%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : DAT032_1 : TPTP v9.2.1. Released v5.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n011.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 08:14:23 AM UTC 2026 % Result : Theorem 0.45s 0.67s % Output : Proof 0.45s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : DAT032_1 : TPTP v9.2.1. Released v5.0.0. % 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 : n011.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 : Mon Jun 1 22:26:20 EDT 2026 % 0.16/0.34 % CPUTime : % 0.29/0.48 %----Proving TF0_ARI % 0.45/0.67 --- Run --finite-model-find --decision=internal at 45... % 0.45/0.67 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 60... % 0.45/0.67 % SZS status Theorem % 0.45/0.67 % SZS output start Proof % 0.45/0.67 ( % 0.45/0.67 (declare-sort tptp.collection 0) % 0.45/0.67 (declare-const tptp.count (-> tptp.collection Int)) % 0.45/0.67 (declare-const tptp.remove (-> Int tptp.collection tptp.collection)) % 0.45/0.67 (declare-const tptp.add (-> Int tptp.collection tptp.collection)) % 0.45/0.67 (declare-const tptp.in (-> Int tptp.collection Bool)) % 0.45/0.67 (declare-const tptp.empty tptp.collection) % 0.45/0.67 (define @t1 () (@var "U" Int)) % 0.45/0.67 (define @t2 () (@var "W" tptp.collection)) % 0.45/0.67 (define @t3 () (@var "V" Int)) % 0.45/0.67 (define @t4 () (@var "Y" tptp.collection)) % 0.45/0.67 (define @t5 () (@var "X" Int)) % 0.45/0.67 (define @t6 () (@var "X1" tptp.collection)) % 0.45/0.67 (define @t7 () (@var "X2" Int)) % 0.45/0.67 (define @t8 () (@var "Z" Int)) % 0.45/0.67 (define @t9 () (@var "X4" tptp.collection)) % 0.45/0.67 (define @t10 () (@var "X5" Int)) % 0.45/0.67 (define @t11 () (@var "X3" Int)) % 0.45/0.67 (define @t12 () (@var "X6" tptp.collection)) % 0.45/0.67 (define @t13 () (@var "X7" tptp.collection)) % 0.45/0.67 (define @t14 () (@var "X9" tptp.collection)) % 0.45/0.67 (define @t15 () (@var "X8" Int)) % 0.45/0.67 (define @t16 () (@var "X11" tptp.collection)) % 0.45/0.67 (define @t17 () (@var "X10" Int)) % 0.45/0.67 (define @t18 () (@var "X13" tptp.collection)) % 0.45/0.67 (define @t19 () (tptp.count @t18)) % 0.45/0.67 (define @t20 () (- @t19 1)) % 0.45/0.67 (define @t21 () (@var "X12" Int)) % 0.45/0.67 (define @t22 () (tptp.count (tptp.remove @t21 @t18))) % 0.45/0.67 (define @t23 () (= @t22 @t20)) % 0.45/0.67 (define @t24 () (tptp.in @t21 @t18)) % 0.45/0.67 (define @t25 () (= @t24 @t23)) % 0.45/0.67 (define @t26 () (forall (@list @t21 @t18) @t25)) % 0.45/0.67 (define @t27 () (@var "X15" tptp.collection)) % 0.45/0.67 (define @t28 () (@var "X14" Int)) % 0.45/0.67 (define @t29 () (@var "X17" tptp.collection)) % 0.45/0.67 (define @t30 () (@var "X16" Int)) % 0.45/0.67 (define @t31 () (@var "U" tptp.collection)) % 0.45/0.67 (define @t32 () (>= (tptp.count (tptp.remove 4 @t31)) 6)) % 0.45/0.67 (define @t33 () (>= (tptp.count (tptp.remove 5 @t31)) 7)) % 0.45/0.67 (define @t34 () (@list @t31)) % 0.45/0.67 (define @t35 () (forall @t34 (=> @t33 @t32))) % 0.45/0.67 (define @t36 () (not @t35)) % 0.45/0.67 (define @t37 () (@quantifiers_skolemize (forall @t34 (or (not @t33) @t32)) 0)) % 0.45/0.67 (define @t38 () (@list 5 @t37)) % 0.45/0.67 (define @t39 () (* -1 1)) % 0.45/0.67 (define @t40 () (+ @t19 @t39)) % 0.45/0.67 (define @t41 () (@list 4 @t37)) % 0.45/0.67 (define @t42 () (tptp.count (tptp.remove 5 @t37))) % 0.45/0.67 (define @t43 () (>= @t42 7)) % 0.45/0.67 (define @t44 () (tptp.count (tptp.remove 4 @t37))) % 0.45/0.67 (define @t45 () (>= @t44 6)) % 0.45/0.67 (define @t46 () (not @t43)) % 0.45/0.67 (define @t47 () (or @t46 @t45)) % 0.45/0.67 (define @t48 () (@list true)) % 0.45/0.67 (define @t49 () (@list @t47)) % 0.45/0.67 (define @t50 () (not @t45)) % 0.45/0.67 (define @t51 () (tptp.count @t37)) % 0.45/0.67 (define @t52 () (= @t44 @t51)) % 0.45/0.67 (define @t53 () (not @t52)) % 0.45/0.67 (define @t54 () (= @t42 @t51)) % 0.45/0.67 (define @t55 () (not @t54)) % 0.45/0.67 (define @t56 () (not @t50)) % 0.45/0.67 (define @t57 () (< @t44 6)) % 0.45/0.67 (define @t58 () (not @t57)) % 0.45/0.67 (define @t59 () (not true)) % 0.45/0.67 (define @t60 () (* -1 7)) % 0.45/0.67 (define @t61 () (* -1 0)) % 0.45/0.67 (define @t62 () (+ 6 0 @t61 @t60)) % 0.45/0.67 (define @t63 () (* -1 @t42)) % 0.45/0.67 (define @t64 () (= (+ @t63 0 0 @t42) 0)) % 0.45/0.67 (define @t65 () (* 0 @t44)) % 0.45/0.67 (define @t66 () (= @t65 0)) % 0.45/0.67 (define @t67 () (* 0 @t51)) % 0.45/0.67 (define @t68 () (= @t67 0)) % 0.45/0.67 (define @t69 () (+ @t63 @t67 @t65 @t42)) % 0.45/0.67 (define @t70 () (* -1 @t51)) % 0.45/0.67 (define @t71 () (+ @t44 @t70)) % 0.45/0.67 (define @t72 () (* -1 @t71)) % 0.45/0.67 (define @t73 () (+ @t42 @t70)) % 0.45/0.67 (define @t74 () (+ @t44 @t73 @t72 @t63)) % 0.45/0.67 (define @t75 () (= @t74 @t69)) % 0.45/0.67 (define @t76 () (>= @t74 @t62)) % 0.45/0.67 (define @t77 () (< -1 0)) % 0.45/0.67 (define @t78 () (= @t71 0)) % 0.45/0.67 (define @t79 () (= (* 1 (- @t71 0)) (* 1 (- @t44 @t51)))) % 0.45/0.67 (define @t80 () (= @t78 @t52)) % 0.45/0.67 (define @t81 () (and @t43 @t52 @t54 @t50)) % 0.45/0.67 (define @t82 () (tptp.in 5 @t37)) % 0.45/0.67 (define @t83 () (not @t82)) % 0.45/0.67 (define @t84 () (= @t83 @t54)) % 0.45/0.67 (define @t85 () (not @t84)) % 0.45/0.67 (define @t86 () (+ -1 @t51)) % 0.45/0.67 (define @t87 () (= @t42 @t86)) % 