%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : PUZ062-2 : TPTP v9.2.1. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n027.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 08:44:06 AM UTC 2026 % Result : Unsatisfiable 0.38s 0.56s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : PUZ062-2 : TPTP v9.2.1. Released v3.2.0. % 0.00/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n027.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 13:16:21 EDT 2026 % 0.16/0.34 % CPUTime : % 0.30/0.49 %----Proving TF0_NAR, FOF, or CNF % 0.30/0.50 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.38/0.56 % SZS status Unsatisfiable % 0.38/0.56 % SZS output start Proof % 0.38/0.56 ( % 0.38/0.56 (declare-sort $$unsorted 0) % 0.38/0.56 (declare-const tptp.c_Pair (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.38/0.56 (declare-const tptp.v_i $$unsorted) % 0.38/0.56 (declare-const tptp.v_j $$unsorted) % 0.38/0.56 (declare-const tptp.v_a $$unsorted) % 0.38/0.56 (declare-const tptp.c_Mutil_Ocoloured (-> $$unsorted $$unsorted)) % 0.38/0.56 (declare-const tptp.c_0 $$unsorted) % 0.38/0.56 (declare-const tptp.c_Suc (-> $$unsorted $$unsorted)) % 0.38/0.56 (declare-const tptp.c_insert (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.38/0.56 (declare-const tptp.c_in (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.38/0.56 (declare-const tptp.v_m $$unsorted) % 0.38/0.56 (declare-const tptp.tc_prod (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.56 (declare-const tptp.tc_set (-> $$unsorted $$unsorted)) % 0.38/0.56 (declare-const tptp.c_Finite__Set_Ocard (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.56 (declare-const tptp.v_t $$unsorted) % 0.38/0.56 (declare-const tptp.c_Mutil_Odomino $$unsorted) % 0.38/0.56 (declare-const tptp.c_Finite__Set_OFinites $$unsorted) % 0.38/0.56 (declare-const tptp.c_inter (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.38/0.56 (declare-const tptp.tc_nat $$unsorted) % 0.38/0.56 (declare-const tptp.v_n $$unsorted) % 0.38/0.56 (declare-const tptp.c_Mutil_Otiling (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.56 (declare-const tptp.c_emptyset $$unsorted) % 0.38/0.56 (define @t1 () (@var "T_a" $$unsorted)) % 0.38/0.56 (define @t2 () (@var "V_A" $$unsorted)) % 0.38/0.56 (define @t3 () (@var "V_x" $$unsorted)) % 0.38/0.56 (define @t4 () (tptp.c_insert @t3 @t2 @t1)) % 0.38/0.56 (define @t5 () (tptp.tc_set @t1)) % 0.38/0.56 (define @t6 () (@var "V_G" $$unsorted)) % 0.38/0.56 (define @t7 () (@var "V_F" $$unsorted)) % 0.38/0.56 (define @t8 () (tptp.tc_prod tptp.tc_nat tptp.tc_nat)) % 0.38/0.56 (define @t9 () (tptp.tc_set @t8)) % 0.38/0.56 (define @t10 () (@var "V_t" $$unsorted)) % 0.38/0.56 (define @t11 () (tptp.c_Mutil_Otiling tptp.c_Mutil_Odomino @t8)) % 