%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYN036+2 : TPTP v9.2.1. Released v2.0.0. % 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 09:07:49 AM UTC 2026 % Result : Theorem 0.40s 0.57s % Output : Proof 0.40s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYN036+2 : TPTP v9.2.1. Released v2.0.0. % 0.13/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n015.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 23:18:19 EDT 2026 % 0.17/0.35 % CPUTime : % 0.31/0.49 %----Proving TF0_NAR, FOF, or CNF % 0.40/0.57 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.40/0.57 % SZS status Theorem % 0.40/0.57 % SZS output start Proof % 0.40/0.57 ( % 0.40/0.57 (declare-sort $$unsorted 0) % 0.40/0.57 (declare-const tptp.big_p (-> $$unsorted Bool)) % 0.40/0.57 (declare-const tptp.big_q (-> $$unsorted Bool)) % 0.40/0.57 (define @t1 () (@var "W1" $$unsorted)) % 0.40/0.57 (define @t2 () (forall (@list @t1) (tptp.big_q @t1))) % 0.40/0.57 (define @t3 () (@var "U1" $$unsorted)) % 0.40/0.57 (define @t4 () (tptp.big_p @t3)) % 0.40/0.57 (define @t5 () (@list @t3)) % 0.40/0.57 (define @t6 () (exists @t5 @t4)) % 0.40/0.57 (define @t7 () (= @t6 @t2)) % 0.40/0.57 (define @t8 () (@var "Y1" $$unsorted)) % 0.40/0.57 (define @t9 () (tptp.big_q @t8)) % 0.40/0.57 (define @t10 () (@var "X1" $$unsorted)) % 0.40/0.57 (define @t11 () (@list @t8)) % 0.40/0.57 (define @t12 () (forall @t11 (= (tptp.big_q @t10) @t9))) % 0.40/0.57 (define @t13 () (@list @t10)) % 0.40/0.57 (define @t14 () (exists @t13 @t12)) % 0.40/0.57 (define @t15 () (= @t14 @t7)) % 0.40/0.57 (define @t16 () (@var "W" $$unsorted)) % 0.40/0.57 (define @t17 () (forall (@list @t16) (tptp.big_p @t16))) % 0.40/0.57 (define @t18 () (@var "U" $$unsorted)) % 0.40/0.57 (define @t19 () (tptp.big_q @t18)) % 0.40/0.57 (define @t20 () (@list @t18)) % 0.40/0.57 (define @t21 () (exists @t20 @t19)) % 0.40/0.57 (define @t22 () (= @t21 @t17)) % 0.40/0.57 (define @t23 () (@var "Y" $$unsorted)) % 0.40/0.57 (define @t24 () (tptp.big_p @t23)) % 0.40/0.57 (define @t25 () (@var "X" $$unsorted)) % 0.40/0.57 (define @t26 () (@list @t23)) % 0.40/0.57 (define @t27 () (forall @t26 (= (tptp.big_p @t25) @t24))) % 0.40/0.57 (define @t28 () (@list @t25)) % 0.40/0.57 (define @t29 () (exists @t28 @t27)) % 0.40/0.57 (define @t30 () (= @t29 @t22)) % 0.40/0.57 (define @t31 () (= @t30 @t15)) % 0.40/0.57 (define @t32 () (not @t31)) % 0.40/0.57 (define @t33 () (forall @t13 (not @t12))) % 0.40/0.57 (define @t34 () (@quantifiers_skolemize @t33 0)) % 0.40/0.57 (define @t35 () (tptp.big_q @t34)) % 0.40/0.57 (define @t36 () (forall @t11 (= @t35 @t9))) % 0.40/0.57 (define @t37 () (not @t36)) % 0.40/0.57 (define @t38 () (@list @t34)) % 0.40/0.57 (define @t39 () (forall @t5 (not @t4))) % 0.40/0.57 (define @t40 () (not @t39)) % 0.40/0.57 (define @t41 () (not @t33)) % 0.40/0.57 (define @t42 () (forall @t20 (not @t19))) % 0.40/0.57 (define @t43 () (not @t42)) % 0.40/0.57 (define @t44 () (forall @t28 (not @t27))) % 0.40/0.57 (define @t45 () (not @t44)) % 0.40/0.57 (define @t46 () (@quantifiers_skolemize @t44 0)) % 0.40/0.57 (define @t47 () (tptp.big_p @t46)) % 0.40/0.57 (define @t48 () (forall @t26 (= @t24 @t47))) % 0.40/0.57 (define @t49 () (not @t45)) % 0.40/0.57 (define @t50 () (forall @t26 (= @t47 @t24))) % 0.40/0.57 (define @t51 () (not (not @t50))) % 0.40/0.57 (define @t52 () (@quantifiers_skolemize @t17 0)) % 0.40/0.57 (define @t53 () (tptp.big_p @t52)) % 0.40/0.57 (define @t54 () (= @t53 @t47)) % 0.40/0.57 (define @t55 () (@quantifiers_skolemize @t39 0)) % 0.40/0.57 (define @t56 () (tptp.big_p @t55)) % 0.40/0.57 (define @t57 () (= @t56 @t47)) % 0.40/0.57 (define @t58 () (= @t47 @t56)) % 0.40/0.57 (define @t59 () (not @t56)) % 0.40/0.57 (define @t60 () (@list @t46)) % 0.40/0.57 (define @t61 () (not @t40)) % 0.40/0.57 (define @t62 () (not @t59)) % 0.40/0.57 (define @t63 () (= @t17 @t43)) % 0.40/0.57 (define @t64 () (= @t45 @t63)) % 0.40/0.57 (define @t65 () (not @t64)) % 0.40/0.57 (define @t66 () (not @t63)) % 0.40/0.57 (define @t67 () (not @t43)) % 0.40/0.57 (define @t68 () (not @t35)) % 0.40/0.57 (define @t69 () (= @t2 @t40)) % 0.40/0.57 (define @t70 () (not @t69)) % 0.40/0.57 (define @t71 () (= @t41 @t69)) % 0.40/0.57 (define @t72 () (not @t41)) % 0.40/0.57 (define @t73 () (forall @t11 (= @t9 @t35))) % 0.40/0.57 (define @t74 () (@quantifiers_skolemize @t73 0)) % 0.40/0.57 (define @t75 () (tptp.big_q @t74)) % 0.40/0.57 (define @t76 () (= @t35 @t75)) % 0.40/0.57 (define @t77 () (not @t76)) % 0.40/0.57 (define @t78 () (not @t73)) % 0.40/0.57 (define @t79 () (not (= @t75 @t35))) % 0.40/0.57 (define @t80 () (@list @t74)) % 0.40/0.57 (define @t81 () (not @t75)) % 0.40/0.57 (define @t82 () (@quantifiers_skolemize @t42 0)) % 0.40/0.57 (define @t83 () (tptp.big_q @t82)) % 0.40/0.57 (define @t84 () (not @t83)) % 0.40/0.57 (define @t85 () (not @t84)) % 0.40/0.57 (define @t86 () (= @t35 @t83)) % 0.40/0.57 (define @t87 () (= @t83 @t35)) % 0.40/0.57 (define @t88 () (not @t37)) % 0.40/0.57 (define @t89 () (not @t71)) % 0.40/0.57 (define @t90 () (not @t2)) % 0.40/0.57 (define @t91 () (@quantifiers_skolemize @t2 0)) % 0.40/0.57 (define @t92 () (tptp.big_q @t91)) % 0.40/0.57 (define @t93 () (= @t92 @t35)) % 0.40/0.57 (define @t94 () (not @t92)) % 0.40/0.57 (define @t95 () (= @t35 @t92)) % 0.40/0.57 (define @t96 () (= @t47 @t53)) % 0.40/0.57 (define @t97 () (not @t47)) % 0.40/0.57 (define @t98 () (not @t53)) % 0.40/0.57 (define @t99 () (not @t17)) % 0.40/0.57 (define @t100 () (tptp.big_p @t74)) % 0.40/0.57 (define @t101 () (forall @t26 (= @t24 @t100))) % 0.40/0.57 (define @t102 () (@quantifiers_skolemize @t101 0)) % 0.40/0.57 (define @t103 () (@list @t102)) % 0.40/0.57 (define @t104 () (tptp.big_p @t102)) % 0.40/0.57 (define @t105 () (@quantifiers_skolemize @t48 0)) % 0.40/0.57 (define @t106 () (tptp.big_p @t105)) % 0.40/0.57 (define @t107 () (forall @t26 (= @t100 @t24))) % 0.40/0.57 (define @t108 () (not @t107)) % 0.40/0.57 (define @t109 () (not @t101)) % 0.40/0.57 (define @t110 () (@list false)) % 0.40/0.57 (define @t111 () (= @t100 @t104)) % 0.40/0.57 (define @t112 () (not @t111)) % 0.40/0.57 (define @t113 () (not (= @t104 @t100))) % 0.40/0.57 (define @t114 () (@list true)) % 0.40/0.57 (define @t115 () (not @t104)) % 0.40/0.57 (define @t116 () (not @t100)) % 0.40/0.57 (define @t117 () (= @t47 @t106)) % 0.40/0.57 (define @t118 () (= @t47 @t100)) % 0.40/0.57 (define @t119 () (not @t117)) % 0.40/0.57 (define @t120 () (not @t48)) % 0.40/0.57 (define @t121 () (not (= @t106 @t47))) % 0.40/0.57 (define @t122 () (= @t100 @t47)) % 0.40/0.57 (define @t123 () (@list @t73)) % 0.40/0.57 (define @t124 () (@list false false)) % 0.40/0.57 (define @t125 () (@list true true)) % 0.40/0.57 (assume @p1 @t32) % 0.40/0.57 (assume @p2 true) % 0.40/0.57 (step @p3 :rule eq-symm :args (@t35 @t9)) % 0.40/0.57 (step @p4 :rule cong :premises (@p3) :args (@t36)) % 0.40/0.57 (step @p5 :rule cong :premises (@p4) :args (@t37)) % 0.40/0.57 (step @p6 :rule refl :args (@t33)) % 0.40/0.57 (step @p7 :rule cong :premises (@p6 @p5) :args ((=> @t33 @t37))) % 0.40/0.57 (assume-push @p353 @t33) % 0.40/0.57 (step @p9 :rule instantiate :premises (@p353) :args (@t38)) % 0.40/0.57 (step-pop @p354 :rule scope :premises (@p9)) % 0.40/0.57 (step @p10 :rule process_scope :premises (@p354) :args (@t37)) % 0.40/0.57 (step @p12 :rule eq_resolve :premises (@p10 @p7)) % 0.40/0.57 (step @p13 :rule implies_elim :premises (@p12)) % 0.40/0.57 (step @p14 :rule eq-symm :args (@t40 @t2)) % 0.40/0.57 (step @p15 :rule refl :args (@t2)) % 0.40/0.57 (step @p16 :rule exists-elim :args ((= @t6 @t40))) % 0.40/0.57 (step @p17 :rule cong :premises (@p16 @p15) :args (@t7)) % 0.40/0.57 (step @p18 :rule trans :premises (@p17 @p14)) % 0.40/0.57 (step @p19 :rule exists-elim :args ((= @t14 @t41))) % 0.40/0.57 (step @p20 :rule cong :premises (@p19 @p18) :args (@t15)) % 0.40/0.57 (step @p21 :rule eq-symm :args (@t43 @t17)) % 0.40/0.57 (step @p22 :rule refl :args (@t17)) % 0.40/0.57 (step @p23 :rule exists-elim :args ((= @t21 @t43))) % 0.40/0.57 (step @p24 :rule cong :premises (@p23 @p22) :args (@t22)) % 0.40/0.57 (step @p25 :rule trans :premises (@p24 @p21)) % 0.40/0.57 (step @p26 :rule exists-elim :args ((= @t29 @t45))) % 0.40/0.57 (step @p27 :rule cong :premises (@p26 @p25) :args (@t30)) % 0.40/0.57 (step @p28 :rule cong :premises (@p27 @p20) :args (@t31)) % 0.40/0.57 (step @p29 :rule cong :premises (@p28) :args (@t32)) % 0.40/0.57 (step @p30 :rule eq_resolve :premises (@p1 @p29)) % 0.40/0.57 (step @p31 :rule not_equiv_elim2 :premises (@p30)) % 0.40/0.57 (step @p32 :rule refl :args (@t48)) % 0.40/0.57 (step @p33 :rule bool-double-not-elim :args (@t44)) % 0.40/0.57 (step @p34 :rule nary_cong :premises (@p33 @p32) :args ((or @t49 @t48))) % 0.40/0.57 (step @p35 :rule eq-symm :args (@t47 @t24)) % 0.40/0.57 (step @p36 :rule cong :premises (@p35) :args (@t50)) % 0.40/0.57 (step @p37 :rule bool-double-not-elim :args (@t50)) % 0.40/0.57 (step @p38 :rule trans :premises (@p37 @p36)) % 0.40/0.57 (step @p39 :rule refl :args (@t45)) % 0.40/0.57 (step @p40 :rule cong :premises (@p39 @p38) :args ((=> @t45 @t51))) % 0.40/0.57 (assume-push @p355 @t45) % 0.40/0.57 (step @p42 :rule skolemize :premises (@p355)) % 0.40/0.57 (step-pop @p356 :rule scope :premises (@p42)) % 0.40/0.57 (step @p43 :rule process_scope :premises (@p356) :args (@t51)) % 0.40/0.57 (step @p45 :rule eq_resolve :premises (@p43 @p40)) % 0.40/0.57 (step @p46 :rule implies_elim :premises (@p45)) % 0.40/0.57 (step @p47 :rule eq_resolve :premises (@p46 @p34)) % 0.40/0.57 (step @p48 :rule eq-symm :args (@t53 @t47)) % 0.40/0.57 (step @p49 :rule cong :premises (@p32 @p48) :args ((=> @t48 @t54))) % 0.40/0.57 (assume-push @p357 @t48) % 0.40/0.57 (step @p51 :rule instantiate :premises (@p357) :args ((@list @t52))) % 0.40/0.57 (step-pop @p358 :rule scope :premises (@p51)) % 0.40/0.57 (step @p52 :rule process_scope :premises (@p358) :args (@t54)) % 0.40/0.57 (step @p54 :rule eq_resolve :premises (@p52 @p49)) % 0.40/0.57 (step @p55 :rule implies_elim :premises (@p54)) % 0.40/0.57 (step @p56 :rule eq-symm :args (@t56 @t47)) % 0.40/0.57 (step @p57 :rule cong :premises (@p32 @p56) :args ((=> @t48 @t57))) % 0.40/0.57 (assume-push @p359 @t48) % 0.40/0.57 (step @p59 :rule instantiate :premises (@p359) :args ((@list @t55))) % 0.40/0.57 (step-pop @p360 :rule scope :premises (@p59)) % 0.40/0.57 (step @p60 :rule process_scope :premises (@p360) :args (@t57)) % 0.40/0.57 (step @p62 :rule eq_resolve :premises (@p60 @p57)) % 0.40/0.57 (step @p63 :rule implies_elim :premises (@p62)) % 0.40/0.57 (step @p64 :rule cnf_equiv_pos2 :args (@t58)) % 0.40/0.57 (step @p65 :rule reordering :premises (@p64) :args ((or @t47 @t59 (not @t58)))) % 0.40/0.57 (assume-push @p361 @t17) % 0.40/0.57 (step @p67 :rule instantiate :premises (@p361) :args (@t60)) % 0.40/0.57 (step-pop @p362 :rule scope :premises (@p67)) % 0.40/0.57 (step @p68 :rule process_scope :premises (@p362) :args (@t47)) % 0.40/0.57 (step @p70 :rule implies_elim :premises (@p68)) % 0.40/0.57 (step @p71 :rule refl :args (@t56)) % 0.40/0.57 (step @p72 :rule bool-double-not-elim :args (@t39)) % 0.40/0.57 (step @p73 :rule nary_cong :premises (@p72 @p71) :args ((or @t61 @t56))) % 0.40/0.57 (step @p74 :rule bool-double-not-elim :args (@t56)) % 0.40/0.57 (step @p75 :rule refl :args (@t40)) % 0.40/0.57 (step @p76 :rule cong :premises (@p75 @p74) :args ((=> @t40 @t62))) % 0.40/0.57 (assume-push @p363 @t40) % 0.40/0.57 (step @p78 :rule skolemize :premises (@p363)) % 0.40/0.57 (step-pop @p364 :rule scope :premises (@p78)) % 0.40/0.57 (step @p79 :rule process_scope :premises (@p364) :args (@t62)) % 0.40/0.57 (step @p81 :rule eq_resolve :premises (@p79 @p76)) % 0.40/0.57 (step @p82 :rule implies_elim :premises (@p81)) % 0.40/0.57 (step @p83 :rule eq_resolve :premises (@p82 @p73)) % 0.40/0.57 (step @p84 :rule not_equiv_elim1 :premises (@p30)) % 0.40/0.57 (step @p85 :rule refl :args (@t63)) % 0.40/0.57 (step @p86 :rule refl :args (@t65)) % 0.40/0.57 (step @p87 :rule nary_cong :premises (@p86 @p33 @p85) :args ((or @t65 @t49 @t63))) % 0.40/0.57 (step @p88 :rule cnf_equiv_pos1 :args (@t64)) % 0.40/0.57 (step @p89 :rule eq_resolve :premises (@p88 @p87)) % 0.40/0.57 (step @p90 :rule reordering :premises (@p89) :args ((or @t44 @t63 @t65))) % 0.40/0.57 (step @p91 :rule