0.45/0.67 (define @t88 () (= @t82 @t87)) % 0.45/0.67 (define @t89 () (not @t87)) % 0.45/0.67 (define @t90 () (+ 6 -1 @t61 @t60)) % 0.45/0.67 (define @t91 () (>= @t74 @t90)) % 0.45/0.67 (define @t92 () (= (* 1 (- @t73 -1)) (* 1 (- @t42 @t86)))) % 0.45/0.67 (define @t93 () (= @t73 -1)) % 0.45/0.67 (define @t94 () (= @t93 @t87)) % 0.45/0.67 (define @t95 () (and @t43 @t52 @t87 @t50)) % 0.45/0.67 (define @t96 () (tptp.in 4 @t37)) % 0.45/0.67 (define @t97 () (not @t96)) % 0.45/0.67 (define @t98 () (= @t97 @t52)) % 0.45/0.67 (define @t99 () (not @t98)) % 0.45/0.67 (define @t100 () (@list true false)) % 0.45/0.67 (define @t101 () (= @t44 @t86)) % 0.45/0.67 (define @t102 () (= @t96 @t101)) % 0.45/0.67 (define @t103 () (>= @t73 1)) % 0.45/0.67 (define @t104 () (not @t101)) % 0.45/0.67 (define @t105 () (not @t103)) % 0.45/0.67 (define @t106 () (* -1 -1)) % 0.45/0.67 (define @t107 () (+ 1 @t60 @t106 5)) % 0.45/0.67 (define @t108 () (+ @t73 @t63 @t72 @t44)) % 0.45/0.67 (define @t109 () (>= @t108 @t107)) % 0.45/0.67 (define @t110 () (= @t71 -1)) % 0.45/0.67 (define @t111 () (- @t86 @t51)) % 0.45/0.67 (define @t112 () (+ @t51 @t39)) % 0.45/0.67 (define @t113 () (+ @t63 @t51)) % 0.45/0.67 (define @t114 () (* -1 @t73)) % 0.45/0.67 (define @t115 () (+ @t42 @t114)) % 0.45/0.67 (define @t116 () (@list false)) % 0.45/0.67 (define @t117 () (@list @t103)) % 0.45/0.67 (define @t118 () (+ -1 @t39)) % 0.45/0.67 (define @t119 () (* 0 @t42)) % 0.45/0.67 (define @t120 () (+ @t67 @t119)) % 0.45/0.67 (define @t121 () (+ @t73 @t114)) % 0.45/0.67 (assume @p1 (forall (@list @t1) (not (tptp.in @t1 tptp.empty)))) % 0.45/0.67 (assume @p2 (forall (@list @t3 @t2) (tptp.in @t3 (tptp.add @t3 @t2)))) % 0.45/0.67 (assume @p3 (forall (@list @t5 @t4) (not (tptp.in @t5 (tptp.remove @t5 @t4))))) % 0.45/0.67 (assume @p4 (forall (@list @t8 @t6 @t7) (= (or (tptp.in @t8 @t6) (= @t8 @t7)) (tptp.in @t8 (tptp.add @t7 @t6))))) % 0.45/0.67 (assume @p5 (forall (@list @t11 @t9 @t10) (= (and (tptp.in @t11 @t9) (not (= @t11 @t10))) (tptp.in @t11 (tptp.remove @t10 @t9))))) % 0.45/0.67 (assume @p6 (forall (@list @t12) (>= (tptp.count @t12) 0))) % 0.45/0.67 (assume @p7 (forall (@list @t13) (= (= @t13 tptp.empty) (= (tptp.count @t13) 0)))) % 0.45/0.67 (assume @p8 (forall (@list @t15 @t14) (= (not (tptp.in @t15 @t14)) (= (tptp.count (tptp.add @t15 @t14)) (+ (tptp.count @t14) 1))))) % 0.45/0.67 (assume @p9 (forall (@list @t17 @t16) (= (tptp.in @t17 @t16) (= (tptp.count (tptp.add @t17 @t16)) (tptp.count @t16))))) % 0.45/0.67 (assume @p10 @t26) % 0.45/0.67 (assume @p11 (forall (@list @t28 @t27) (= (not (tptp.in @t28 @t27)) (= (tptp.count (tptp.remove @t28 @t27)) (tptp.count @t27))))) % 