%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : KRS263+1 : TPTP v9.2.1. Bugfixed v5.4.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n001.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 08:29:11 AM UTC 2026 % Result : Theorem 203.03s 203.39s % Output : Proof 203.03s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : KRS263+1 : TPTP v9.2.1. Bugfixed v5.4.0. % 0.12/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.19/0.35 % Computer : n001.cluster.edu % 0.19/0.35 % Model : x86_64 x86_64 % 0.19/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.19/0.35 % Memory : 8042.1875MB % 0.19/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.19/0.35 % CPULimit : 300 % 0.19/0.35 % WCLimit : 300 % 0.19/0.35 % DateTime : Tue Jun 2 05:37:35 EDT 2026 % 0.19/0.35 % CPUTime : % 0.33/0.51 %----Proving TF0_NAR, FOF, or CNF % 203.03/203.39 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 203.03/203.39 --- Run --no-e-matching --full-saturate-quant at 6... % 203.03/203.39 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 6... % 203.03/203.39 --- Run --finite-model-find --uf-ss=no-minimal at 6... % 203.03/203.39 --- Run --multi-trigger-when-single --full-saturate-quant at 30... % 203.03/203.39 --- Run --trigger-sel=max --full-saturate-quant at 15... % 203.03/203.39 --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 33... % 203.03/203.39 --- Run --multi-trigger-cache --full-saturate-quant at 15... % 203.03/203.39 --- Run --prenex-quant=none --full-saturate-quant at 30... % 203.03/203.39 --- Run --enum-inst-interleave --decision=internal --full-saturate-quant at 15... % 203.03/203.39 --- Run --relevant-triggers --full-saturate-quant at 30... % 203.03/203.39 --- Run --finite-model-find --e-matching --sort-inference --uf-ss-fair at 15... % 203.03/203.39 % SZS status Theorem % 203.03/203.39 % SZS output start Proof % 203.03/203.39 ( % 203.03/203.39 (declare-sort $$unsorted 0) % 203.03/203.39 (declare-const tptp.xora (-> $$unsorted $$unsorted Bool)) % 203.03/203.39 (declare-const tptp.nevera (-> $$unsorted $$unsorted Bool)) % 203.03/203.39 (declare-const tptp.nota (-> $$unsorted $$unsorted Bool)) % 203.03/203.39 (declare-const tptp.mighta (-> $$unsorted $$unsorted Bool)) % 203.03/203.39 (declare-const tptp.noc $$unsorted) % 203.03/203.39 (declare-const tptp.uns $$unsorted) % 203.03/203.39 (declare-const tptp.not (-> $$unsorted $$unsorted)) % 203.03/203.39 (declare-const tptp.tca $$unsorted) % 203.03/203.39 (declare-const tptp.sca $$unsorted) % 203.03/203.39 (declare-const tptp.wth $$unsorted) % 203.03/203.39 (declare-const tptp.unp $$unsorted) % 203.03/203.39 (declare-const tptp.wca $$unsorted) % 203.03/203.39 (declare-const tptp.wec $$unsorted) % 203.03/203.39 (declare-const tptp.sap $$unsorted) % 203.03/203.39 (declare-const tptp.wtc $$unsorted) % 203.03/203.39 (declare-const tptp.model (-> $$unsorted $$unsorted Bool)) % 203.03/203.39 (declare-const tptp.sat $$unsorted) % 203.03/203.39 (declare-const tptp.cax $$unsorted) % 203.03/203.39 (declare-const tptp.eqv $$unsorted) % 203.03/203.39 (declare-const tptp.esa $$unsorted) % 203.03/203.39 (declare-const tptp.csa $$unsorted) % 203.03/203.39 (declare-const tptp.status (-> $$unsorted $$unsorted $$unsorted Bool)) % 203.03/203.39 (declare-const tptp.thm $$unsorted) % 203.03/203.39 (declare-const tptp.isa (-> $$unsorted $$unsorted Bool)) % 203.03/203.39 (declare-const tptp.eth $$unsorted) % 203.03/203.39 (declare-const tptp.tac $$unsorted) % 203.03/203.39 (declare-const tptp.tau $$unsorted) % 203.03/203.39 (define @t1 () (@var "C" $$unsorted)) % 203.03/203.39 (define @t2 () (@var "Ax" $$unsorted)) % 203.03/203.39 (define @t3 () (@var "I2" $$unsorted)) % 203.03/203.39 (define @t4 () (tptp.model @t3 @t1)) % 203.03/203.39 (define @t5 () (@list @t3)) % 203.03/203.39 (define @t6 () (exists @t5 @t4)) % 203.03/203.39 (define @t7 () (@var "I1" $$unsorted)) % 203.03/203.39 (define @t8 () (tptp.model @t7 @t2)) % 203.03/203.39 (define @t9 () (@list @t7)) % 203.03/203.39 (define @t10 () (exists @t9 @t8)) % 203.03/203.39 (define @t11 () (not @t10)) % 203.03/203.39 (define @t12 () (@list @t2 @t1)) % 203.03/203.39 (define @t13 () (tptp.model @t7 @t1)) % 203.03/203.39 (define @t14 () (and @t8 @t13)) % 203.03/203.39 (define @t15 () (exists @t9 @t14)) % 203.03/203.39 (define @t16 () (tptp.status @t2 @t1 tptp.thm)) % 203.03/203.39 (define @t17 () (forall @t9 (=> @t8 @t13))) % 203.03/203.39 (define @t18 () (= @t17 @t16)) % 203.03/203.39 (define @t19 () (forall @t12 @t18)) % 203.03/203.39 (define @t20 () (tptp.model @t3 @t2)) % 203.03/203.39 (define @t21 () (forall @t5 @t4)) % 203.03/203.39 (define @t22 () (@var "I3" $$unsorted)) % 203.03/203.39 (define @t23 () (tptp.model @t22 @t2)) % 203.03/203.39 (define @t24 () (not @t23)) % 203.03/203.39 (define @t25 () (tptp.model @t22 @t1)) % 203.03/203.39 (define @t26 () (@list @t22)) % 203.03/203.39 (define @t27 () (exists @t26 (and @t25 @t24))) % 203.03/203.39 (define @t28 () (forall @t5 (=> @t20 @t4))) % 203.03/203.39 (define @t29 () (not @t20)) % 203.03/203.39 (define @t30 () (exists @t5 @t29)) % 203.03/203.39 (define @t31 () (tptp.status @t2 @t1 tptp.wtc)) % 203.03/203.39 (define @t32 () (forall @t26 @t25)) % 203.03/203.39 (define @t33 () (and @t10 @t30 @t32)) % 203.03/203.39 (define @t34 () (= @t33 @t31)) % 203.03/203.39 (define @t35 () (forall @t12 @t34)) % 203.03/203.39 (define @t36 () (@var "I4" $$unsorted)) % 203.03/203.39 (define @t37 () (exists (@list @t36) (not (tptp.model @t36 @t1)))) % 203.03/203.39 (define @t38 () (tptp.not @t1)) % 203.03/203.39 (define @t39 () (tptp.model @t3 @t38)) % 203.03/203.39 (define @t40 () (@var "S2" $$unsorted)) % 203.03/203.39 (define @t41 () (@var "S1" $$unsorted)) % 203.03/203.39 (define @t42 () (tptp.mighta @t41 @t40)) % 203.03/203.39 (define @t43 () (tptp.status @t2 @t1 @t40)) % 203.03/203.39 (define @t44 () (tptp.status @t2 @t1 @t41)) % 203.03/203.39 (define @t45 () (and @t44 @t43)) % 203.03/203.39 (define @t46 () (exists @t12 @t45)) % 203.03/203.39 (define @t47 () (= @t46 @t42)) % 203.03/203.39 (define @t48 () (@list @t41 @t40)) % 203.03/203.39 (define @t49 () (forall @t48 @t47)) % 203.03/203.39 (define @t50 () (not @t43)) % 203.03/203.39 (define @t51 () (@var "F" $$unsorted)) % 203.03/203.39 (define @t52 () (@var "I" $$unsorted)) % 203.03/203.39 (define @t53 () (tptp.model @t52 (tptp.not @t51))) % 203.03/203.39 (define @t54 () (tptp.model @t52 @t51)) % 203.03/203.39 (define @t55 () (@list @t52 @t51)) % 203.03/203.39 (define @t56 () (@list @t52)) % 203.03/203.39 (define @t57 () (forall @t56 @t54)) % 203.03/203.39 (define @t58 () (@list @t51)) % 203.03/203.39 (define @t59 () (exists @t58 @t57)) % 203.03/203.39 (define @t60 () (tptp.model @t3 @t51)) % 203.03/203.39 (define @t61 () (not @t60)) % 203.03/203.39 (define @t62 () (exists @t5 @t61)) % 203.03/203.39 (define @t63 () (tptp.model @t7 @t51)) % 203.03/203.39 (define @t64 () (exists @t9 @t63)) % 203.03/203.39 (define @t65 () (and @t64 @t62)) % 203.03/203.39 (define @t66 () (exists @t58 @t65)) % 203.03/203.39 (define @t67 () (not (tptp.mighta tptp.wtc tptp.thm))) % 203.03/203.39 (define @t68 () (@var "b_I" it_8_$$unsorted)) % 203.03/203.39 (define @t69 () (@const 0 (-> it_8_$$unsorted $$unsorted Bool))) % 203.03/203.39 (define @t70 () (@list @t68)) % 203.03/203.39 (define @t71 () (forall @t58 (not (forall @t70 (_ @t69 @t68 @t51))))) % 203.03/203.39 (define @t72 () (not @t71)) % 203.03/203.39 (define @t73 () (not (forall @t58 (not @t57)))) % 203.03/203.39 (define @t74 () (@quantifiers_skolemize @t71 0)) % 203.03/203.39 (define @t75 () (forall @t70 (_ @t69 @t68 @t74))) % 203.03/203.39 (define @t76 () (not (not @t75))) % 203.03/203.39 (define @t77 () (@list true)) % 203.03/203.39 (define @t78 () (@var "b_I1" it_8_$$unsorted)) % 203.03/203.39 (define @t79 () (@list @t78)) % 203.03/203.39 (define @t80 () (@const 1 it_7_$$unsorted)) % 203.03/203.39 (define @t81 () (@const 2 (-> $$unsorted $$unsorted it_7_$$unsorted Bool))) % 203.03/203.39 (define @t82 () (_ @t81 @t2 @t1 @t80)) % 203.03/203.39 (define @t83 () (not @t8)) % 203.03/203.39 (define @t84 () (forall @t9 (or @t83 @t13))) % 203.03/203.39 (define @t85 () (@var "b_BOUND_VARIABLE_7854" it_8_$$unsorted)) % 203.03/203.39 (define @t86 () (@var "b_BOUND_VARIABLE_7850" it_8_$$unsorted)) % 203.03/203.39 (define @t87 () (forall (@list @t51 @t86 @t85) (or (not (_ @t69 @t86 @t51)) (_ @t69 @t85 @t51)))) % 203.03/203.39 (define @t88 () (@quantifiers_skolemize @t87 0)) % 203.03/203.39 (define @t89 () (@list @t88 @t74)) % 203.03/203.39 (define @t90 () (@var "b_S2" it_7_$$unsorted)) % 203.03/203.39 (define @t91 () (@var "b_S1" it_7_$$unsorted)) % 203.03/203.39 (define @t92 () (@const 3 (-> it_7_$$unsorted it_7_$$unsorted Bool))) % 203.03/203.39 (define @t93 () (not (forall @t12 (or (not @t44) @t50)))) % 203.03/203.39 (define @t94 () (forall @t12 (not @t45))) % 203.03/203.39 (define @t95 () (not @t94)) % 203.03/203.39 (define @t96 () (@const 4 it_7_$$unsorted)) % 203.03/203.39 (define @t97 () (_ @t92 @t96 @t80)) % 203.03/203.39 (define @t98 () (_ @t81 @t2 @t1 @t96)) % 203.03/203.39 (define @t99 () (forall @t12 (or (not @t98) (not @t82)))) % 203.03/203.39 (define @t100 () (not @t99)) % 203.03/203.39 (define @t101 () (= @t97 @t100)) % 203.03/203.39 (define @t102 () (not @t101)) % 203.03/203.39 (define @t103 () (@list true false)) % 203.03/203.39 (define @t104 () (@var "b_I3" it_8_$$unsorted)) % 203.03/203.39 (define @t105 () (@list @t104)) % 203.03/203.39 (define @t106 () (@var "b_I2" it_8_$$unsorted)) % 203.03/203.39 (define @t107 () (@list @t106)) % 203.03/203.39 (define @t108 () (@var "b_I1" it_8_$$unsorted)) % 203.03/203.39 (define @t109 () (@list @t108)) % 203.03/203.39 (define @t110 () (not (forall @t9 @t83))) % 203.03/203.39 (define @t111 () (and @t110 (not (forall @t5 @t20)) @t32)) % 203.03/203.39 (define @t112 () (forall @t5 (not @t29))) % 203.03/203.39 (define @t113 () (not @t112)) % 203.03/203.39 (define @t114 () (forall @t105 (_ @t69 @t104 @t74))) % 203.03/203.39 (define @t115 () (@list false)) % 203.03/203.39 (define @t116 () (@var "BOUND_VARIABLE_7854" $$unsorted)) % 203.03/203.39 (define @t117 () (tptp.model @t116 @t51)) % 203.03/203.39 (define @t118 () (@var "BOUND_VARIABLE_7850" $$unsorted)) % 203.03/203.39 (define @t119 () (not (tptp.model @t118 @t51))) % 203.03/203.39 (define @t120 () (or @t119 @t117)) % 203.03/203.39 (define @t121 () (forall (@list @t51 @t118 @t116) @t120)) % 203.03/203.39 (define @t122 () (forall (@list @t118 @t116) @t120)) % 203.03/203.39 (define @t123 () (forall (@list @t116) @t117)) % 203.03/203.39 (define @t124 () (forall (@list @t118) @t119)) % 203.03/203.39 (define @t125 () (or @t124 @t123)) % 203.03/203.39 (define @t126 () (forall @t5 @t60)) % 203.03/203.39 (define @t127 () (forall @t9 (not @t63))) % 203.03/203.39 (define @t128 () (not @t126)) % 203.03/203.39 (define @t129 () (not @t127)) % 203.03/203.39 (define @t130 () (and @t129 @t128)) % 203.03/203.39 (define @t131 () (forall @t58 (not @t130))) % 203.03/203.39 (define @t132 () (not @t131)) % 203.03/203.39 (define @t133 () (forall @t5 (not @t61))) % 203.03/203.39 (define @t134 () (not @t133)) % 203.03/203.39 (define @t135 () (@quantifiers_skolemize @t87 2)) % 203.03/203.39 (define @t136 () (_ @t69 @t135 @t88)) % 203.03/203.39 (define @t137 () (@quantifiers_skolemize @t87 1)) % 203.03/203.39 (define @t138 () (_ @t69 @t137 @t88)) % 203.03/203.39 (define @t139 () (not @t138)) % 203.03/203.39 (define @t140 () (or @t139 @t136)) % 203.03/203.39 (define @t141 () (@list @t140)) % 203.03/203.39 (define @t142 () (@var "b_I2" it_8_$$unsorted)) % 203.03/203.39 (define @t143 () (forall (@list @t142) (_ @t69 @t142 @t88))) % 203.03/203.39 (define @t144 () (not @t143)) % 203.03/203.39 (define @t145 () (forall @t107 (_ @t69 @t106 @t88))) % 203.03/203.39 (define @t146 () (not @t145)) % 203.03/203.39 (define @t147 () (@var "b_I1" it_8_$$unsorted)) % 203.03/203.39 (define @t148 () (forall (@list @t147) (not (_ @t69 @t147 @t88)))) % 203.03/203.39 (define @t149 () (not @t148)) % 203.03/203.39 (define @t150 () (forall @t109 (not (_ @t69 @t108 @t88)))) % 203.03/203.39 (define @t151 () (not @t150)) % 203.03/203.39 (define @t152 () (not @t114)) % 203.03/203.39 (define @t153 () (and @t151 @t146 @t114)) % 203.03/203.39 (define @t154 () (_ @t81 @t88 @t74 @t96)) % 203.03/203.39 (define @t155 () (= @t154 @t153)) % 203.03/203.39 (define @t156 () (@list false false)) % 203.03/203.39 (define @t157 () (_ @t81 @t88 @t74 @t80)) % 203.03/203.39 (define @t158 () (not @t157)) % 203.03/203.39 (define @t159 () (not @t154)) % 203.03/203.39 (define @t160 () (or @t159 @t158)) % 203.03/203.39 (define @t161 () (forall @t79 (or (not (_ @t69 @t78 @t88)) (_ @t69 @t78 @t74)))) % 203.03/203.39 (define @t162 () (= @t157 @t161)) % 203.03/203.39 (define @t163 () (not @t161)) % 203.03/203.39 (define @t164 () (@quantifiers_skolemize @t161 0)) % 203.03/203.39 (define @t165 () (_ @t69 @t164 @t74)) % 203.03/203.39 (define @t166 () (or (not (_ @t69 @t164 @t88)) @t165)) % 203.03/203.39 (define @t167 () (not @t166)) % 203.03/203.39 (assume @p1 (forall @t12 (= (=> @t11 (not @t6)) (tptp.status @t2 @t1 tptp.unp)))) % 203.03/203.39 (assume @p2 (forall @t12 (= (=> @t10 @t6) (tptp.status @t2 @t1 tptp.sap)))) % 203.03/203.39 (assume @p3 (forall @t12 (= (= @t10 @t6) (tptp.status @t2 @t1 tptp.esa)))) % 203.03/203.39 (assume @p4 (forall @t12 (= @t15 (tptp.status @t2 @t1 tptp.sat)))) % 203.03/203.39 (assume @p5 @t19) % 203.03/203.39 (assume @p6 (forall @t12 (= (and @t10 (forall @t5 (= @t20 @t4))) (tptp.status @t2 @t1 tptp.eqv)))) % 203.03/203.39 (assume @p7 (forall @t12 (= (and @t10 @t21) (tptp.status @t2 @t1 tptp.tac)))) % 203.03/203.39 (assume @p8 (forall @t12 (= (and @t10 @t28 @t27) (tptp.status @t2 @t1 tptp.wec)))) % 203.03/203.39 (assume @p9 (forall @t12 (= (and @t10 @t30 (forall @t26 (= @t23 @t25))) (tptp.status @t2 @t1 tptp.eth)))) % 203.03/203.39 (assume @p10 (forall @t12 (= (forall @t9 @t14) (tptp.status @t2 @t1 tptp.tau)))) % 203.03/203.39 (assume @p11 @t35) % 203.03/203.39 (assume @p12 (forall @t12 (= (and @t10 @t28 @t27 @t37) (tptp.status @t2 @t1 tptp.wth)))) % 203.03/203.39 (assume @p13 (forall @t12 (= @t11 (tptp.status @t2 @t1 tptp.cax)))) % 203.03/203.39 (assume @p14 (forall @t12 (= (and @t11 @t6) (tptp.status @t2 @t1 tptp.sca)))) % 203.03/203.39 (assume @p15 (forall @t12 (= (and @t11 @t21) (tptp.status @t2 @t1 tptp.tca)))) % 203.03/203.39 (assume @p16 (forall @t12 (= (and @t11 @t6 (exists @t26 (not @t25))) (tptp.status @t2 @t1 tptp.wca)))) % 203.03/203.39 (assume @p17 (forall @t12 (= (exists @t9 (and @t8 (tptp.model @t7 @t38))) (tptp.status @t2 @t1 tptp.csa)))) % 203.03/203.39 (assume @p18 (forall @t12 (= (and (forall @t9 @t8) (forall @t5 @t39)) (tptp.status @t2 @t1 tptp.uns)))) % 203.03/203.39 (assume @p19 (forall @t12 (= (and @t15 (exists @t5 (and @t20 @t39))) (tptp.status @t2 @t1 tptp.noc)))) % 203.03/203.39 (assume @p20 @t49) % 203.03/203.39 (assume @p21 (forall @t48 (= (forall @t12 (=> @t44 @t43)) (tptp.isa @t41 @t40)))) % 203.03/203.39 (assume @p22 (forall @t48 (= (exists @t12 (and @t44 @t50)) (tptp.nota @t41 @t40)))) % 203.03/203.39 (assume @p23 (forall @t48 (= (forall @t12 (=> @t44 @t50)) (tptp.nevera @t41 @t40)))) % 203.03/203.39 (assume @p24 (forall @t48 (= (forall @t12 (xor @t44 @t43)) (tptp.xora @t41 @t40)))) % 203.03/203.39 (assume @p25 (forall @t55 (xor @t54 @t53))) % 203.03/203.39 (assume @p26 (forall @t55 (= @t54 (not @t53)))) % 203.03/203.39 (assume @p27 @t59) % 203.03/203.39 (assume @p28 @t66) % 203.03/203.39 (assume @p29 (exists @t58 (forall @t56 (not @t54)))) % 203.03/203.39 (assume @p30 (exists @t12 (and @t15 (exists @t5 (or @t29 (not @t4)))))) % 203.03/203.39 (assume @p31 (exists @t12 (and @t10 @t28 (exists @t26 (and @t24 @t25)) @t37))) % 203.03/203.39 (assume @p32 (exists (@list @t7 @t2 @t1) (and @t8 (not @t13) @t6))) % 203.03/203.39 (assume @p33 @t67) % 203.03/203.39 (assume @p34 true) % 203.03/203.39 ; WARNING: add trust step for TRUST % 203.03/203.39 ; trust TRUST PREPROCESS_SORT_INFER % 203.03/203.39 (step @p35 :rule trust :premises () :args ((= @t73 @t72))) % 203.03/203.39 (step @p36 :rule exists-elim :args ((= @t59 @t73))) % 203.03/203.39 (step @p37 :rule trans :premises (@p36 @p35)) % 203.03/203.39 (step @p38 :rule eq_resolve :premises (@p27 @p37)) % 203.03/203.39 (step @p39 :rule refl :args (@t75)) % 203.03/203.39 (step @p40 :rule bool-double-not-elim :args (@t71)) % 203.03/203.39 (step @p41 :rule nary_cong :premises (@p40 @p39) :args ((or (not @t72) @t75))) % 203.03/203.39 (step @p42 :rule bool-double-not-elim :args (@t75)) % 203.03/203.39 (step @p43 :rule refl :args (@t72)) % 203.03/203.39 (step @p44 :rule cong :premises (@p43 @p42) :args ((=> @t72 @t76))) % 203.03/203.39 (assume-push @p206 @t72) % 203.03/203.39 (step @p46 :rule skolemize :premises (@p38)) % 203.03/203.39 (step-pop @p207 :rule scope :premises (@p46)) % 203.03/203.39 (step @p47 :rule process_scope :premises (@p207) :args (@t76)) % 203.03/203.39 (step @p49 :rule eq_resolve :premises (@p47 @p44)) % 203.03/203.39 (step @p50 :rule implies_elim :premises (@p49)) % 203.03/203.39 (step @p51 :rule eq_resolve :premises (@p50 @p41)) % 203.03/203.39 (step @p52 :rule chain_m_resolution :premises (@p51 @p38) :args (@t75 @t77 (@list @t71))) % 203.03/203.39 ; trust TRUST PREPROCESS_SORT_INFER % 203.03/203.39 (step @p53 :rule trust :premises () :args ((= (forall @t12 (= @t16 @t84)) (forall @t12 (= @t82 (forall @t79 (or (not (_ @t69 @t78 @t2)) (_ @t69 @t78 @t1)))))))) % 203.03/203.39 (step @p54 :rule eq-symm :args (@t84 @t16)) % 203.03/203.39 (step @p55 :rule refl :args (@t16)) % 203.03/203.39 (step @p56 :rule bool-impl-elim :args (@t8 @t13)) % 203.03/203.39 (step @p57 :rule cong :premises (@p56) :args (@t17)) % 203.03/203.39 (step @p58 :rule cong :premises (@p57 @p55) :args (@t18)) % 203.03/203.39 (step @p59 :rule trans :premises (@p58 @p54)) % 203.03/203.39 (step @p60 :rule cong :premises (@p59) :args (@t19)) % 203.03/203.39 (step @p61 :rule trans :premises (@p60 @p53)) % 203.03/203.39 (step @p62 :rule eq_resolve :premises (@p5 @p61)) % 203.03/203.39 (step @p63 :rule instantiate :premises (@p62) :args (@t89)) % 203.03/203.39 ; trust TRUST PREPROCESS_SORT_INFER % 203.03/203.39 (step @p64 :rule trust :premises () :args ((= (forall @t48 (= @t42 @t93)) (forall (@list @t91 @t90) (= (_ @t92 @t91 @t90) (not (forall @t12 (or (not (_ @t81 @t2 @t1 @t91)) (not (_ @t81 @t2 @t1 @t90)))))))))) % 203.03/203.39 (step @p65 :rule eq-symm :args (@t93 @t42)) % 203.03/203.39 (step @p66 :rule refl :args (@t42)) % 203.03/203.39 (step @p67 :rule bool-and-de-morgan :args (@t44 @t43 true)) % 