bool-double-not-elim :args (@t42)) % 0.40/0.57 (step @p92 :rule refl :args (@t66)) % 0.40/0.57 (step @p93 :rule nary_cong :premises (@p92 @p22 @p91) :args ((or @t66 @t17 @t67))) % 0.40/0.57 (step @p94 :rule cnf_equiv_pos2 :args (@t63)) % 0.40/0.57 (step @p95 :rule eq_resolve :premises (@p94 @p93)) % 0.40/0.57 (step @p96 :rule reordering :premises (@p95) :args ((or @t17 @t42 @t66))) % 0.40/0.57 (assume-push @p365 @t42) % 0.40/0.57 (step @p98 :rule instantiate :premises (@p365) :args (@t38)) % 0.40/0.57 (step-pop @p366 :rule scope :premises (@p98)) % 0.40/0.57 (step @p99 :rule process_scope :premises (@p366) :args (@t68)) % 0.40/0.57 (step @p101 :rule implies_elim :premises (@p99)) % 0.40/0.57 (assume-push @p367 @t2) % 0.40/0.57 (step @p103 :rule instantiate :premises (@p367) :args (@t38)) % 0.40/0.57 (step-pop @p368 :rule scope :premises (@p103)) % 0.40/0.57 (step @p104 :rule process_scope :premises (@p368) :args (@t35)) % 0.40/0.57 (step @p106 :rule implies_elim :premises (@p104)) % 0.40/0.57 (step @p107 :rule cnf_equiv_neg1 :args (@t69)) % 0.40/0.57 (step @p108 :rule reordering :premises (@p107) :args ((or @t2 @t40 @t69))) % 0.40/0.57 (step @p109 :rule refl :args (@t70)) % 0.40/0.57 (step @p110 :rule bool-double-not-elim :args (@t33)) % 0.40/0.57 (step @p111 :rule refl :args (@t71)) % 0.40/0.57 (step @p112 :rule nary_cong :premises (@p111 @p110 @p109) :args ((or @t71 @t72 @t70))) % 0.40/0.57 (step @p113 :rule cnf_equiv_neg2 :args (@t71)) % 0.40/0.57 (step @p114 :rule eq_resolve :premises (@p113 @p112)) % 0.40/0.57 (step @p115 :rule reordering :premises (@p114) :args ((or @t33 @t71 @t70))) % 0.40/0.57 (step @p116 :rule refl :args (@t77)) % 0.40/0.57 (step @p117 :rule bool-double-not-elim :args (@t73)) % 0.40/0.57 (step @p118 :rule nary_cong :premises (@p117 @p116) :args ((or (not @t78) @t77))) % 0.40/0.57 (step @p119 :rule eq-symm :args (@t75 @t35)) % 0.40/0.57 (step @p120 :rule cong :premises (@p119) :args (@t79)) % 0.40/0.57 (step @p121 :rule refl :args (@t78)) % 0.40/0.57 (step @p122 :rule cong :premises (@p121 @p120) :args ((=> @t78 @t79))) % 0.40/0.57 (assume-push @p369 @t78) % 0.40/0.57 (step @p124 :rule skolemize :premises (@p369)) % 0.40/0.57 (step-pop @p370 :rule scope :premises (@p124)) % 0.40/0.57 (step @p125 :rule process_scope :premises (@p370) :args (@t79)) % 0.40/0.57 (step @p127 :rule eq_resolve :premises (@p125 @p122)) % 0.40/0.57 (step @p128 :rule implies_elim :premises (@p127)) % 0.40/0.57 (step @p129 :rule eq_resolve :premises (@p128 @p118)) % 0.40/0.57 (step @p130 :rule cnf_equiv_neg1 :args (@t76)) % 0.40/0.57 (step @p131 :rule reordering :premises (@p130) :args ((or @t35 @t75 @t76))) % 0.40/0.57 (assume-push @p371 @t42) % 0.40/0.57 (step @p133 :rule instantiate :premises (@p371) :args (@t80)) % 0.40/0.57 (step-pop @p372 :rule scope :premises (@p133)) % 0.40/0.57 (step @p134 :rule process_scope :premises (@p372) :args (@t81)) % 0.40/0.57 (step @p136 :rule implies_elim :premises (@p134)) % 0.40/0.57 (step @p137 :rule chain_m_resolution :premises (@p136 @p131 @p129 @p13 @p115 @p108 @p106 @p101 @p96 @p90 @p84) :args ((or @t17 @t44 @t40 @t71) (@list false true true false false true true false false false) (@list @t75 @t76 @t73 @t33 @t69 @t2 @t35 @t42 @t63 @t64))) % 0.40/0.57 (step @p138 :rule refl :args (@t64)) % 0.40/0.57 (step @p139 :rule nary_cong :premises (@p138 @p33 @p92) :args ((or @t64 @t49 @t66))) % 0.40/0.57 (step @p140 :rule cnf_equiv_neg2 :args (@t64)) % 0.40/0.57 (step @p141 :rule eq_resolve :premises (@p140 @p139)) % 0.40/0.57 (step @p142 :rule reordering :premises (@p141) :args ((or @t44 @t64 @t66))) % 0.40/0.57 (step @p143 :rule cnf_equiv_neg1 :args (@t63)) % 0.40/0.57 (step @p144 :rule reordering :premises (@p143) :args ((or @t17 @t43 @t63))) % 0.40/0.57 (step @p145 :rule refl :args (@t83)) % 0.40/0.57 (step @p146 :rule nary_cong :premises (@p91 @p145) :args ((or @t67 @t83))) % 0.40/0.57 (step @p147 :rule bool-double-not-elim :args (@t83)) % 0.40/0.57 (step @p148 :rule refl :args (@t43)) % 0.40/0.57 (step @p149 :rule cong :premises (@p148 @p147) :args ((=> @t43 @t85))) % 0.40/0.57 (assume-push @p373 @t43) % 0.40/0.57 (step @p151 :rule skolemize :premises (@p373)) % 0.40/0.57 (step-pop @p374 :rule scope :premises (@p151)) % 0.40/0.57 (step @p152 :rule process_scope :premises (@p374) :args (@t85)) % 0.40/0.57 (step @p154 :rule eq_resolve :premises (@p152 @p149)) % 0.40/0.57 (step @p155 :rule implies_elim :premises (@p154)) % 0.40/0.57 (step @p156 :rule eq_resolve :premises (@p155 @p146)) % 0.40/0.57 (step @p157 :rule cnf_equiv_pos2 :args (@t86)) % 0.40/0.57 (step @p158 :rule reordering :premises (@p157) :args ((or @t35 @t84 (not @t86)))) % 0.40/0.57 (step @p159 :rule eq-symm :args (@t83 @t35)) % 0.40/0.57 (step @p160 :rule refl :args (@t73)) % 0.40/0.57 (step @p161 :rule cong :premises (@p160 @p159) :args ((=> @t73 @t87))) % 0.40/0.57 (assume-push @p375 @t73) % 0.40/0.57 (step @p163 :rule instantiate :premises (@p375) :args ((@list @t82))) % 0.40/0.57 (step-pop @p376 :rule scope :premises (@p163)) % 0.40/0.57 (step @p164 :rule process_scope :premises (@p376) :args (@t87)) % 0.40/0.57 (step @p166 :rule eq_resolve :premises (@p164 @p161)) % 0.40/0.57 (step @p167 :rule implies_elim :premises (@p166)) % 0.40/0.57 (step @p168 :rule nary_cong :premises (@p110 @p160) :args ((or @t72 @t73))) % 0.40/0.57 (step @p169 :rule bool-double-not-elim :args (@t36)) % 0.40/0.57 (step @p170 :rule trans :premises (@p169 @p4)) % 0.40/0.57 (step @p171 :rule refl :args (@t41)) % 0.40/0.57 (step @p172 :rule cong :premises (@p171 @p170) :args ((=> @t41 @t88))) % 0.40/0.57 (assume-push @p377 @t41) % 0.40/0.57 (step @p174 :rule skolemize :premises (@p377)) % 0.40/0.57 (step-pop @p378 :rule scope :premises (@p174)) % 0.40/0.57 (step @p175 :rule process_scope :premises (@p378) :args (@t88)) % 0.40/0.57 (step @p177 :rule eq_resolve :premises (@p175 @p172)) % 0.40/0.57 (step @p178 :rule implies_elim :premises (@p177)) % 0.40/0.57 (step @p179 :rule eq_resolve :premises (@p178 @p168)) % 0.40/0.57 (step @p180 :rule cnf_equiv_pos2 :args (@t71)) % 0.40/0.57 (step @p181 :rule reordering :premises (@p180) :args ((or @t41 @t70 @t89))) % 0.40/0.57 (step @p182 :rule chain_m_resolution :premises (@p181 @p179 @p108 @p167 @p106 @p158) :args ((or @t40 @t89 @t35 @t84) (@list false false true true true) (@list @t33 @t69 @t73 @t2 @t86))) % 0.40/0.57 (step @p183 :rule cnf_equiv_neg2 :args (@t76)) % 0.40/0.57 (step @p184 :rule reordering :premises (@p183) :args ((or @t68 @t76 @t81))) % 0.40/0.57 (assume-push @p379 @t2) % 0.40/0.57 (step @p186 :rule instantiate :premises (@p379) :args (@t80)) % 0.40/0.57 (step-pop @p380 :rule scope :premises (@p186)) % 0.40/0.57 (step @p187 :rule process_scope :premises (@p380) :args (@t75)) % 0.40/0.57 (step @p189 :rule implies_elim :premises (@p187)) % 0.40/0.57 (step @p190 :rule chain_m_resolution :premises (@p189 @p184 @p129 @p108 @p13 @p181) :args ((or @t41 @t40 @t89 @t68) (@list true true false true true) (@list @t75 @t76 @t2 @t73 @t69))) % 0.40/0.57 (step @p191 :rule refl :args (@t69)) % 0.40/0.57 (step @p192 :rule refl :args (@t89)) % 0.40/0.57 (step @p193 :rule nary_cong :premises (@p192 @p110 @p191) :args ((or @t89 @t72 @t69))) % 0.40/0.57 (step @p194 :rule cnf_equiv_pos1 :args (@t71)) % 0.40/0.57 (step @p195 :rule eq_resolve :premises (@p194 @p193)) % 0.40/0.57 (step @p196 :rule reordering :premises (@p195) :args ((or @t33 @t69 @t89))) % 0.40/0.57 (step @p197 :rule cnf_equiv_pos1 :args (@t69)) % 0.40/0.57 (step @p198 :rule reordering :premises (@p197) :args ((or @t40 @t90 @t70))) % 0.40/0.58 (step @p199 :rule eq-symm :args (@t92 @t35)) % 0.40/0.58 (step @p200 :rule cong :premises (@p160 @p199) :args ((=> @t73 @t93))) % 0.40/0.58 (assume-push @p381 @t73) % 0.40/0.58 (step @p202 :rule instantiate :premises (@p381) :args ((@list @t91))) % 0.40/0.58 (step-pop @p382 :rule scope :premises (@p202)) % 0.40/0.58 (step @p203 :rule process_scope :premises (@p382) :args (@t93)) % 0.40/0.58 (step @p205 :rule eq_resolve :premises (@p203 @p200)) % 0.40/0.58 (step @p206 :rule implies_elim :premises (@p205)) % 0.40/0.58 (step @p207 :rule refl :args (@t94)) % 0.40/0.58 (step @p208 :rule bool-double-not-elim :args (@t2)) % 0.40/0.58 (step @p209 :rule nary_cong :premises (@p208 @p207) :args ((or (not @t90) @t94))) % 0.40/0.58 (assume-push @p383 @t90) % 0.40/0.58 (step @p211 :rule skolemize :premises (@p383)) % 0.40/0.58 (step-pop @p384 :rule scope :premises (@p211)) % 0.40/0.58 (step @p212 :rule process_scope :premises (@p384) :args (@t94)) % 0.40/0.58 (step @p214 :rule implies_elim :premises (@p212)) % 0.40/0.58 (step @p215 :rule eq_resolve :premises (@p214 @p209)) % 0.40/0.58 (step @p216 :rule cnf_equiv_pos1 :args (@t95)) % 0.40/0.58 (step @p217 :rule reordering :premises (@p216) :args ((or @t92 @t68 (not @t95)))) % 0.40/0.58 (step @p218 :rule chain_m_resolution :premises (@p217 @p215 @p206 @p198 @p179 @p196 @p190 @p182 @p156 @p144 @p142 @p31 @p137 @p83 @p70 @p65 @p63 @p47) :args ((or @t44 @t47) (@list true false true false false true false false true true true false false true true false false) (@list @t92 @t95 @t2 @t73 @t69 @t33 @t35 @t83 @t42 @t63 @t64 @t71 @t39 @t17 @t56 @t58 @t48))) % 0.40/0.58 (step @p219 :rule cnf_equiv_pos1 :args (@t96)) % 0.40/0.58 (step @p220 :rule reordering :premises (@p219) :args ((or @t97 @t53 (not @t96)))) % 0.40/0.58 (assume-push @p385 @t39) % 0.40/0.58 (step @p222 :rule instantiate :premises (@p385) :args (@t60)) % 0.40/0.58 (step-pop @p386 :rule scope :premises (@p222)) % 0.40/0.58 (step @p223 :rule process_scope :premises (@p386) :args (@t97)) % 0.40/0.58 (step @p225 :rule implies_elim :premises (@p223)) % 0.40/0.58 (step @p226 :rule refl :args (@t98)) % 0.40/0.58 (step @p227 :rule bool-double-not-elim :args (@t17)) % 0.40/0.58 (step @p228 :rule nary_cong :premises (@p227 @p226) :args ((or (not @t99) @t98))) % 0.40/0.58 (assume-push @p387 @t99) % 0.40/0.58 (step @p230 :rule skolemize :premises (@p387)) % 0.40/0.58 (step-pop @p388 :rule scope :premises (@p230)) % 0.40/0.58 (step @p231 :rule process_scope :premises (@p388) :args (@t98)) % 0.40/0.58 (step @p233 :rule implies_elim :premises (@p231)) % 0.40/0.58 (step @p234 :rule eq_resolve :premises (@p233 @p228)) % 0.40/0.58 (step @p235 :rule nary_cong :premises (@p109 @p15 @p72) :args ((or @t70 @t2 @t61))) % 0.40/0.58 (step @p236 :rule cnf_equiv_pos2 :args (@t69)) % 0.40/0.58 (step @p237 :rule eq_resolve :premises (@p236 @p235)) % 0.40/0.58 (step @p238 :rule reordering :premises (@p237) :args ((or @t2 @t39 @t70))) % 0.40/0.58 (step @p239 :rule cnf_equiv_pos1 :args (@t63)) % 0.40/0.58 (step @p240 :rule reordering :premises (@p239) :args ((or @t43 @t99 @t66))) % 0.40/0.58 (step @p241 :rule chain_m_resolution :premises (@p240 @p90 @p156 @p84 @p158 @p196 @p217 @p13 @p206 @p167 @p234 @p220 @p55 @p47 @p218) :args ((or @t44 @t69 @t78 @t92) (@list false false false true true true true false false false false false false false) (@list @t63 @t42 @t64 @t83 @t71 @t35 @t33 @t95 @t86 @t17 @t53 @t96 @t48 @t47))) % 0.40/0.58 (step @p242 :rule cnf_equiv_neg1 :args (@t71)) % 0.40/0.58 (step @p243 :rule reordering :premises (@p242) :args ((or @t41 @t69 @t71))) % 0.40/0.58 (step @p244 :rule refl :args (@t99)) % 0.40/0.58 (step @p245 :rule nary_cong :premises (@p85 @p244 @p91) :args ((or @t63 @t99 @t67))) % 0.40/0.58 (step @p246 :rule cnf_equiv_neg2 :args (@t63)) % 0.40/0.58 (step @p247 :rule eq_resolve :premises (@p246 @p245)) % 0.40/0.58 (step @p248 :rule reordering :premises (@p247) :args ((or @t42 @t63 @t99))) % 0.40/0.58 (step @p249 :rule chain_m_resolution :premises (@p131 @p136 @p101 @p248 @p142 @p31 @p243 @p129 @p179 @p241 @p238 @p215 @p225 @p234 @p220 @p55 @p47 @p218) :args ((or @t2 @t44) (@list true true false true true false true false true true true true false false false false false) (@list @t75 @t35 @t42 @t63 @t64 @t71 @t76 @t33 @t73 @t69 @t92 @t39 @t17 @t53 @t96 @t48 @t47))) % 0.40/0.58 (step @p250 :rule refl :args (@t90)) % 0.40/0.58 (step @p251 :rule nary_cong :premises (@p191 @p250 @p72) :args ((or @t69 @t90 @t61))) % 0.40/0.58 (step @p252 :rule cnf_equiv_neg2 :args (@t69)) % 0.40/0.58 (step @p253 :rule eq_resolve :premises (@p252 @p251)) % 0.40/0.58 (step @p254 :rule reordering :premises (@p253) :args ((or @t39 @t69 @t90))) % 0.40/0.58 (step @p255 :rule chain_m_resolution :premises (@p115 @p31 @p13 @p142 @p129 @p248 @p184 @p101 @p189 @p106 @p254 @p249 @p234 @p225 @p220 @p218 @p55 @p47) :args (@t44 (@list true true false false false false true false false false false false true false false false false) (@list @t71 @t33 @t64 @t73 @t63 @t76 @t42 @t75 @t35 @t69 @t2 @t17 @t39 @t53 @t47 @t96 @t48))) % 0.40/0.58 (step @p256 :rule cnf_equiv_neg1 :args (@t64)) % 0.40/0.58 (step @p257 :rule reordering :premises (@p256) :args ((or @t45 @t63 @t64))) % 0.40/0.58 (assume-push @p389 @t17) % 0.40/0.58 (step @p259 :rule instantiate :premises (@p389) :args (@t103)) % 0.40/0.58 (step-pop @p390 :rule scope :premises (@p259)) % 0.40/0.58 (step @p260 :rule process_scope :premises (@p390) :args (@t104)) % 0.40/0.58 (step @p262 :rule implies_elim :premises (@p260)) % 0.40/0.58 (assume-push @p391 @t17) % 0.40/0.58 (step @p264 :rule instantiate :premises (@p391) :args ((@list @t105))) % 0.40/0.58 (step-pop @p392 :rule scope :premises (@p264)) % 0.40/0.58 (step @p265 :rule process_scope :premises (@p392) :args (@t106)) % 0.40/0.58 (step @p267 :rule implies_elim :premises (@p265)) % 0.40/0.58 (step @p268 :rule eq-symm :args (@t100 @t24)) % 0.40/0.58 (step @p269 :rule cong :premises (@p268) :args (@t107)) % 0.40/0.58 (step @p270 :rule cong :premises (@p269) :args (@t108)) % 0.40/0.58 (step @p271 :rule refl :args (@t44)) % 0.40/0.58 (step @p272 :rule cong :premises (@p271 @p270) :args ((=> @t44 @t108))) % 0.40/0.58 (assume-push @p393 @t44) % 0.40/0.58 (step @p274 :rule instantiate :premises (@p393) :args (@t80)) % 0.40/0.58 (step-pop @p394 :rule scope :premises (@p274)) % 0.40/0.58 (step @p275 :rule process_scope :premises (@p394) :args (@t108)) % 0.40/0.58 (step @p277 :rule eq_resolve :premises (@p275 @p272)) % 0.40/0.58 (step @p278 :rule implies_elim :premises (@p277)) % 0.40/0.58 (step @p279 :rule chain_m_resolution :premises (@p278 @p255) :args (@t109 @t110 (@list @t44))) % 0.40/0.58 (step @p280 :rule refl :args (@t112)) % 0.40/0.58 (step @p281 :rule bool-double-not-elim :args (@t101)) % 0.40/0.58 (step @p282 :rule nary_cong :premises (@p281 @p280) :args ((or (not @t109) @t112))) % 0.40/0.58 (step @p283 :rule eq-symm :args (@t104 @t100)) % 0.40/0.58 (step @p284 :rule cong :premises (@p283) :args (@t113)) % 0.40/0.58 (step @p285 :rule refl :args (@t109)) % 0.40/0.58 (step @p286 :rule cong :premises (@p285 @p284) :args ((=> @t109 @t113))) % 0.40/0.58 (assume-push @p395 @t109) % 0.40/0.58 (step @p288 :rule skolemize :premises (@p395)) % 0.40/0.58 (step-pop @p396 :rule scope :premises (@p288)) % 0.40/0.58 (step @p289 :rule process_scope :premises (@p396) :args (@t113)) % 0.40/0.58 (step @p291 :rule eq_resolve :premises (@p289 @p286)) % 0.40/0.58 (step @p292 :rule implies_elim :premises (@p291)) % 0.40/0.58 (step @p293 :rule eq_resolve :premises (@p292 @p282)) % 0.40/0.58 (step @p294 :rule chain_m_resolution :premises (@p293 @p279) :args (@t112 @t114 (@list @t101))) % 0.40/0.58 (step @p295 :rule cnf_equiv_neg2 :args (@t111)) % 0.40/0.58 (step @p296 :rule reordering :premises (@p295) :args ((or @t116 @t111 @t115))) % 0.40/0.58 (step @p297 :rule cnf_equiv_neg2 :args (@t117)) % 0.40/0.58 (step @p298 :rule reordering :premises (@p297) :args ((or @t97 @t117 (not @t106)))) % 0.40/0.58 (step @p299 :rule cnf_equiv_pos1 :args (@t118)) % 0.40/0.58 (step @p300 :rule reordering :premises (@p299) :args ((or @t97 @t100 (not @t118)))) % 0.40/0.58 (step @p301 :rule refl :args (@t119)) % 0.40/0.58 (step @p302 :rule bool-double-not-elim :args (@t48)) % 0.40/0.58 (step @p303 :rule nary_cong :premises (@p302 @p301) :args ((or (not @t120) @t119))) % 0.40/0.58 (step @p304 :rule eq-symm :args (@t106 @t47)) % 0.40/0.58 (step @p305 :rule cong :premises (@p304) :args (@t121)) % 0.40/0.58 (step @p306 :rule refl :args (@t120)) % 0.40/0.58 (step @p307 :rule cong :premises (@p306 @p305) :args ((=> @t120 @t121))) % 0.40/0.58 (assume-push @p397 @t120) % 0.40/0.58 (step @p309 :rule skolemize :premises (@p397)) % 0.40/0.58 (step-pop @p398 :rule scope :premises (@p309)) % 0.40/0.58 (step @p310 :rule process_scope :premises (@p398) :args (@t121)) % 0.40/0.58 (step @p312 :rule eq_resolve :premises (@p310 @p307)) % 0.40/0.58 (step @p313 :rule implies_elim :premises (@p312)) % 0.40/0.58 (step @p314 :rule eq_resolve :premises (@p313 @p303)) % 0.40/0.58 (step @p315 :rule eq-symm :args (@t100 @t47)) % 0.40/0.58 (step @p316 :rule cong :premises (@p32 @p315) :args ((=> @t48 @t122))) % 0.40/0.58 (assume-push @p399 @t48) % 0.40/0.58 (step @p318 :rule instantiate :premises (@p399) :args (@t80)) % 0.40/0.58 (step-pop @p400 :rule scope :premises (@p318)) % 0.40/0.58 (step @p319 :rule process_scope :premises (@p400) :args (@t122)) % 0.40/0.58 (step @p321 :rule eq_resolve :premises (@p319 @p316)) % 0.40/0.58 (step @p322 :rule implies_elim :premises (@p321)) % 0.40/0.58 (step @p323 :rule chain_m_resolution :premises (@p322 @p314 @p300 @p298 @p296 @p294 @p267 @p262 @p70) :args (@t99 (@list false true false true true false false false) (@list @t48 @t118 @t117 @t100 @t111 @t106 @t104 @t47))) % 0.40/0.58 (assume-push @p401 @t39) % 0.40/0.58 (step @p325 :rule instantiate :premises (@p401) :args (@t103)) % 0.40/0.58 (step-pop @p402 :rule scope :premises (@p325)) % 0.40/0.58 (step @p326 :rule process_scope :premises (@p402) :args (@t115)) % 0.40/0.58 (step @p328 :rule implies_elim :premises (@p326)) % 0.40/0.58 (step @p329 :rule cnf_equiv_neg1 :args (@t111)) % 0.40/0.58 (step @p330 :rule reordering :premises (@p329) :args ((or @t100 @t104 @t111))) % 0.40/0.58 (assume-push @p403 @t39) % 0.40/0.58 (step @p332 :rule instantiate :premises (@p403) :args (@t80)) % 0.40/0.58 (step-pop @p404 :rule scope :premises (@p332)) % 0.40/0.58 (step @p333 :rule process_scope :premises (@p404) :args (@t116)) % 0.40/0.58 (step @p335 :rule implies_elim :premises (@p333)) % 0.40/0.58 (step @p336 :rule chain_m_resolution :premises (@p335 @p330 @p294 @p328) :args (@t40 (@list false true true) (@list @t100 @t111 @t104))) % 0.40/0.58 (step @p337 :rule chain_m_resolution :premises (@p13 @p196 @p129 @p238 @p336 @p131 @p106 @p136 @p101 @p96 @p323 @p257 @p255 @p31) :args (@t89 (@list false false true true false true true true false true false false true) (@list @t33 @t73 @t69 @t39 @t76 @t2 @t75 @t35 @t42 @t17 @t63 @t44 @t64))) % 0.40/0.58 (step @p338 :rule chain_m_resolution :premises (@p184 @p189 @p106 @p238 @p336 @p129 @p243 @p337 @p13) :args (@t41 (@list false false false true true false true true) (@list @t75 @t35 @t2 @t39 @t76 @t69 @t71 @t73))) % 0.40/0.58 (step @p339 :rule chain_m_resolution :premises (@p179 @p338) :args (@t73 @t114 (@list @t33))) % 0.40/0.58 (step @p340 :rule chain_m_resolution :premises (@p206 @p339) :args (@t95 @t110 @t123)) % 0.40/0.58 (step @p341 :rule chain_m_resolution :premises (@p167 @p339) :args (@t86 @t110 @t123)) % 0.40/0.58 (step @p342 :rule chain_m_resolution :premises (@p84 @p337) :args (@t64 @t114 (@list @t71))) % 0.40/0.58 (step @p343 :rule cnf_equiv_pos2 :args (@t64)) % 0.40/0.58 (step @p344 :rule reordering :premises (@p343) :args ((or @t45 @t66 @t65))) % 0.40/0.58 (step @p345 :rule chain_m_resolution :premises (@p344 @p255 @p342) :args (@t66 @t124 (@list @t44 @t64))) % 0.40/0.58 (step @p346 :rule chain_m_resolution :premises (@p144 @p323 @p345) :args (@t43 @t125 (@list @t17 @t63))) % 0.40/0.58 (step @p347 :rule chain_m_resolution :premises (@p156 @p346) :args (@t83 @t114 (@list @t42))) % 0.40/0.58 (step @p348 :rule chain_m_resolution :premises (@p158 @p347 @p341) :args (@t35 @t124 (@list @t83 @t86))) % 0.40/0.58 (step @p349 :rule chain_m_resolution :premises (@p115 @p338 @p337) :args (@t70 @t125 (@list @t33 @t71))) % 0.40/0.58 (step @p350 :rule chain_m_resolution :premises (@p254 @p336 @p349) :args (@t90 @t125 (@list @t39 @t69))) % 0.40/0.58 (step @p351 :rule chain_m_resolution :premises (@p215 @p350) :args (@t94 @t114 (@list @t2))) % 0.40/0.58 (step @p352 false :rule chain_m_resolution :premises (@p217 @p351 @p348 @p340) :args (false (@list true false false) (@list @t92 @t35 @t95))) % 0.40/0.58 ) % 0.40/0.58 % SZS output end Proof % 0.40/0.58 % cvc5 exiting %------------------------------------------------------------------------------