59/0.89 (step @p182 :rule symm :premises (@p153)) % 0.59/0.89 (step @p183 :rule cong :premises (@p182 @p153) :args ((tptp.addition @t78 @t100))) % 0.59/0.89 (step @p184 :rule refl :args (@t78)) % 0.59/0.89 (step @p185 :rule cong :premises (@p184 @p182) :args ((tptp.addition @t78 @t78))) % 0.59/0.89 (step @p186 :rule instantiate :premises (@p117) :args ((@list @t78))) % 0.59/0.89 (step @p187 :rule trans :premises (@p152 @p134 @p133 @p130 @p129 @p127 @p186 @p185 @p183 @p181 @p179 @p163)) % 0.59/0.89 (step @p188 :rule refl :args (tptp.one)) % 0.59/0.89 (step @p189 :rule cong :premises (@p188 @p187) :args (@t107)) % 0.59/0.89 (step @p190 :rule eq-symm :args (@t107 @t83)) % 0.59/0.89 (step @p191 :rule cong :premises (@p136 @p190) :args ((=> @t7 @t108))) % 0.59/0.89 (assume-push @p263 @t7) % 0.59/0.89 (step @p193 :rule instantiate :premises (@p2) :args (@t109)) % 0.59/0.89 (step-pop @p264 :rule scope :premises (@p193)) % 0.59/0.89 (step @p194 :rule process_scope :premises (@p264) :args (@t108)) % 0.59/0.89 (step @p196 :rule eq_resolve :premises (@p194 @p191)) % 0.59/0.89 (step @p197 :rule implies_elim :premises (@p196)) % 0.59/0.89 (step @p198 :rule chain_m_resolution :premises (@p197 @p2) :args ((= @t83 @t107) @t71 @t96)) % 0.59/0.89 (step @p199 :rule trans :premises (@p107 @p198 @p189 @p159 @p158 @p157 @p156)) % 0.59/0.89 (step @p200 :rule symm :premises (@p199)) % 0.59/0.89 (step @p201 :rule symm :premises (@p186)) % 0.59/0.89 (step @p202 :rule symm :premises (@p185)) % 0.59/0.89 (step @p203 :rule symm :premises (@p183)) % 0.59/0.89 (step @p204 :rule symm :premises (@p179)) % 0.59/0.89 (step @p205 :rule trans :premises (@p204 @p180 @p203 @p202 @p201 @p126 @p165 @p164 @p158 @p157 @p156)) % 0.59/0.89 (step @p206 :rule trans :premises (@p205 @p200)) % 0.59/0.89 (step @p207 :rule cong :premises (@p206 @p199) :args ((tptp.leq @t103 @t76))) % 0.59/0.89 (step @p193 :rule instantiate :premises (@p2) :args (@t109)) % 0.59/0.89 (step @p208 :rule symm :premises (@p189)) % 0.59/0.89 (step @p209 :rule eq-symm :args (@t110 @t111)) % 0.59/0.89 (step @p210 :rule cong :premises (@p136 @p209) :args ((=> @t7 @t112))) % 0.59/0.89 (assume-push @p265 @t7) % 0.59/0.89 (step-pop @p266 :rule scope :premises (@p159)) % 0.59/0.89 (step @p212 :rule process_scope :premises (@p266) :args (@t112)) % 0.59/0.89 (step @p214 :rule eq_resolve :premises (@p212 @p210)) % 0.59/0.89 (step @p215 :rule implies_elim :premises (@p214)) % 0.59/0.89 (step @p216 :rule chain_m_resolution :premises (@p215 @p2) :args ((= @t111 @t110) @t71 @t96)) % 0.59/0.89 (step @p217 :rule trans :premises (@p126 @p165 @p164 @p216 @p208 @p193 @p108)) % 0.59/0.89 (step @p218 :rule symm :premises (@p205)) % 0.59/0.89 (step @p219 :rule trans :premises (@p182 @p218)) % 0.59/0.89 (step @p220 :rule cong :premises (@p219 @p217) :args ((tptp.leq @t78 @t78))) % 0.59/0.89 (step @p221 :rule symm :premises (@p217)) % 0.59/0.89 (step @p222 :rule cong :premises (@p108 @p151) :args ((tptp.addition @t83 @t80))) % 0.59/0.89 (step @p223 :rule instantiate :premises (@p2) :args ((@list @t80 @t76 @t81))) % 0.59/0.89 (step @p224 :rule instantiate :premises (@p1) :args ((@list @t81 @t102))) % 0.59/0.89 (step @p225 :rule symm :premises (@p224)) % 0.59/0.89 (step @p226 :rule refl :args (@t81)) % 0.59/0.89 (step @p227 :rule cong :premises (@p160 @p226) :args (@t113)) % 0.59/0.89 (step @p228 :rule trans :premises (@p227 @p225 @p223 @p222 @p161)) % 0.59/0.89 (step @p229 :rule trans :premises (@p228 @p153)) % 0.59/0.89 (step @p230 :rule cong :premises (@p229 @p221) :args ((tptp.leq @t113 @t76))) % 0.59/0.89 (step @p231 :rule symm :premises (@p229)) % 0.59/0.89 (step @p232 :rule cong :premises (@p231 @p154) :args (@t114)) % 0.59/0.89 (step @p233 :rule trans :premises (@p232 @p230 @p220 @p207 @p155 @p125)) % 0.59/0.89 (step @p234 :rule true_elim :premises (@p233)) % 0.59/0.89 (step @p235 :rule cnf_or_pos :args (@t117)) % 0.59/0.89 (step @p236 :rule reordering :premises (@p235) :args ((or @t115 @t116 (not @t117)))) % 0.59/0.89 (step @p237 :rule chain_m_resolution :premises (@p236 @p234 @p98) :args (@t115 @t47 (@list @t114 @t117))) % 0.59/0.89 (step @p238 :rule refl :args (@t118)) % 0.59/0.89 (step @p239 :rule bool-double-not-elim :args (@t74)) % 0.59/0.89 (step @p240 :rule nary_cong :premises (@p239 @p238) :args ((or (not @t119) @t118))) % 0.59/0.89 (assume-push @p267 @t119) % 0.59/0.89 (step @p242 :rule skolemize :premises (@p267)) % 0.59/0.89 (step-pop @p268 :rule scope :premises (@p242)) % 0.59/0.89 (step @p243 :rule process_scope :premises (@p268) :args (@t118)) % 0.59/0.89 (step @p245 :rule implies_elim :premises (@p243)) % 0.59/0.89 (step @p246 :rule eq_resolve :premises (@p245 @p240)) % 0.59/0.89 (step @p247 :rule chain_m_resolution :premises (@p246 @p237) :args (@t74 @t71 (@list @t115))) % 0.70/0.90 (step @p248 :rule alpha_equiv :args (@t120 @t121 (@list @t35))) % 0.70/0.90 (step @p249 :rule alpha_equiv :args (@t122 @t121 (@list @t72))) % 0.70/0.90 (step @p250 :rule nary_cong :premises (@p249 @p248) :args (@t123)) % 0.70/0.90 (step @p251 :rule quant-miniscope-and :args ((= @t33 @t123))) % 0.70/0.90 (step @p252 :rule trans :premises (@p251 @p250)) % 0.70/0.90 (step @p253 :rule cong :premises (@p252) :args (@t34)) % 0.70/0.90 (step @p254 :rule eq_resolve :premises (@p17 @p253)) % 0.70/0.90 (step @p255 :rule not_and :premises (@p254)) % 0.70/0.90 (step @p256 false :rule chain_m_resolution :premises (@p255 @p247 @p97) :args (false @t47 (@list @t74 @t37))) % 0.70/0.90 ) % 0.70/0.90 % SZS output end Proof % 0.70/0.90 % cvc5 exiting %------------------------------------------------------------------------------