203.03/203.39 (step @p68 :rule cong :premises (@p67) :args (@t94)) % 203.03/203.39 (step @p69 :rule cong :premises (@p68) :args (@t95)) % 203.03/203.39 (step @p70 :rule exists-elim :args ((= @t46 @t95))) % 203.03/203.39 (step @p71 :rule trans :premises (@p70 @p69)) % 203.03/203.39 (step @p72 :rule cong :premises (@p71 @p66) :args (@t47)) % 203.03/203.39 (step @p73 :rule trans :premises (@p72 @p65)) % 203.03/203.39 (step @p74 :rule cong :premises (@p73) :args (@t49)) % 203.03/203.39 (step @p75 :rule trans :premises (@p74 @p64)) % 203.03/203.39 (step @p76 :rule eq_resolve :premises (@p20 @p75)) % 203.03/203.39 (step @p77 :rule instantiate :premises (@p76) :args ((@list @t96 @t80))) % 203.03/203.39 ; trust TRUST PREPROCESS_SORT_INFER % 203.03/203.39 (step @p78 :rule trust :premises () :args ((= @t67 (not @t97)))) % 203.03/203.39 (step @p79 :rule eq_resolve :premises (@p33 @p78)) % 203.03/203.39 (step @p80 :rule bool-double-not-elim :args (@t99)) % 203.03/203.39 (step @p81 :rule refl :args (@t97)) % 203.03/203.39 (step @p82 :rule refl :args (@t102)) % 203.03/203.39 (step @p83 :rule nary_cong :premises (@p82 @p81 @p80) :args ((or @t102 @t97 (not @t100)))) % 203.03/203.39 (step @p84 :rule cnf_equiv_pos2 :args (@t101)) % 203.03/203.39 (step @p85 :rule eq_resolve :premises (@p84 @p83)) % 203.03/203.39 (step @p86 :rule reordering :premises (@p85) :args ((or @t97 @t99 @t102))) % 203.03/203.39 (step @p87 :rule chain_m_resolution :premises (@p86 @p79 @p77) :args (@t99 @t103 (@list @t97 @t101))) % 203.03/203.39 (step @p88 :rule instantiate :premises (@p87) :args (@t89)) % 203.03/203.39 ; trust TRUST PREPROCESS_SORT_INFER % 203.03/203.39 (step @p89 :rule trust :premises () :args ((= (forall @t12 (= @t31 @t111)) (forall @t12 (= @t98 (and (not (forall @t109 (not (_ @t69 @t108 @t2)))) (not (forall @t107 (_ @t69 @t106 @t2))) (forall @t105 (_ @t69 @t104 @t1)))))))) % 203.03/203.39 (step @p90 :rule eq-symm :args (@t111 @t31)) % 203.03/203.39 (step @p91 :rule refl :args (@t31)) % 203.03/203.39 (step @p92 :rule refl :args (@t32)) % 203.03/203.39 (step @p93 :rule bool-double-not-elim :args (@t20)) % 203.03/203.39 (step @p94 :rule cong :premises (@p93) :args (@t112)) % 203.03/203.39 (step @p95 :rule cong :premises (@p94) :args (@t113)) % 203.03/203.39 (step @p96 :rule exists-elim :args ((= @t30 @t113))) % 203.03/203.39 (step @p97 :rule trans :premises (@p96 @p95)) % 203.03/203.39 (step @p98 :rule exists-elim :args ((= @t10 @t110))) % 203.03/203.39 (step @p99 :rule nary_cong :premises (@p98 @p97 @p92) :args (@t33)) % 203.03/203.39 (step @p100 :rule cong :premises (@p99 @p91) :args (@t34)) % 203.03/203.39 (step @p101 :rule trans :premises (@p100 @p90)) % 203.03/203.39 (step @p102 :rule cong :premises (@p101) :args (@t35)) % 203.03/203.39 (step @p103 :rule trans :premises (@p102 @p89)) % 203.03/203.39 (step @p104 :rule eq_resolve :premises (@p11 @p103)) % 203.03/203.39 (step @p105 :rule instantiate :premises (@p104) :args (@t89)) % 203.03/203.39 (step @p106 :rule alpha_equiv :args (@t75 (@list @t68) (@list @t104))) % 203.03/203.39 (step @p107 :rule equiv_elim1 :premises (@p106)) % 203.03/203.39 (step @p108 :rule chain_m_resolution :premises (@p107 @p52) :args (@t114 @t115 (@list @t75))) % 203.03/203.39 ; trust TRUST PREPROCESS_SORT_INFER % 203.03/203.39 (step @p109 :rule trust :premises () :args ((= (not @t121) (not @t87)))) % 203.03/203.39 (step @p110 :rule quant-merge-prenex :args ((= (forall @t58 @t122) @t121))) % 203.03/203.39 (step @p111 :rule alpha_equiv :args (@t123 (@list @t116) (@list @t3))) % 203.03/203.39 (step @p112 :rule alpha_equiv :args (@t124 (@list @t118) (@list @t7))) % 203.03/203.39 (step @p113 :rule nary_cong :premises (@p112 @p111) :args (@t125)) % 