%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : KLE139+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 : n003.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 08:28:22 AM UTC 2026 % Result : Theorem 0.72s 0.97s % Output : Proof 0.72s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : KLE139+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 : n003.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 05:19:29 EDT 2026 % 0.16/0.35 % CPUTime : % 0.29/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.72/0.97 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.72/0.97 % SZS status Theorem % 0.72/0.97 % SZS output start Proof % 0.72/0.97 ( % 0.72/0.97 (declare-sort $$unsorted 0) % 0.72/0.97 (declare-const tptp.strong_iteration (-> $$unsorted $$unsorted)) % 0.72/0.97 (declare-const tptp.star (-> $$unsorted $$unsorted)) % 0.72/0.97 (declare-const tptp.leq (-> $$unsorted $$unsorted Bool)) % 0.72/0.97 (declare-const tptp.multiplication (-> $$unsorted $$unsorted $$unsorted)) % 0.72/0.97 (declare-const tptp.zero $$unsorted) % 0.72/0.97 (declare-const tptp.one $$unsorted) % 0.72/0.97 (declare-const tptp.addition (-> $$unsorted $$unsorted $$unsorted)) % 0.72/0.97 (define @t1 () (@var "A" $$unsorted)) % 0.72/0.97 (define @t2 () (@var "B" $$unsorted)) % 0.72/0.97 (define @t3 () (tptp.addition @t1 @t2)) % 0.72/0.97 (define @t4 () (@list @t1 @t2)) % 0.72/0.97 (define @t5 () (@var "C" $$unsorted)) % 0.72/0.97 (define @t6 () (tptp.addition @t2 @t5)) % 0.72/0.97 (define @t7 () (@list @t1)) % 0.72/0.97 (define @t8 () (tptp.addition @t1 @t1)) % 0.72/0.97 (define @t9 () (forall @t7 (= @t8 @t1))) % 0.72/0.97 (define @t10 () (tptp.multiplication @t1 @t2)) % 0.72/0.97 (define @t11 () (tptp.multiplication @t2 @t5)) % 0.72/0.97 (define @t12 () (@list @t1 @t2 @t5)) % 0.72/0.97 (define @t13 () (tptp.multiplication @t1 tptp.one)) % 0.72/0.97 (define @t14 () (forall @t7 (= @t13 @t1))) % 0.72/0.97 (define @t15 () (tptp.multiplication tptp.one @t1)) % 0.72/0.97 (define @t16 () (forall @t7 (= @t15 @t1))) % 0.72/0.97 (define @t17 () (tptp.multiplication @t1 @t5)) % 0.72/0.97 (define @t18 () (tptp.multiplication tptp.zero @t1)) % 0.72/0.97 (define @t19 () (forall @t7 (= @t18 tptp.zero))) % 0.72/0.97 (define @t20 () (tptp.star @t1)) % 0.72/0.97 (define @t21 () (tptp.addition tptp.one (tptp.multiplication @t20 @t1))) % 0.72/0.97 (define @t22 () (forall @t7 (= @t21 @t20))) % 0.72/0.97 (define @t23 () (tptp.addition @t17 @t2)) % 0.72/0.97 (define @t24 () (tptp.strong_iteration @t1)) % 0.72/0.97 (define @t25 () (tptp.leq @t1 @t2)) % 0.72/0.97 (define @t26 () (= @t25 (= @t3 @t2))) % 0.72/0.97 (define @t27 () (forall @t4 @t26)) % 0.72/0.97 (define @t28 () (@var "X0" $$unsorted)) % 0.72/0.97 (define @t29 () (tptp.strong_iteration @t28)) % 