0.38/0.56 (define @t12 () (@var "V_B" $$unsorted)) % 0.38/0.56 (define @t13 () (@var "V_c" $$unsorted)) % 0.38/0.56 (define @t14 () (tptp.c_in @t13 @t12 @t1)) % 0.38/0.56 (define @t15 () (tptp.c_in @t13 (tptp.c_inter @t2 @t12 @t1) @t1)) % 0.38/0.56 (define @t16 () (forall (@list @t13 @t1) (not (tptp.c_in @t13 tptp.c_emptyset @t1)))) % 0.38/0.56 (define @t17 () (tptp.c_in tptp.v_t @t11 @t9)) % 0.38/0.56 (define @t18 () (tptp.c_Mutil_Ocoloured (tptp.c_Suc tptp.c_0))) % 0.38/0.56 (define @t19 () (tptp.c_inter @t18 tptp.v_t @t8)) % 0.38/0.56 (define @t20 () (tptp.c_Finite__Set_Ocard @t19 @t8)) % 0.38/0.56 (define @t21 () (tptp.c_Mutil_Ocoloured tptp.c_0)) % 0.38/0.56 (define @t22 () (tptp.c_inter @t21 tptp.v_t @t8)) % 0.38/0.56 (define @t23 () (tptp.c_Finite__Set_Ocard @t22 @t8)) % 0.38/0.56 (define @t24 () (tptp.c_inter tptp.v_a tptp.v_t @t8)) % 0.38/0.56 (define @t25 () (tptp.c_Pair tptp.v_i tptp.v_j tptp.tc_nat tptp.tc_nat)) % 0.38/0.56 (define @t26 () (tptp.c_inter @t21 tptp.v_a @t8)) % 0.38/0.56 (define @t27 () (tptp.c_Pair tptp.v_m tptp.v_n tptp.tc_nat tptp.tc_nat)) % 0.38/0.56 (define @t28 () (tptp.c_inter @t18 tptp.v_a @t8)) % 0.38/0.56 (define @t29 () (tptp.c_Finite__Set_Ocard (tptp.c_insert @t27 @t19 @t8) @t8)) % 0.38/0.56 (define @t30 () (tptp.c_Finite__Set_Ocard (tptp.c_insert @t25 @t22 @t8) @t8)) % 0.38/0.56 (define @t31 () (tptp.c_in @t25 @t26 @t8)) % 0.38/0.56 (define @t32 () (tptp.c_in @t25 tptp.v_a @t8)) % 0.38/0.56 (define @t33 () (not @t31)) % 0.38/0.56 (define @t34 () (or @t33 @t32)) % 0.38/0.56 (define @t35 () (@list false false)) % 0.38/0.56 (define @t36 () (tptp.c_in @t27 @t28 @t8)) % 0.38/0.56 (define @t37 () (tptp.c_in @t27 tptp.v_a @t8)) % 0.38/0.56 (define @t38 () (not @t36)) % 0.38/0.56 (define @t39 () (or @t38 @t37)) % 0.38/0.56 (define @t40 () (tptp.c_in @t27 @t24 @t8)) % 0.38/0.56 (define @t41 () (not @t37)) % 0.38/0.56 (define @t42 () (tptp.c_in @t27 tptp.v_t @t8)) % 0.38/0.56 (define @t43 () (not @t42)) % 0.38/0.56 (define @t44 () (or @t43 @t41 @t40)) % 0.38/0.56 (define @t45 () (tptp.c_in @t27 @t19 @t8)) % 0.38/0.56 (define @t46 () (not @t45)) % 0.38/0.56 (define @t47 () (or @t46 @t42)) % 0.38/0.56 (define @t48 () (tptp.c_in tptp.v_t tptp.c_Finite__Set_OFinites @t9)) % 0.38/0.56 (define @t49 () (not @t17)) % 0.38/0.56 (define @t50 () (or @t49 @t48)) % 0.38/0.56 (define @t51 () (tptp.c_in @t19 tptp.c_Finite__Set_OFinites @t9)) % 0.38/0.56 (define @t52 () (not @t48)) % 0.38/0.56 (define @t53 () (or @t52 @t51)) % 0.38/0.56 (define @t54 () (= @t29 (tptp.c_Suc @t20))) % 0.38/0.56 (define @t55 () (not @t51)) % 0.38/0.56 (define @t56 () (or @t55 @t45 @t54)) % 0.38/0.56 (define @t57 () (@list false true false)) % 0.38/0.56 (define @t58 () (tptp.c_Suc @t23)) % 0.38/0.56 (define @t59 () (= @t30 @t58)) % 0.38/0.56 (define @t60 () (tptp.c_in @t22 tptp.c_Finite__Set_OFinites @t9)) % 0.38/0.56 (define @t61 () (or @t52 @t60)) % 0.38/0.56 (define @t62 () (tptp.c_in @t25 @t22 @t8)) % 0.38/0.56 (define @t63 () (not @t60)) % 0.38/0.56 (define @t64 () (or @t63 @t62 @t59)) % 0.38/0.56 (define @t65 () (tptp.c_in @t25 tptp.v_t @t8)) % 0.38/0.56 (define @t66 () (not @t62)) % 0.38/0.56 (define @t67 () (or @t66 @t65)) % 0.38/0.56 (define @t68 () (tptp.c_in @t25 @t24 @t8)) % 0.38/0.56 (define @t69 () (not @t32)) % 0.38/0.56 (define @t70 () (not @t65)) % 0.38/0.56 (define @t71 () (or @t70 @t69 @t68)) % 0.38/0.56 (define @t72 () (tptp.c_in @t25 tptp.c_emptyset @t8)) % 0.38/0.56 (assume @p1 (forall (@list @t2 @t1 @t3) (or (not (tptp.c_in @t2 tptp.c_Finite__Set_OFinites @t5)) (tptp.c_in @t3 @t2 @t1) (= (tptp.c_Finite__Set_Ocard @t4 @t1) (tptp.c_Suc (tptp.c_Finite__Set_Ocard @t2 @t1)))))) % 0.38/0.56 (assume @p2 (forall (@list @t6 @t1 @t7) (or (not (tptp.c_in @t6 tptp.c_Finite__Set_OFinites @t5)) (tptp.c_in (tptp.c_inter @t7 @t6 @t1) tptp.c_Finite__Set_OFinites @t5)))) % 0.38/0.56 (assume @p3 (forall (@list @t10) (or (not (tptp.c_in @t10 @t11 @t9)) (tptp.c_in @t10 tptp.c_Finite__Set_OFinites @t9)))) % 0.38/0.56 (assume @p4 (forall (@list @t13 @t2 @t12 @t1) (or (not @t15) @t14))) % 0.38/0.56 (assume @p5 (forall (@list @t13 @t12 @t1 @t2) (or (not @t14) (not (tptp.c_in @t13 @t2 @t1)) @t15))) % 0.38/0.56 (assume @p6 (forall (@list @t3 @t2 @t1) (tptp.c_in @t3 @t4 @t1))) % 0.38/0.56 (assume @p7 @t16) % 0.38/0.56 (assume @p8 @t17) % 0.38/0.56 (assume @p9 (= @t23 @t20)) % 0.38/0.56 (assume @p10 (= @t24 tptp.c_emptyset)) % 0.38/0.56 (assume @p11 (= @t26 (tptp.c_insert @t25 tptp.c_emptyset @t8))) % 0.38/0.56 (assume @p12 (= @t28 (tptp.c_insert @t27 tptp.c_emptyset @t8))) % 0.38/0.56 (assume @p13 (not (= @t30 @t29))) % 0.38/0.56 (step @p14 :rule instantiate :premises (@p5) :args ((@list @t25 tptp.v_t @t8 tptp.v_a))) % 0.38/0.56 (step @p15 :rule instantiate :premises (@p4) :args ((@list @t25 @t21 tptp.v_a @t8))) % 0.38/0.56 (step @p16 :rule instantiate :premises (@p6) :args ((@list @t25 tptp.c_emptyset @t8))) % 0.38/0.56 (step @p17 :rule true_intro :premises (@p16)) % 0.38/0.56 (step @p18 :rule refl :args (@t8)) % 0.38/0.56 (step @p19 :rule refl :args (@t25)) % 0.38/0.56 (step @p20 :rule cong :premises (@p19 @p11 @p18) :args (@t31)) % 0.38/0.56 (step @p21 :rule trans :premises (@p20 @p17)) % 0.38/0.56 (step @p22 :rule true_elim :premises (@p21)) % 0.38/0.56 (step @p23 :rule cnf_or_pos :args (@t34)) % 0.38/0.56 (step @p24 :rule reordering :premises (@p23) :args ((or @t33 @t32 (not @t34)))) % 0.38/0.56 (step @p25 :rule chain_m_resolution :premises (@p24 @p22 @p15) :args (@t32 @t35 (@list @t31 @t34))) % 0.38/0.56 (step @p26 :rule instantiate :premises (@p4) :args ((@list @t25 @t21 tptp.v_t @t8))) % 0.38/0.56 (step @p27 :rule instantiate :premises (@p1) :args ((@list @t22 @t8 @t25))) % 0.38/0.56 (step @p28 :rule false_intro :premises (@p13)) % 0.38/0.56 (step @p29 :rule instantiate :premises (@p1) :args ((@list @t19 @t8 @t27))) % 0.38/0.56 (step @p30 :rule instantiate :premises (@p4) :args ((@list @t27 @t18 tptp.v_t @t8))) % 0.38/0.56 (step @p31 :rule instantiate :premises (@p5) :args ((@list @t27 tptp.v_t @t8 tptp.v_a))) % 0.38/0.56 (step @p32 :rule instantiate :premises (@p4) :args ((@list @t27 @t18 tptp.v_a @t8))) % 0.38/0.56 (step @p33 :rule instantiate :premises (@p6) :args ((@list @t27 tptp.c_emptyset @t8))) % 0.38/0.56 (step @p34 :rule true_intro :premises (@p33)) % 0.38/0.56 (step @p35 :rule refl :args (@t27)) % 0.38/0.56 (step @p36 :rule cong :premises (@p35 @p12 @p18) :args (@t36)) % 0.38/0.56 (step @p37 :rule trans :premises (@p36 @p34)) % 0.38/0.56 (step @p38 :rule true_elim :premises (@p37)) % 0.38/0.56 (step @p39 :rule cnf_or_pos :args (@t39)) % 0.38/0.56 (step @p40 :rule reordering :premises (@p39) :args ((or @t38 @t37 (not @t39)))) % 0.38/0.56 (step @p41 :rule chain_m_resolution :premises (@p40 @p38 @p32) :args (@t37 @t35 (@list @t36 @t39))) % 0.38/0.56 (step @p42 :rule instantiate :premises (@p7) :args ((@list @t27 @t8))) % 0.38/0.56 (step @p43 :rule false_intro :premises (@p42)) % 0.38/0.56 (step @p44 :rule cong :premises (@p35 @p10 @p18) :args (@t40)) % 0.38/0.56 (step @p45 :rule trans :premises (@p44 @p43)) % 0.38/0.56 (step @p46 :rule false_elim :premises (@p45)) % 0.38/0.56 (step @p47 :rule cnf_or_pos :args (@t44)) % 0.38/0.56 (step @p48 :rule reordering :premises (@p47) :args ((or @t40 @t43 @t41 (not @t44)))) % 0.38/0.56 (step @p49 :rule chain_m_resolution :premises (@p48 @p46 @p41 @p31) :args (@t43 (@list true false false) (@list @t40 @t37 @t44))) % 0.38/0.56 (step @p50 :rule cnf_or_pos :args (@t47)) % 0.38/0.56 (step @p51 :rule reordering :premises (@p50) :args ((or @t46 @t42 (not @t47)))) % 0.38/0.56 (step @p52 :rule chain_m_resolution :premises (@p51 @p49 @p30) :args (@t46 (@list true false) (@list @t42 @t47))) % 0.38/0.56 (step @p53 :rule instantiate :premises (@p2) :args ((@list tptp.v_t @t8 @t18))) % 0.38/0.56 (step @p54 :rule instantiate :premises (@p3) :args ((@list tptp.v_t))) % 0.38/0.56 (step @p55 :rule cnf_or_pos :args (@t50)) % 0.38/0.56 (step @p56 :rule reordering :premises (@p55) :args ((or @t49 @t48 (not @t50)))) % 0.38/0.56 (step @p57 :rule chain_m_resolution :premises (@p56 @p8 @p54) :args (@t48 @t35 (@list @t17 @t50))) % 0.38/0.56 (step @p58 :rule cnf_or_pos :args (@t53)) % 0.38/0.56 (step @p59 :rule reordering :premises (@p58) :args ((or @t51 @t52 (not @t53)))) % 0.38/0.56 (step @p60 :rule chain_m_resolution :premises (@p59 @p57 @p53) :args (@t51 @t35 (@list @t48 @t53))) % 0.38/0.56 (step @p61 :rule cnf_or_pos :args (@t56)) % 0.38/0.56 (step @p62 :rule reordering :premises (@p61) :args ((or @t55 @t45 @t54 (not @t56)))) % 0.38/0.56 (step @p63 :rule chain_m_resolution :premises (@p62 @p60 @p52 @p29) :args (@t54 @t57 (@list @t51 @t45 @t56))) % 0.38/0.56 (step @p64 :rule symm :premises (@p63)) % 0.38/0.56 (step @p65 :rule cong :premises (@p9) :args (@t58)) % 0.38/0.56 (step @p66 :rule trans :premises (@p65 @p64)) % 0.38/0.56 (step @p67 :rule refl :args (@t30)) % 0.38/0.56 (step @p68 :rule cong :premises (@p67 @p66) :args (@t59)) % 0.38/0.56 (step @p69 :rule trans :premises (@p68 @p28)) % 0.38/0.56 (step @p70 :rule false_elim :premises (@p69)) % 0.38/0.56 (step @p71 :rule instantiate :premises (@p2) :args ((@list tptp.v_t @t8 @t21))) % 0.38/0.56 (step @p72 :rule cnf_or_pos :args (@t61)) % 0.38/0.56 (step @p73 :rule reordering :premises (@p72) :args ((or @t60 @t52 (not @t61)))) % 0.38/0.56 (step @p74 :rule chain_m_resolution :premises (@p73 @p57 @p71) :args (@t60 @t35 (@list @t48 @t61))) % 0.38/0.56 (step @p75 :rule cnf_or_pos :args (@t64)) % 0.38/0.56 (step @p76 :rule reordering :premises (@p75) :args ((or @t63 @t62 @t59 (not @t64)))) % 0.38/0.56 (step @p77 :rule chain_m_resolution :premises (@p76 @p74 @p70 @p27) :args (@t62 @t57 (@list @t60 @t59 @t64))) % 0.38/0.56 (step @p78 :rule cnf_or_pos :args (@t67)) % 0.38/0.56 (step @p79 :rule reordering :premises (@p78) :args ((or @t66 @t65 (not @t67)))) % 0.38/0.56 (step @p80 :rule chain_m_resolution :premises (@p79 @p77 @p26) :args (@t65 @t35 (@list @t62 @t67))) % 0.38/0.56 (step @p81 :rule cnf_or_pos :args (@t71)) % 0.38/0.56 (step @p82 :rule reordering :premises (@p81) :args ((or @t70 @t69 @t68 (not @t71)))) % 0.38/0.56 (step @p83 :rule chain_m_resolution :premises (@p82 @p80 @p25 @p14) :args (@t68 (@list false false false) (@list @t65 @t32 @t71))) % 0.38/0.56 (step @p84 :rule true_intro :premises (@p83)) % 0.38/0.56 (step @p85 :rule symm :premises (@p10)) % 0.38/0.56 (step @p86 :rule cong :premises (@p19 @p85 @p18) :args (@t72)) % 0.38/0.56 (step @p87 :rule trans :premises (@p86 @p84)) % 0.38/0.56 (step @p88 :rule true_elim :premises (@p87)) % 0.38/0.56 (assume-push @p95 @t16) % 0.38/0.56 (step @p90 :rule instantiate :premises (@p7) :args ((@list @t25 @t8))) % 0.38/0.56 (step-pop @p96 :rule scope :premises (@p90)) % 0.38/0.56 (step @p91 :rule process_scope :premises (@p96) :args ((not @t72))) % 0.38/0.56 (step @p93 :rule implies_elim :premises (@p91)) % 0.38/0.56 (step @p94 false :rule chain_m_resolution :premises (@p93 @p88 @p7) :args (false @t35 (@list @t72 @t16))) % 0.38/0.56 ) % 0.38/0.56 % SZS output end Proof % 0.38/0.57 % cvc5 exiting %------------------------------------------------------------------------------