0.45/0.67 (assume @p12 (forall (@list @t30 @t29) (=> (tptp.in @t30 @t29) (= @t29 (tptp.add @t30 (tptp.remove @t30 @t29)))))) % 0.45/0.67 (assume @p13 @t36) % 0.45/0.67 (assume @p14 true) % 0.45/0.67 (step @p15 :rule instantiate :premises (@p11) :args (@t38)) % 0.45/0.67 (step @p16 :rule arith_poly_norm :args ((= (+ @t19 -1) (+ -1 @t19)))) % 0.45/0.67 (step @p17 :rule evaluate :args (@t39)) % 0.45/0.67 (step @p18 :rule refl :args (@t19)) % 0.45/0.67 (step @p19 :rule nary_cong :premises (@p18 @p17) :args (@t40)) % 0.45/0.67 (step @p20 :rule trans :premises (@p19 @p16)) % 0.45/0.67 (step @p21 :rule arith_poly_norm :args ((= @t20 @t40))) % 0.45/0.67 (step @p22 :rule trans :premises (@p21 @p20)) % 0.45/0.67 (step @p23 :rule refl :args (@t22)) % 0.45/0.67 (step @p24 :rule cong :premises (@p23 @p22) :args (@t23)) % 0.45/0.67 (step @p25 :rule refl :args (@t24)) % 0.45/0.67 (step @p26 :rule cong :premises (@p25 @p24) :args (@t25)) % 0.45/0.67 (step @p27 :rule cong :premises (@p26) :args (@t26)) % 0.45/0.67 (step @p28 :rule eq_resolve :premises (@p10 @p27)) % 0.45/0.67 (step @p29 :rule instantiate :premises (@p28) :args (@t41)) % 0.45/0.67 (step @p30 :rule instantiate :premises (@p11) :args (@t41)) % 0.45/0.67 (step @p31 :rule bool-impl-elim :args (@t33 @t32)) % 0.45/0.67 (step @p32 :rule cong :premises (@p31) :args (@t35)) % 0.45/0.67 (step @p33 :rule cong :premises (@p32) :args (@t36)) % 0.45/0.67 (step @p34 :rule eq_resolve :premises (@p13 @p33)) % 0.45/0.67 (step @p35 :rule skolemize :premises (@p34)) % 0.45/0.67 (step @p36 :rule bool-double-not-elim :args (@t43)) % 0.45/0.67 (step @p37 :rule refl :args (@t47)) % 0.45/0.67 (step @p38 :rule nary_cong :premises (@p37 @p36) :args ((or @t47 (not @t46)))) % 0.45/0.67 (step @p39 :rule cnf_or_neg :args (@t47 0)) % 0.45/0.67 (step @p40 :rule eq_resolve :premises (@p39 @p38)) % 0.45/0.67 (step @p41 :rule reordering :premises (@p40) :args ((or @t43 @t47))) % 0.45/0.67 (step @p42 :rule chain_m_resolution :premises (@p41 @p35) :args (@t43 @t48 @t49)) % 0.45/0.67 (step @p43 :rule cnf_or_neg :args (@t47 1)) % 0.45/0.67 (step @p44 :rule chain_m_resolution :premises (@p43 @p35) :args (@t50 @t48 @t49)) % 0.45/0.67 (step @p45 :rule refl :args (@t53)) % 0.45/0.67 (step @p46 :rule refl :args (@t55)) % 0.45/0.67 (step @p47 :rule bool-double-not-elim :args (@t45)) % 0.45/0.67 (step @p48 :rule refl :args (@t46)) % 0.45/0.67 (step @p49 :rule nary_cong :premises (@p48 @p47 @p46 @p45) :args ((or @t46 @t56 @t55 @t53))) % 0.45/0.67 (assume-push @p316 @t43) % 0.45/0.67 (assume-push @p317 @t52) % 0.45/0.67 (assume-push @p318 @t54) % 0.45/0.67 (assume-push @p319 @t50) % 0.45/0.67 (step @p54 :rule arith-elim-lt :args (@t44 6)) % 0.45/0.67 (step @p55 :rule cong :premises (@p54) :args (@t58)) % 0.45/0.67 (step @p56 :rule trans :premises (@p55 @p47)) % 0.45/0.67 (step @p57 :rule symm :premises (@p56)) % 0.45/0.67 (assume-push @p320 @t57) % 0.45/0.67 (step @p59 :rule evaluate :args (@t59)) % 0.45/0.67 (step @p60 :rule evaluate :args ((>= 0 -1))) % 0.45/0.67 (step @p61 :rule evaluate :args ((+ 6 0 0 -7))) % 0.45/0.67 (step @p62 :rule evaluate :args (@t60)) % 0.45/0.67 (step @p63 :rule evaluate :args (@t61)) % 0.45/0.67 (step @p64 :rule refl :args (0)) % 0.45/0.67 (step @p65 :rule refl :args (6)) % 0.45/0.67 (step @p66 :rule nary_cong :premises (@p65 @p64 @p63 @p62) :args (@t62)) % 0.45/0.67 (step @p67 :rule trans :premises (@p66 @p61)) % 0.45/0.67 (step @p68 :rule arith_poly_norm :args (@t64)) % 0.45/0.67 (step @p69 :rule refl :args (@t42)) % 0.45/0.67 (step @p70 :rule arith_poly_norm :args (@t66)) % 0.45/0.67 (step @p71 :rule arith_poly_norm :args (@t68)) % 0.45/0.67 (step @p72 :rule refl :args (@t63)) % 0.45/0.67 (step @p73 :rule nary_cong :premises (@p72 @p71 @p70 @p69) :args (@t69)) % 0.45/0.67 (step @p74 :rule trans :premises (@p73 @p68)) % 0.45/0.67 (step @p75 :rule arith_poly_norm :args (@t75)) % 0.45/0.67 (step @p76 :rule trans :premises (@p75 @p74)) % 0.45/0.67 (step @p77 :rule cong :premises (@p76 @p67) :args (@t76)) % 0.45/0.67 (step @p78 :rule trans :premises (@p77 @p60)) % 0.45/0.67 (step @p79 :rule cong :premises (@p78) :args ((not @t76))) % 0.45/0.67 (step @p80 :rule trans :premises (@p79 @p59)) % 0.45/0.67 (step @p81 :rule arith-elim-lt :args (@t74 @t62)) % 0.45/0.67 (step @p82 :rule trans :premises (@p81 @p80)) % 0.45/0.67 (step @p83 :rule arith_mult_neg :args (-1 @t43)) % 0.45/0.67 (step @p84 :rule evaluate :args (@t77)) % 0.45/0.67 (step @p85 :rule true_elim :premises (@p84)) % 0.45/0.67 (step @p86 :rule and_intro :premises (@p85 @p42)) % 0.45/0.67 (step @p87 :rule modus_ponens :premises (@p86 @p83)) % 0.45/0.67 (step @p88 :rule arith_mult_neg :args (-1 @t78)) % 0.45/0.67 (step @p89 :rule arith_poly_norm :args (@t79)) % 0.45/0.67 (step @p90 :rule arith_poly_norm_rel :premises (@p89) :args (@t80)) % 0.45/0.67 (step @p91 :rule symm :premises (@p90)) % 0.45/0.67 (step @p92 :rule eq_resolve :premises (@p317 @p91)) % 0.45/0.67 (step @p93 :rule and_intro :premises (@p85 @p92)) % 0.45/0.67 (step @p94 :rule modus_ponens :premises (@p93 @p88)) % 0.45/0.67 (step @p95 :rule arith_poly_norm :args ((= (* 1 (- @t73 0)) (* 1 (- @t42 @t51))))) % 0.45/0.67 (step @p96 :rule arith_poly_norm_rel :premises (@p95) :args ((= (= @t73 0) @t54))) % 0.45/0.67 (step @p97 :rule symm :premises (@p96)) % 0.45/0.67 (step @p98 :rule