0.72/0.97 (define @t30 () (tptp.addition (tptp.multiplication @t29 @t28) tptp.one)) % 0.72/0.97 (define @t31 () (tptp.leq @t30 @t29)) % 0.72/0.97 (define @t32 () (tptp.leq @t29 @t30)) % 0.72/0.97 (define @t33 () (@list @t28)) % 0.72/0.97 (define @t34 () (forall @t33 (and @t32 @t31))) % 0.72/0.97 (define @t35 () (not @t34)) % 0.72/0.97 (define @t36 () (@var "BOUND_VARIABLE_7550" $$unsorted)) % 0.72/0.97 (define @t37 () (tptp.strong_iteration @t36)) % 0.72/0.97 (define @t38 () (forall (@list @t36) (tptp.leq @t37 (tptp.addition (tptp.multiplication @t37 @t36) tptp.one)))) % 0.72/0.97 (define @t39 () (@quantifiers_skolemize @t38 0)) % 0.72/0.97 (define @t40 () (tptp.strong_iteration @t39)) % 0.72/0.97 (define @t41 () (tptp.multiplication @t40 @t39)) % 0.72/0.97 (define @t42 () (tptp.addition @t41 tptp.one)) % 0.72/0.97 (define @t43 () (@list @t39)) % 0.72/0.97 (define @t44 () (tptp.multiplication @t40 tptp.zero)) % 0.72/0.97 (define @t45 () (tptp.star @t39)) % 0.72/0.97 (define @t46 () (tptp.addition @t45 @t44)) % 0.72/0.97 (define @t47 () (tptp.multiplication @t39 @t40)) % 0.72/0.97 (define @t48 () (tptp.multiplication @t44 @t39)) % 0.72/0.97 (define @t49 () (tptp.multiplication @t45 @t39)) % 0.72/0.97 (define @t50 () (tptp.multiplication @t44 tptp.zero)) % 0.72/0.97 (define @t51 () (tptp.multiplication @t45 tptp.zero)) % 0.72/0.97 (define @t52 () (tptp.addition tptp.one @t49)) % 0.72/0.97 (define @t53 () (tptp.multiplication tptp.zero @t39)) % 0.72/0.97 (define @t54 () (tptp.multiplication @t40 tptp.one)) % 0.72/0.97 (define @t55 () (@list tptp.zero)) % 0.72/0.97 (define @t56 () (tptp.multiplication tptp.zero tptp.zero)) % 0.72/0.97 (define @t57 () (tptp.multiplication @t56 @t39)) % 0.72/0.97 (define @t58 () (tptp.multiplication tptp.one tptp.zero)) % 0.72/0.97 (define @t59 () (= @t42 (tptp.addition @t40 @t42))) % 0.72/0.97 (define @t60 () (tptp.leq @t40 @t42)) % 0.72/0.97 (define @t61 () (= @t60 @t59)) % 0.72/0.97 (define @t62 () (@list false false)) % 0.72/0.97 (define @t63 () (not @t60)) % 0.72/0.97 (define @t64 () (not @t38)) % 0.72/0.97 (define @t65 () (@list false)) % 0.72/0.97 (define @t66 () (@var "BOUND_VARIABLE_7558" $$unsorted)) % 0.72/0.97 (define @t67 () (tptp.strong_iteration @t66)) % 0.72/0.97 (define @t68 () (forall (@list @t66) (tptp.leq (tptp.addition (tptp.multiplication @t67 @t66) tptp.one) @t67))) % 0.72/0.97 (define @t69 () (@quantifiers_skolemize @t68 0)) % 0.72/0.97 (define @t70 () (tptp.strong_iteration @t69)) % 0.72/0.97 (define @t71 () (tptp.multiplication @t70 @t69)) % 0.72/0.97 (define @t72 () (tptp.addition @t71 tptp.one)) % 0.72/0.97 (define @t73 () (@list @t72 @t70)) % 0.72/0.97 (define @t74 () (@list @t69)) % 0.72/0.97 (define @t75 () (tptp.multiplication @t70 tptp.zero)) % 0.72/0.97 (define @t76 () (tptp.star @t69)) % 0.72/0.97 (define @t77 () (tptp.addition @t76 @t75)) % 0.72/0.97 (define @t78 () (tptp.multiplication @t75 @t69)) % 0.72/0.97 (define @t79 () (tptp.multiplication @t76 @t69)) % 0.72/0.97 (define @t80 () (tptp.multiplication @t75 tptp.zero)) % 0.72/0.97 (define @t81 () (tptp.multiplication @t76 tptp.zero)) % 0.72/0.97 (define @t82 () (tptp.addition tptp.one @t79)) % 0.72/0.97 (define @t83 () (tptp.multiplication tptp.zero @t69)) % 0.72/0.97 (define @t84 () (tptp.multiplication @t70 tptp.one)) % 0.72/0.97 (define @t85 () (tptp.multiplication @t56 @t69)) % 0.72/0.97 (define @t86 () (= @t70 (tptp.addition @t72 @t70))) % 0.72/0.97 (define @t87 () (tptp.leq @t72 @t70)) % 0.72/0.97 (define @t88 () (= @t87 @t86)) % 0.72/0.97 (define @t89 () (not @t87)) % 0.72/0.97 (define @t90 () (not @t68)) % 0.72/0.97 (define @t91 () (forall @t33 @t31)) % 0.72/0.97 (define @t92 () (@list @t28)) % 0.72/0.97 (define @t93 () (forall @t33 @t32)) % 0.72/0.97 (define @t94 () (and @t93 @t91)) % 0.72/0.97 (assume @p1 (forall @t4 (= @t3 (tptp.addition @t2 @t1)))) % 0.72/0.97 (assume @p2 (forall (@list @t5 @t2 @t1) (= (tptp.addition @t1 @t6) (tptp.addition @t3 @t5)))) % 0.72/0.97 (assume @p3 (forall @t7 (= (tptp.addition @t1 tptp.zero) @t1))) % 0.72/0.97 (assume @p4 @t9) % 0.72/0.97 (assume @p5 (forall @t12 (= (tptp.multiplication @t1 @t11) (tptp.multiplication @t10 @t5)))) % 0.72/0.97 (assume @p6 @t14) % 0.72/0.97 (assume @p7 @t16) % 0.72/0.97 (assume @p8 (forall @t12 (= (tptp.multiplication @t1 @t6) (tptp.addition @t10 @t17)))) % 0.72/0.97 (assume @p9 (forall @t12 (= (tptp.multiplication @t3 @t5) (tptp.addition @t17 @t11)))) % 0.72/0.97 (assume @p10 @t19) % 0.72/0.97 (assume @p11 (forall @t7 (= (tptp.addition tptp.one (tptp.multiplication @t1 @t20)) @t20))) % 0.72/0.97 (assume @p12 @t22) % 0.72/0.97 (assume @p13 (forall @t12 (=> (tptp.leq @t23 @t5) (tptp.leq (tptp.multiplication @t20 @t2) @t5)))) % 0.72/0.97 (assume @p14 (forall @t12 (=> (tptp.leq (tptp.addition (tptp.multiplication @t5 @t1) @t2) @t5) (tptp.leq (tptp.multiplication @t2 @t20) @t5)))) % 0.72/0.97 (assume @p15 (forall @t7 (= @t24 (tptp.addition (tptp.multiplication @t1 @t24) tptp.one)))) % 0.72/0.97 (assume @p16 (forall @t12 (=> (tptp.leq @t5 @t23) (tptp.leq @t5 (tptp.multiplication @t24 @t2))))) % 0.72/0.97 (assume @p17 (forall @t7 (= @t24 (tptp.addition @t20 (tptp.multiplication @t24 tptp.zero))))) % 0.72/0.97 (assume @p18 @t27) % 0.72/0.97 (assume @p19 @t35) % 0.72/0.97 (assume @p20 true) % 0.72/0.97 (step @p21 :rule eq-symm :args (@t3 @t2)) % 0.72/0.97 (step @p22 :rule refl :args (@t25)) % 0.72/0.97 (step @p23 :rule cong :premises (@p22 @p21) :args (@t26)) % 0.72/0.97 (step @p24 :rule cong :premises (@p23) :args (@t27)) % 0.72/0.97 (step @p25 :rule