203.03/203.39 (step @p114 :rule quant-miniscope-or :args ((= @t122 @t125))) % 203.03/203.39 (step @p115 :rule trans :premises (@p114 @p113)) % 203.03/203.39 (step @p116 :rule symm :premises (@p115)) % 203.03/203.39 (step @p117 :rule cong :premises (@p116) :args ((forall @t58 (or @t127 @t126)))) % 203.03/203.39 (step @p118 :rule trans :premises (@p117 @p110)) % 203.03/203.39 (step @p119 :rule bool-double-not-elim :args (@t126)) % 203.03/203.39 (step @p120 :rule bool-double-not-elim :args (@t127)) % 203.03/203.39 (step @p121 :rule nary_cong :premises (@p120 @p119) :args ((or (not @t129) (not @t128)))) % 203.03/203.39 (step @p122 :rule bool-and-de-morgan :args (@t129 @t128 true)) % 203.03/203.39 (step @p123 :rule trans :premises (@p122 @p121)) % 203.03/203.39 (step @p124 :rule cong :premises (@p123) :args (@t131)) % 203.03/203.39 (step @p125 :rule trans :premises (@p124 @p118)) % 203.03/203.39 (step @p126 :rule cong :premises (@p125) :args (@t132)) % 203.03/203.39 (step @p127 :rule exists-elim :args ((= (exists @t58 @t130) @t132))) % 203.03/203.39 (step @p128 :rule trans :premises (@p127 @p126)) % 203.03/203.39 (step @p129 :rule bool-double-not-elim :args (@t60)) % 203.03/203.39 (step @p130 :rule cong :premises (@p129) :args (@t133)) % 203.03/203.39 (step @p131 :rule cong :premises (@p130) :args (@t134)) % 203.03/203.39 (step @p132 :rule exists-elim :args ((= @t62 @t134))) % 203.03/203.39 (step @p133 :rule trans :premises (@p132 @p131)) % 203.03/203.39 (step @p134 :rule exists-elim :args ((= @t64 @t129))) % 203.03/203.39 (step @p135 :rule nary_cong :premises (@p134 @p133) :args (@t65)) % 203.03/203.39 (step @p136 :rule cong :premises (@p135) :args (@t66)) % 203.03/203.39 (step @p137 :rule trans :premises (@p136 @p128)) % 203.03/203.39 (step @p138 :rule trans :premises (@p137 @p109)) % 203.03/203.39 (step @p139 :rule eq_resolve :premises (@p28 @p138)) % 203.03/203.39 (step @p140 :rule skolemize :premises (@p139)) % 203.03/203.39 (step @p141 :rule cnf_or_neg :args (@t140 1)) % 203.03/203.39 (step @p142 :rule chain_m_resolution :premises (@p141 @p140) :args ((not @t136) @t77 @t141)) % 203.03/203.39 (assume-push @p208 @t143) % 203.03/203.39 (step @p144 :rule instantiate :premises (@p208) :args ((@list @t135))) % 203.03/203.39 (step-pop @p209 :rule scope :premises (@p144)) % 203.03/203.39 (step @p145 :rule process_scope :premises (@p209) :args (@t136)) % 203.03/203.39 (step @p147 :rule implies_elim :premises (@p145)) % 203.03/203.39 (step @p148 :rule reordering :premises (@p147) :args ((or @t136 @t144))) % 203.03/203.39 (step @p149 :rule chain_m_resolution :premises (@p148 @p142) :args (@t144 @t77 (@list @t136))) % 203.03/203.39 (step @p150 :rule alpha_equiv :args (@t143 (@list @t142) (@list @t106))) % 203.03/203.39 (step @p151 :rule equiv_elim2 :premises (@p150)) % 203.03/203.39 (step @p152 :rule chain_m_resolution :premises (@p151 @p149) :args (@t146 @t77 (@list @t143))) % 203.03/203.39 (step @p153 :rule bool-double-not-elim :args (@t138)) % 203.03/203.39 (step @p154 :rule refl :args (@t140)) % 203.03/203.39 (step @p155 :rule nary_cong :premises (@p154 @p153) :args ((or @t140 (not @t139)))) % 203.03/203.39 (step @p156 :rule cnf_or_neg :args (@t140 0)) % 203.03/203.39 (step @p157 :rule eq_resolve :premises (@p156 @p155)) % 203.03/203.39 (step @p158 :rule reordering :premises (@p157) :args ((or @t138 @t140))) % 203.03/203.39 (step @p159 :rule chain_m_resolution :premises (@p158 @p140) :args (@t138 @t77 @t141)) % 203.03/203.39 (assume-push @p210 @t148) % 203.03/203.39 (step @p161 :rule instantiate :premises (@p210) :args ((@list @t137))) % 203.03/203.39 (step-pop @p211 :rule scope :premises (@p161)) % 203.03/203.39 (step @p162 :rule process_scope :premises (@p211) :args (@t139)) % 203.03/203.39 (step @p164 :rule implies_elim :premises (@p162)) % 203.03/203.39 (step @p165 :rule reordering :premises (@p164) :args ((or @t139 @t149))) % 203.03/203.39 (step @p166 :rule chain_m_resolution :premises (@p165 @p159) :args (@t149 @t115 (@list @t138))) % 203.03/203.39 (step @p167 :rule alpha_equiv :args (@t148 (@list @t147) (@list @t108))) % 203.03/203.39 (step @p168 :rule equiv_elim2 :premises (@p167)) % 203.03/203.39 (step @p169 :rule chain_m_resolution :premises (@p168 @p166) :args (@t151 @t77 (@list @t148))) % 203.03/203.39 (step @p170 :rule refl :args (@t152)) % 203.03/203.39 (step @p171 :rule bool-double-not-elim :args (@t145)) % 203.03/203.39 (step @p172 :rule bool-double-not-elim :args (@t150)) % 203.03/203.39 (step @p173 :rule refl :args (@t153)) % 203.03/203.39 (step @p174 :rule nary_cong :premises (@p173 @p172 @p171 @p170) :args ((or @t153 (not @t151) (not @t146) @t152))) % 203.03/203.39 (step @p175 :rule cnf_and_neg :args (@t153)) % 203.03/203.39 (step @p176 :rule eq_resolve :premises (@p175 @p174)) % 203.03/203.39 (step @p177 :rule reordering :premises (@p176) :args ((or @t150 @t145 @t153 @t152))) % 203.03/203.39 (step @p178 :rule chain_m_resolution :premises (@p177 @p169 @p152 @p108) :args (@t153 (@list true true false) (@list @t150 @t145 @t114))) % 203.03/203.39 (step @p179 :rule cnf_equiv_pos2 :args (@t155)) % 203.03/203.39 (step @p180 :rule reordering :premises (@p179) :args ((or @t154 (not @t153) (not @t155)))) % 203.03/203.39 (step @p181 :rule chain_m_resolution :premises (@p180 @p178 @p105) :args (@t154 @t156 (@list @t153 @t155))) % 203.03/203.39 (step @p182 :rule cnf_or_pos :args (@t160)) % 203.03/203.39 (step @p183 :rule reordering :premises (@p182) :args ((or @t159 @t158 (not @t160)))) % 203.03/203.39 (step @p184 :rule chain_m_resolution :premises (@p183 @p181 @p88) :args (@t158 @t156 (@list @t154 @t160))) % 203.03/203.39 (step @p185 :rule cnf_equiv_pos2 :args (@t162)) % 203.03/203.39 (step @p186 :rule reordering :premises (@p185) :args ((or @t157 @t163 (not @t162)))) % 203.03/203.39 (step @p187 :rule chain_m_resolution :premises (@p186 @p184 @p63) :args (@t163 @t103 (@list @t157 @t162))) % 203.03/203.39 (step @p188 :rule refl :args (@t167)) % 203.03/203.39 (step @p189 :rule bool-double-not-elim :args (@t161)) % 203.03/203.39 (step @p190 :rule nary_cong :premises (@p189 @p188) :args ((or (not @t163) @t167))) % 203.03/203.39 (assume-push @p212 @t163) % 203.03/203.39 (step @p192 :rule skolemize :premises (@p212)) % 203.03/203.39 (step-pop @p213 :rule scope :premises (@p192)) % 203.03/203.39 (step @p193 :rule process_scope :premises (@p213) :args (@t167)) % 203.03/203.39 (step @p195 :rule implies_elim :premises (@p193)) % 203.03/203.39 (step @p196 :rule eq_resolve :premises (@p195 @p190)) % 203.03/203.39 (step @p197 :rule chain_m_resolution :premises (@p196 @p187) :args (@t167 @t77 (@list @t161))) % 203.03/203.39 (step @p198 :rule cnf_or_neg :args (@t166 1)) % 203.03/203.39 (step @p199 :rule chain_m_resolution :premises (@p198 @p197) :args ((not @t165) @t77 (@list @t166))) % 203.03/203.39 (assume-push @p214 @t75) % 203.03/203.39 (step @p201 :rule instantiate :premises (@p52) :args ((@list @t164))) % 203.03/203.39 (step-pop @p215 :rule scope :premises (@p201)) % 203.03/203.39 (step @p202 :rule process_scope :premises (@p215) :args (@t165)) % 203.03/203.39 (step @p204 :rule implies_elim :premises (@p202)) % 203.03/203.39 (step @p205 false :rule chain_m_resolution :premises (@p204 @p199 @p52) :args (false @t103 (@list @t165 @t75))) % 203.03/203.39 ) % 203.03/203.39 % SZS output end Proof % 203.03/203.39 % cvc5 exiting %------------------------------------------------------------------------------