eq_resolve :premises (@p318 @p97)) % 0.45/0.67 (step @p99 :rule symm :premises (@p54)) % 0.45/0.67 (step @p100 :rule chain_m_resolution :premises (@p43 @p35) :args (@t50 @t48 @t49)) % 0.45/0.67 (step @p101 :rule eq_resolve :premises (@p100 @p99)) % 0.45/0.67 (step @p102 :rule arith_sum_ub :premises (@p101 @p98 @p94 @p87)) % 0.45/0.67 (step @p103 false :rule eq_resolve :premises (@p102 @p82)) % 0.45/0.67 (step-pop @p321 :rule scope :premises (@p103)) % 0.45/0.67 (step @p104 :rule process_scope :premises (@p321) :args (false)) % 0.45/0.67 (step @p106 :rule eq_resolve :premises (@p104 @p56)) % 0.45/0.67 (step @p107 :rule eq_resolve :premises (@p106 @p57)) % 0.45/0.67 (step @p99 :rule symm :premises (@p54)) % 0.45/0.67 (step @p108 :rule eq_resolve :premises (@p44 @p99)) % 0.45/0.67 (step @p109 false :rule contra :premises (@p108 @p107)) % 0.45/0.67 (step-pop @p322 :rule scope :premises (@p109)) % 0.45/0.67 (step-pop @p323 :rule scope :premises (@p322)) % 0.45/0.67 (step-pop @p324 :rule scope :premises (@p323)) % 0.45/0.67 (step-pop @p325 :rule scope :premises (@p324)) % 0.45/0.67 (step @p110 :rule process_scope :premises (@p325) :args (false)) % 0.45/0.67 (assume-push @p326 @t43) % 0.45/0.67 (assume-push @p327 @t50) % 0.45/0.67 (assume-push @p328 @t54) % 0.45/0.67 (assume-push @p329 @t52) % 0.45/0.67 (step @p119 :rule and_intro :premises (@p42 @p329 @p328 @p44)) % 0.45/0.67 (step-pop @p330 :rule scope :premises (@p119)) % 0.45/0.67 (step-pop @p331 :rule scope :premises (@p330)) % 0.45/0.67 (step-pop @p332 :rule scope :premises (@p331)) % 0.45/0.67 (step-pop @p333 :rule scope :premises (@p332)) % 0.45/0.67 (step @p120 :rule process_scope :premises (@p333) :args (@t81)) % 0.45/0.67 (step @p125 :rule implies_elim :premises (@p120)) % 0.45/0.67 (step @p126 :rule resolution :premises (@p125 @p110) :args (true @t81)) % 0.45/0.67 (step @p127 :rule not_and :premises (@p126)) % 0.45/0.67 (step @p128 :rule eq_resolve :premises (@p127 @p49)) % 0.45/0.67 (step @p129 :rule refl :args (@t54)) % 0.45/0.67 (step @p130 :rule bool-double-not-elim :args (@t82)) % 0.45/0.67 (step @p131 :rule refl :args (@t85)) % 0.45/0.67 (step @p132 :rule nary_cong :premises (@p131 @p130 @p129) :args ((or @t85 (not @t83) @t54))) % 0.45/0.67 (step @p133 :rule cnf_equiv_pos1 :args (@t84)) % 0.45/0.67 (step @p134 :rule eq_resolve :premises (@p133 @p132)) % 0.45/0.67 (step @p135 :rule reordering :premises (@p134) :args ((or @t82 @t54 @t85))) % 0.45/0.67 (step @p136 :rule instantiate :premises (@p28) :args (@t38)) % 0.45/0.67 (step @p137 :rule cnf_equiv_pos1 :args (@t88)) % 0.45/0.67 (step @p138 :rule reordering 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