eq_resolve :premises (@p18 @p24)) % 0.72/0.97 (step @p26 :rule instantiate :premises (@p25) :args ((@list @t40 @t42))) % 0.72/0.97 (step @p27 :rule refl :args (@t42)) % 0.72/0.97 (step @p28 :rule instantiate :premises (@p17) :args (@t43)) % 0.72/0.97 (step @p29 :rule symm :premises (@p28)) % 0.72/0.97 (step @p30 :rule cong :premises (@p29 @p27) :args ((tptp.addition @t46 @t42))) % 0.72/0.97 (step @p31 :rule eq-symm :args (@t13 @t1)) % 0.72/0.97 (step @p32 :rule cong :premises (@p31) :args (@t14)) % 0.72/0.97 (step @p33 :rule eq_resolve :premises (@p6 @p32)) % 0.72/0.97 (step @p34 :rule instantiate :premises (@p33) :args ((@list @t40))) % 0.72/0.97 (step @p35 :rule symm :premises (@p34)) % 0.72/0.97 (step @p36 :rule refl :args (tptp.one)) % 0.72/0.97 (step @p37 :rule instantiate :premises (@p15) :args (@t43)) % 0.72/0.97 (step @p38 :rule symm :premises (@p37)) % 0.72/0.97 (step @p39 :rule instantiate :premises (@p1) :args ((@list @t47 tptp.one))) % 0.72/0.97 (step @p40 :rule symm :premises (@p39)) % 0.72/0.97 (step @p41 :rule trans :premises (@p40 @p38)) % 0.72/0.97 (step @p42 :rule cong :premises (@p41 @p36) :args ((tptp.multiplication (tptp.addition tptp.one @t47) tptp.one))) % 0.72/0.97 (step @p43 :rule instantiate :premises (@p9) :args ((@list tptp.one @t47 tptp.one))) % 0.72/0.97 (step @p44 :rule symm :premises (@p43)) % 0.72/0.97 (step @p45 :rule trans :premises (@p44 @p42 @p35)) % 0.72/0.97 (step @p46 :rule trans :premises (@p45 @p28)) % 0.72/0.97 (step @p47 :rule cong :premises (@p46 @p27) :args ((tptp.addition (tptp.addition (tptp.multiplication tptp.one tptp.one) (tptp.multiplication @t47 tptp.one)) @t42))) % 0.72/0.97 (step @p48 :rule instantiate :premises (@p1) :args ((@list @t41 tptp.one))) % 0.72/0.97 (step @p49 :rule symm :premises (@p48)) % 0.72/0.97 (step @p50 :rule refl :args (@t39)) % 0.72/0.97 (step @p51 :rule cong :premises (@p29 @p50) :args ((tptp.multiplication @t46 @t39))) % 0.72/0.97 (step @p52 :rule instantiate :premises (@p9) :args ((@list @t45 @t44 @t39))) % 0.72/0.97 (step @p53 :rule symm :premises (@p52)) % 0.72/0.97 (step @p54 :rule trans :premises (@p53 @p51)) % 0.72/0.97 (step @p55 :rule cong :premises (@p36 @p54) :args ((tptp.addition tptp.one (tptp.addition @t49 @t48)))) % 0.72/0.97 (step @p56 :rule instantiate :premises (@p2) :args ((@list @t48 @t49 tptp.one))) % 0.72/0.97 (step @p57 :rule symm :premises (@p56)) % 0.72/0.97 (step @p58 :rule refl :args (tptp.zero)) % 0.72/0.97 (step @p59 :rule cong :premises (@p29 @p58) :args ((tptp.multiplication @t46 tptp.zero))) % 0.72/0.97 (step @p60 :rule instantiate :premises (@p9) :args ((@list @t45 @t44 tptp.zero))) % 0.72/0.97 (step @p61 :rule symm :premises (@p60)) % 0.72/0.97 (step @p62 :rule trans :premises (@p61 @p59)) % 0.72/0.97 (step @p63 :rule cong :premises (@p62 @p50) :args ((tptp.multiplication (tptp.addition @t51 @t50) @t39))) % 0.72/0.97 (step @p64 :rule instantiate :premises (@p9) :args ((@list @t51 @t50 @t39))) % 0.72/0.97 (step @p65 :rule symm :premises (@p64)) % 0.72/0.97 (step @p66 :rule trans :premises (@p65 @p63)) % 0.72/0.97 (step @p67 :rule refl :args (@t52)) % 0.72/0.97 (step @p68 :rule cong :premises (@p67 @p66) :args ((tptp.addition @t52 (tptp.addition (tptp.multiplication @t51 @t39) (tptp.multiplication @t50 @t39))))) % 0.72/0.97 (step @p69 :rule symm :premises (@p63)) % 0.72/0.97 (step @p70 :rule instantiate :premises (@p5) :args ((@list @t40 tptp.zero @t39))) % 0.72/0.97 (step @p71 :rule refl :args (@t53)) % 0.72/0.97 (step @p72 :rule cong :premises (@p35 @p71) :args ((tptp.multiplication @t54 @t53))) % 0.72/0.97 (step @p73 :rule eq-symm :args (@t18 tptp.zero)) % 0.72/0.97 (step @p74 :rule cong :premises (@p73) :args (@t19)) % 0.72/0.97 (step @p75 :rule eq_resolve :premises (@p10 @p74)) % 0.72/0.97 (step @p76 :rule instantiate :premises (@p75) :args (@t55)) % 0.72/0.97 (step @p77 :rule symm :premises (@p76)) % 0.72/0.97 (step @p78 :rule cong :premises (@p77 @p50) :args (@t57)) % 0.72/0.97 (step @p79 :rule cong :premises (@p34 @p78) :args ((tptp.multiplication @t40 @t57))) % 0.72/0.97 (step @p80 :rule symm :premises (@p78)) % 0.72/0.97 (step @p81 :rule instantiate :premises (@p75) :args (@t43)) % 0.72/0.97 (step @p82 :rule eq-symm :args (@t15 @t1)) % 0.72/0.97 (step @p83 :rule cong :premises (@p82) :args (@t16)) % 0.72/0.97 (step @p84 :rule eq_resolve :premises (@p7 @p83)) % 0.72/0.97 (step @p85 :rule instantiate :premises (@p84) :args (@t55)) % 0.72/0.97 (step @p86 :rule symm :premises (@p85)) % 0.72/0.97 (step @p87 :rule trans :premises (@p86 @p81 @p80)) % 0.72/0.97 (step @p88 :rule refl :args (@t40)) % 0.72/0.97 (step @p89 :rule cong :premises (@p88 @p87) :args ((tptp.multiplication @t40 @t58))) % 0.72/0.97 (step @p90 :rule instantiate :premises (@p5) :args ((@list @t40 tptp.one tptp.zero))) % 0.72/0.97 (step @p91 :rule symm :premises (@p90)) % 0.72/0.97 (step @p92 :rule cong :premises (@p34 @p58) :args (@t44)) % 0.72/0.97 (step @p93 :rule trans :premises (@p92 @p91 @p89 @p79 @p72 @p70 @p69 @p64)) % 0.72/0.97 (step @p94 :rule eq-symm :args (@t21 @t20)) % 0.72/0.97 (step @p95 :rule cong :premises (@p94) :args (@t22)) % 0.72/0.97 (step @p96 :rule eq_resolve :premises (@p12 @p95)) % 0.72/0.97 (step @p97 :rule instantiate :premises (@p96) :args (@t43)) % 0.72/0.97 (step @p98 :rule cong :premises (@p97 @p93) :args (@t46)) % 0.72/0.97 (step @p99 :rule trans :premises (@p38 @p28 @p98 @p68 @p57 @p55 @p49)) % 0.72/0.97 (step @p100 :rule symm :premises (@p45)) % 0.72/0.97 (step @p101 :rule cong :premises (@p100 @p99) :args ((tptp.addition @t40 (tptp.addition @t47 tptp.one)))) % 0.72/0.97 (step @p102 :rule trans :premises (@p35 @p37)) % 0.72/0.97 (step @p103 :rule cong :premises (@p35 @p102) :args ((tptp.addition @t54 @t54))) % 0.72/0.97 (step @p104 :rule eq-symm :args (@t8 @t1)) % 0.72/0.97 (step @p105 :rule cong :premises (@p104) :args (@t9)) % 0.72/0.97 (step @p106 :rule eq_resolve :premises (@p4 @p105)) % 0.72/0.97 (step @p107 :rule instantiate :premises (@p106) :args ((@list @t54))) % 0.72/0.97 (step @p108 :rule symm :premises (@p98)) % 0.72/0.97 (step @p109 :rule symm :premises (@p68)) % 0.72/0.97 (step @p110 :rule symm :premises (@p55)) % 0.72/0.97 (step @p111 :rule trans :premises (@p48 @p110 @p56 @p109 @p108 @p29 @p34 @p107 @p103 @p101 @p47 @p30)) % 0.72/0.97 (step @p112 :rule cnf_equiv_pos2 :args (@t61)) % 0.72/0.97 (step @p113 :rule reordering :premises (@p112) :args ((or @t60 (not @t59) (not @t61)))) % 0.72/0.97 (step @p114 :rule chain_m_resolution :premises (@p113 @p111 @p26) :args (@t60 @t62 (@list @t59 @t61))) % 0.72/0.97 (step @p115 :rule refl :args (@t63)) % 0.72/0.97 (step @p116 :rule bool-double-not-elim :args (@t38)) % 0.72/0.97 (step @p117 :rule nary_cong :premises (@p116 @p115) :args ((or (not @t64) @t63))) % 0.72/0.97 (assume-push @p209 @t64) % 0.72/0.97 (step @p119 :rule skolemize :premises (@p209)) % 0.72/0.97 (step-pop @p210 :rule scope :premises (@p119)) % 0.72/0.97 (step @p120 :rule process_scope :premises (@p210) :args (@t63)) % 0.72/0.97 (step @p122 :rule implies_elim :premises (@p120)) % 0.72/0.97 (step @p123 :rule eq_resolve :premises (@p122 @p117)) % 0.72/0.97 (step @p124 :rule chain_m_resolution :premises (@p123 @p114) :args (@t38 @t65 (@list @t60))) % 0.72/0.97 (step @p125 :rule instantiate :premises (@p25) :args (@t73)) % 0.72/0.97 (step @p126 :rule instantiate :premises (@p1) :args (@t73)) % 0.72/0.97 (step @p127 :rule symm :premises (@p126)) % 0.72/0.97 (step @p128 :rule refl :args (@t72)) % 0.72/0.97 (step @p129 :rule instantiate :premises (@p33) :args ((@list @t70))) % 0.72/0.97 (step @p130 :rule symm :premises (@p129)) % 0.72/0.97 (step @p131 :rule instantiate :premises (@p17) :args (@t74)) % 0.72/0.97 (step @p132 :rule symm :premises (@p131)) % 0.72/0.97 (step @p133 :rule instantiate :premises (@p1) :args ((@list @t76 @t75))) % 0.72/0.97 (step @p134 :rule symm :premises (@p133)) % 0.72/0.97 (step @p135 :rule trans :premises (@p134 @p132)) % 0.72/0.97 (step @p136 :rule cong :premises (@p135 @p36) :args ((tptp.multiplication (tptp.addition @t75 @t76) tptp.one))) % 0.72/0.97 (step @p137 :rule instantiate :premises (@p9) :args ((@list @t75 @t76 tptp.one))) % 0.72/0.97 (step @p138 :rule symm :premises (@p137)) % 0.72/0.97 (step @p139 :rule trans :premises (@p138 @p136 @p130)) % 0.72/0.97 (step @p140 :rule cong :premises (@p139 @p128) :args ((tptp.addition (tptp.addition (tptp.multiplication @t75 tptp.one) (tptp.multiplication @t76 tptp.one)) @t72))) % 0.72/0.97 (step @p141 :rule instantiate :premises (@p1) :args ((@list @t71 tptp.one))) % 0.72/0.97 (step @p142 :rule symm :premises (@p141)) % 0.72/0.97 (step @p143 :rule refl :args (@t69)) % 0.72/0.97 (step @p144 :rule cong :premises (@p132 @p143) :args ((tptp.multiplication @t77 @t69))) % 0.72/0.97 (step @p145 :rule instantiate :premises (@p9) :args ((@list @t76 @t75 @t69))) % 0.72/0.97 (step @p146 :rule symm :premises (@p145)) % 0.72/0.97 (step @p147 :rule trans :premises (@p146 @p144)) % 0.72/0.97 (step @p148 :rule cong :premises (@p36 @p147) :args ((tptp.addition tptp.one (tptp.addition @t79 @t78)))) % 0.72/0.97 (step @p149 :rule instantiate :premises (@p2) :args ((@list @t78 @t79 tptp.one))) % 0.72/0.97 (step @p150 :rule symm :premises (@p149)) % 0.72/0.97 (step @p151 :rule cong :premises (@p132 @p58) :args ((tptp.multiplication @t77 tptp.zero))) % 0.72/0.97 (step @p152 :rule instantiate :premises (@p9) :args ((@list @t76 @t75 tptp.zero))) % 0.72/0.97 (step @p153 :rule symm :premises (@p152)) % 0.72/0.97 (step @p154 :rule trans :premises (@p153 @p151)) % 0.72/0.97 (step @p155 :rule cong :premises (@p154 @p143) :args ((tptp.multiplication (tptp.addition @t81 @t80) @t69))) % 0.72/0.97 (step @p156 :rule instantiate :premises (@p9) :args ((@list @t81 @t80 @t69))) % 0.72/0.97 (step @p157 :rule symm :premises (@p156)) % 0.72/0.97 (step @p158 :rule trans :premises (@p157 @p155)) % 0.72/0.97 (step @p159 :rule refl :args (@t82)) % 0.72/0.97 (step @p160 :rule cong :premises (@p159 @p158) :args ((tptp.addition @t82 (tptp.addition (tptp.multiplication @t81 @t69) (tptp.multiplication @t80 @t69))))) % 0.72/0.97 (step @p161 :rule symm :premises (@p155)) % 0.72/0.97 (step @p162 :rule instantiate :premises (@p5) :args ((@list @t70 tptp.zero @t69))) % 0.72/0.97 (step @p163 :rule refl :args (@t83)) % 0.72/0.97 (step @p164 :rule cong :premises (@p130 @p163) :args ((tptp.multiplication @t84 @t83))) % 0.72/0.97 (step @p165 :rule cong :premises (@p77 @p143) :args (@t85)) % 0.72/0.97 (step @p166 :rule cong :premises (@p129 @p165) :args ((tptp.multiplication @t70 @t85))) % 0.72/0.97 (step @p167 :rule symm :premises (@p165)) % 0.72/0.97 (step @p168 :rule instantiate :premises (@p75) :args (@t74)) % 0.72/0.97 (step @p169 :rule trans :premises (@p86 @p168 @p167)) % 0.72/0.97 (step @p170 :rule refl :args (@t70)) % 0.72/0.97 (step @p171 :rule cong :premises (@p170 @p169) :args ((tptp.multiplication @t70 @t58))) % 0.72/0.97 (step @p172 :rule instantiate :premises (@p5) :args ((@list @t70 tptp.one tptp.zero))) % 0.72/0.97 (step @p173 :rule symm :premises (@p172)) % 0.72/0.97 (step @p174 :rule cong :premises (@p129 @p58) :args (@t75)) % 0.72/0.97 (step @p175 :rule trans :premises (@p174 @p173 @p171 @p166 @p164 @p162 @p161 @p156)) % 0.72/0.97 (step @p176 :rule instantiate :premises (@p96) :args (@t74)) % 0.72/0.97 (step @p177 :rule cong :premises (@p176 @p175) :args (@t77)) % 0.72/0.97 (step @p178 :rule instantiate :premises (@p15) :args (@t74)) % 0.72/0.97 (step @p179 :rule symm :premises (@p178)) % 0.72/0.97 (step @p180 :rule trans :premises (@p179 @p131 @p177 @p160 @p150 @p148 @p142)) % 0.72/0.97 (step @p181 :rule symm :premises (@p139)) % 0.72/0.97 (step @p182 :rule cong :premises (@p181 @p180) :args ((tptp.addition @t70 (tptp.addition (tptp.multiplication @t69 @t70) tptp.one)))) % 0.72/0.97 (step @p183 :rule trans :premises (@p130 @p178)) % 0.72/0.97 (step @p184 :rule cong :premises (@p130 @p183) :args ((tptp.addition @t84 @t84))) % 0.72/0.97 (step @p185 :rule instantiate :premises (@p106) :args ((@list @t84))) % 0.72/0.97 (step @p186 :rule trans :premises (@p129 @p185 @p184 @p182 @p140 @p127)) % 0.72/0.98 (step @p187 :rule cnf_equiv_pos2 :args (@t88)) % 0.72/0.98 (step @p188 :rule reordering :premises (@p187) :args ((or @t87 (not @t86) (not @t88)))) % 0.72/0.98 (step @p189 :rule chain_m_resolution :premises (@p188 @p186 @p125) :args (@t87 @t62 (@list @t86 @t88))) % 0.72/0.98 (step @p190 :rule refl :args (@t89)) % 0.72/0.98 (step @p191 :rule bool-double-not-elim :args (@t68)) % 0.72/0.98 (step @p192 :rule nary_cong :premises (@p191 @p190) :args ((or (not @t90) @t89))) % 0.72/0.98 (assume-push @p211 @t90) % 0.72/0.98 (step @p194 :rule skolemize :premises (@p211)) % 0.72/0.98 (step-pop @p212 :rule scope :premises (@p194)) % 0.72/0.98 (step @p195 :rule process_scope :premises (@p212) :args (@t89)) % 0.72/0.98 (step @p197 :rule implies_elim :premises (@p195)) % 0.72/0.98 (step @p198 :rule eq_resolve :premises (@p197 @p192)) % 0.72/0.98 (step @p199 :rule chain_m_resolution :premises (@p198 @p189) :args (@t68 @t65 (@list @t87))) % 0.72/0.98 (step @p200 :rule alpha_equiv :args (@t91 @t92 (@list @t66))) % 0.72/0.98 (step @p201 :rule alpha_equiv :args (@t93 @t92 (@list @t36))) % 0.72/0.98 (step @p202 :rule nary_cong :premises (@p201 @p200) :args (@t94)) % 0.72/0.98 (step @p203 :rule quant-miniscope-and :args ((= @t34 @t94))) % 0.72/0.98 (step @p204 :rule trans :premises (@p203 @p202)) % 0.72/0.98 (step @p205 :rule cong :premises (@p204) :args (@t35)) % 0.72/0.98 (step @p206 :rule eq_resolve :premises (@p19 @p205)) % 0.72/0.98 (step @p207 :rule not_and :premises (@p206)) % 0.72/0.98 (step @p208 false :rule chain_m_resolution :premises (@p207 @p199 @p124) :args (false @t62 (@list @t68 @t38))) % 0.72/0.98 ) % 0.72/0.98 % SZS output end Proof % 0.72/0.98 % cvc5 exiting %------------------------------------------------------------------------------