%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : COM016+4 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n006.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 08:10:25 AM UTC 2026 % Result : Theorem 3.61s 3.89s % Output : Proof 0.33s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : COM016+4 : TPTP v9.2.1. Released v4.0.0. % 0.13/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n006.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 20:28:19 EDT 2026 % 0.16/0.34 % CPUTime : % 0.30/0.49 %----Proving TF0_NAR, FOF, or CNF % 3.61/3.89 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 3.61/3.89 % SZS status Theorem % 3.61/3.89 % SZS output start Proof % 3.61/3.89 ( % 3.61/3.89 (declare-sort $$unsorted 0) % 3.61/3.89 (declare-const tptp.xa $$unsorted) % 3.61/3.89 (declare-const tptp.aElement0 (-> $$unsorted Bool)) % 3.61/3.89 (declare-const tptp.aRewritingSystem0 (-> $$unsorted Bool)) % 3.61/3.89 (declare-const tptp.sdtmndtplgtdt0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 3.61/3.89 (declare-const tptp.sdtmndtasgtdt0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 3.61/3.89 (declare-const tptp.aReductOfIn0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 3.61/3.89 (declare-const tptp.isLocallyConfluent0 (-> $$unsorted Bool)) % 3.61/3.89 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 3.61/3.89 (declare-const tptp.isConfluent0 (-> $$unsorted Bool)) % 3.61/3.89 (declare-const tptp.xR $$unsorted) % 3.61/3.89 (declare-const tptp.isTerminating0 (-> $$unsorted Bool)) % 3.61/3.89 (declare-const tptp.aNormalFormOfIn0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 3.61/3.89 (declare-const tptp.xc $$unsorted) % 3.61/3.89 (declare-const tptp.xb $$unsorted) % 3.61/3.89 (define @t1 () (@var "W0" $$unsorted)) % 3.61/3.89 (define @t2 () (tptp.aElement0 @t1)) % 3.61/3.89 (define @t3 () (@list @t1)) % 3.61/3.89 (define @t4 () (tptp.aRewritingSystem0 @t1)) % 3.61/3.89 (define @t5 () (@var "W2" $$unsorted)) % 3.61/3.89 (define @t6 () (tptp.aElement0 @t5)) % 3.61/3.89 (define @t7 () (@var "W1" $$unsorted)) % 3.61/3.89 (define @t8 () (tptp.aReductOfIn0 @t5 @t1 @t7)) % 3.61/3.89 (define @t9 () (@list @t5)) % 3.61/3.89 (define @t10 () (tptp.aRewritingSystem0 @t7)) % 3.61/3.89 (define @t11 () (and @t2 @t10)) % 3.61/3.89 (define @t12 () (@list @t1 @t7)) % 3.61/3.89 (define @t13 () (tptp.aElement0 @t7)) % 3.61/3.89 (define @t14 () (and @t2 @t13)) % 3.61/3.89 (define @t15 () (tptp.sdtmndtplgtdt0 @t1 @t7 @t5)) % 3.61/3.89 (define @t16 () (and @t2 @t10 @t6)) % 3.61/3.89 (define @t17 () (@list @t1 @t7 @t5)) % 3.61/3.89 (define @t18 () (@var "W3" $$unsorted)) % 3.61/3.89 (define @t19 () (tptp.aElement0 @t18)) % 3.61/3.89 (define @t20 () (@list @t18)) % 3.61/3.89 (define @t21 () (and @t2 @t10 @t6 @t19)) % 3.61/3.89 (define @t22 () (@list @t1 @t7 @t5 @t18)) % 3.61/3.89 (define @t23 () (= @t1 @t5)) % 3.61/3.89 (define @t24 () (tptp.sdtmndtasgtdt0 @t1 @t7 @t5)) % 3.61/3.89 (define @t25 () (@var "W4" $$unsorted)) % 3.61/3.89 (define @t26 () (tptp.aElement0 @t25)) % 3.61/3.89 (define @t27 () (@list @t25)) % 3.61/3.89 (define @t28 () (exists @t27 (and @t26 (tptp.sdtmndtasgtdt0 @t5 @t1 @t25) (tptp.sdtmndtasgtdt0 @t18 @t1 @t25)))) % 3.61/3.89 (define @t29 () (@list @t7 @t5 @t18)) % 3.61/3.89 (define @t30 () (tptp.isTerminating0 @t1)) % 3.61/3.89 (define @t31 () (@list @t7)) % 3.61/3.89 (define @t32 () (tptp.sdtmndtplgtdt0 @t1 tptp.xR @t7)) % 3.61/3.89 (define @t33 () (tptp.aReductOfIn0 @t5 @t1 tptp.xR)) % 3.61/3.89 (define @t34 () (tptp.aReductOfIn0 @t7 @t1 tptp.xR)) % 3.61/3.89 (define @t35 () (tptp.sdtmndtplgtdt0 @t25 tptp.xR @t18)) % 3.61/3.89 (define @t36 () (exists @t20 (and @t19 (or (= @t7 @t18) (and (or (tptp.aReductOfIn0 @t18 @t7 tptp.xR) (exists @t27 (and @t26 (tptp.aReductOfIn0 @t25 @t7 tptp.xR) @t35))) (tptp.sdtmndtplgtdt0 @t7 tptp.xR @t18))) (tptp.sdtmndtasgtdt0 @t7 tptp.xR @t18) (or (= @t5 @t18) (and (or (tptp.aReductOfIn0 @t18 @t5 tptp.xR) (exists @t27 (and @t26 (tptp.aReductOfIn0 @t25 @t5 tptp.xR) @t35))) (tptp.sdtmndtplgtdt0 @t5 tptp.xR @t18))) (tptp.sdtmndtasgtdt0 @t5 tptp.xR @t18)))) % 3.61/3.89 (define @t37 () (tptp.aElement0 tptp.xb)) % 3.61/3.89 (define @t38 () (tptp.aElement0 tptp.xa)) % 3.61/3.89 (define @t39 () (tptp.aReductOfIn0 @t18 @t1 tptp.xR)) % 3.61/3.89 (define @t40 () (tptp.aReductOfIn0 @t1 tptp.xa tptp.xR)) % 3.61/3.89 (define @t41 () (tptp.sdtmndtplgtdt0 tptp.xa tptp.xR tptp.xb)) % 3.61/3.89 (define @t42 () (tptp.sdtmndtplgtdt0 @t1 tptp.xR tptp.xb)) % 3.61/3.89 (define @t43 () (and @t2 @t40 @t42)) % 3.61/3.89 (define @t44 () (exists @t3 @t43)) % 3.61/3.89 (define @t45 () (tptp.aReductOfIn0 tptp.xb tptp.xa tptp.xR)) % 3.61/3.89 (define @t46 () (or @t45 @t44)) % 3.61/3.89 (define @t47 () (tptp.sdtmndtasgtdt0 @t1 tptp.xR tptp.xb)) % 3.61/3.89 (define @t48 () (tptp.sdtmndtplgtdt0 @t7 tptp.xR tptp.xb)) % 3.61/3.89 (define @t49 () (and @t13 @t34 @t48)) % 3.61/3.89 (define @t50 () (exists @t31 @t49)) % 3.61/3.89 (define @t51 () (tptp.aReductOfIn0 tptp.xb @t1 tptp.xR)) % 3.61/3.89 (define @t52 () (= @t1 tptp.xb)) % 3.61/3.89 (define @t53 () (or @t52 @t51 @t50 @t42 @t47)) % 3.61/3.89 (define @t54 () (and @t2 @t40 @t53)) % 3.61/3.89 (define @t55 () (exists @t3 @t54)) % 3.61/3.89 (define @t56 () (not @t55)) % 3.61/3.89 (define @t57 () (not @t47)) % 3.61/3.89 (define @t58 () (not @t42)) % 3.61/3.89 (define @t59 () (@var "BOUND_VARIABLE_8023" $$unsorted)) % 3.61/3.89 (define @t60 () (or (not (tptp.aElement0 @t59)) (not (tptp.aReductOfIn0 @t59 @t1 tptp.xR)) (not (tptp.sdtmndtplgtdt0 @t59 tptp.xR tptp.xb)))) % 3.61/3.89 (define @t61 () (not @t51)) % 3.61/3.89 (define @t62 () (not @t52)) % 3.61/3.89 (define @t63 () (and @t62 @t61 @t60 @t58 @t57)) % 3.61/3.89 (define @t64 () (not @t40)) % 3.61/3.89 (define @t65 () (not @t2)) % 3.61/3.89 (define @t66 () (or @t65 @t64 @t63)) % 3.61/3.89 (define @t67 () (forall (@list @t1 @t59) @t66)) % 3.61/3.89 (define @t68 () (@list @t59)) % 3.61/3.89 (define @t69 () (forall @t68 @t66)) % 3.61/3.89 (define @t70 () (forall @t68 @t57)) % 3.61/3.89 (define @t71 () (forall @t68 @t58)) % 3.61/3.89 (define @t72 () (forall @t68 @t60)) % 3.61/3.89 (define @t73 () (forall @t68 @t61)) % 3.61/3.89 (define @t74 () (forall @t68 @t62)) % 3.61/3.89 (define @t75 () (and @t74 @t73 @t72 @t71 @t70)) % 3.61/3.89 (define @t76 () (forall @t68 @t63)) % 3.61/3.89 (define @t77 () (or @t65 @t64 @t76)) % 3.61/3.89 (define @t78 () (not @t48)) % 3.61/3.89 (define @t79 () (not @t34)) % 3.61/3.89 (define @t80 () (not @t13)) % 3.61/3.89 (define @t81 () (or @t80 @t79 @t78)) % 3.61/3.89 (define @t82 () (forall @t31 @t81)) % 3.61/3.89 (define @t83 () (not @t82)) % 3.61/3.89 (define @t84 () (not @t83)) % 3.61/3.89 (define @t85 () (and @t62 @t61 @t84 @t58 @t57)) % 3.61/3.89 (define @t86 () (or @t52 @t51 @t83 @t42 @t47)) % 3.61/3.89 (define @t87 () (not @t86)) % 3.61/3.89 (define @t88 () (or @t65 @t64 @t87)) % 3.61/3.89 (define @t89 () (and @t2 @t40 @t86)) % 3.61/3.89 (define @t90 () (forall @t3 (not @t89))) % 3.61/3.89 (define @t91 () (not @t90)) % 3.61/3.89 (define @t92 () (forall @t31 (not @t49))) % 3.61/3.89 (define @t93 () (not @t92)) % 3.61/3.89 (define @t94 () (or @t65 @t64 @t58)) % 3.61/3.89 (define @t95 () (forall @t3 @t94)) % 3.61/3.89 (define @t96 () (@quantifiers_skolemize @t95 0)) % 3.61/3.89 (define @t97 () (tptp.aElement0 @t96)) % 3.61/3.89 (define @t98 () (tptp.sdtmndtplgtdt0 @t96 tptp.xR tptp.xb)) % 3.61/3.89 (define @t99 () (not @t98)) % 3.61/3.89 (define @t100 () (tptp.aReductOfIn0 @t96 tptp.xa tptp.xR)) % 3.61/3.89 (define @t101 () (not @t100)) % 3.61/3.89 (define @t102 () (not @t97)) % 3.61/3.89 (define @t103 () (or @t102 @t101 @t99)) % 3.61/3.89 (define @t104 () (not (tptp.sdtmndtasgtdt0 @t96 tptp.xR tptp.xb))) % 3.61/3.89 (define @t105 () (not (tptp.sdtmndtplgtdt0 tptp.xb tptp.xR tptp.xb))) % 3.61/3.89 (define @t106 () (not (tptp.aReductOfIn0 tptp.xb @t96 tptp.xR))) % 3.61/3.89 (define @t107 () (not @t37)) % 3.61/3.89 (define @t108 () (or @t107 @t106 @t105)) % 3.61/3.89 (define @t109 () (not (= @t96 tptp.xb))) % 3.61/3.89 (define @t110 () (and @t109 @t106 @t108 @t99 @t104)) % 3.61/3.89 (define @t111 () (or @t102 @t101 @t110)) % 3.61/3.89 (define @t112 () (and (not (= tptp.xb @t96)) @t106 @t108 @t99 @t104)) % 3.61/3.89 (define @t113 () (or @t102 @t101 @t112)) % 3.61/3.89 (define @t114 () (@list false)) % 3.61/3.89 (define @t115 () (not @t103)) % 3.61/3.89 (define @t116 () (not @t95)) % 3.61/3.89 (define @t117 () (forall @t3 (not @t43))) % 3.61/3.89 (define @t118 () (not @t117)) % 3.61/3.89 (define @t119 () (not @t45)) % 3.61/3.89 (define @t120 () (or @t107 @t119)) % 3.61/3.89 (define @t121 () (not @t120)) % 3.61/3.89 (define @t122 () (not (tptp.sdtmndtasgtdt0 tptp.xb tptp.xR tptp.xb))) % 3.61/3.89 (define @t123 () (or (not @t38) (not (tptp.aReductOfIn0 tptp.xa tptp.xb tptp.xR)) (not @t41))) % 3.61/3.89 (define @t124 () (not (tptp.aReductOfIn0 tptp.xb tptp.xb tptp.xR))) % 3.61/3.89 (define @t125 () (not (= tptp.xb tptp.xb))) % 3.61/3.89 (define @t126 () (and @t125 @t124 @t123 @t105 @t122)) % 3.61/3.89 (define @t127 () (or @t107 @t119 @t126)) % 3.61/3.89 (assume @p1 (forall @t3 (=> @t2 true))) % 3.61/3.89 (assume @p2 (forall @t3 (=> @t4 true))) % 3.61/3.89 (assume @p3 (forall @t12 (=> @t11 (forall @t9 (=> @t8 @t6))))) % 3.61/3.89 (assume @p4 (forall @t12 (=> @t14 (=> (tptp.iLess0 @t1 @t7) true)))) % 3.61/3.89 (assume @p5 (forall @t17 (=> @t16 (=> @t15 true)))) % 3.61/3.89 (assume @p6 (forall @t17 (=> @t16 (= @t15 (or @t8 (exists @t20 (and @t19 (tptp.aReductOfIn0 @t18 @t1 @t7) (tptp.sdtmndtplgtdt0 @t18 @t7 @t5)))))))) % 3.61/3.89 (assume @p7 (forall @t22 (=> @t21 (=> (and @t15 (tptp.sdtmndtplgtdt0 @t5 @t7 @t18)) (tptp.sdtmndtplgtdt0 @t1 @t7 @t18))))) % 3.61/3.89 (assume @p8 (forall @t17 (=> @t16 (= @t24 (or @t23 @t15))))) % 3.61/3.89 (assume @p9 (forall @t22 (=> @t21 (=> (and @t24 (tptp.sdtmndtasgtdt0 @t5 @t7 @t18)) (tptp.sdtmndtasgtdt0 @t1 @t7 @t18))))) % 3.61/3.89 (assume @p10 (forall @t3 (=> @t4 (= (tptp.isConfluent0 @t1) (forall @t29 (=> (and @t13 @t6 @t19 (tptp.sdtmndtasgtdt0 @t7 @t1 @t5) (tptp.sdtmndtasgtdt0 @t7 @t1 @t18)) @t28)))))) % 3.61/3.89 (assume @p11 (forall @t3 (=> @t4 (= (tptp.isLocallyConfluent0 @t1) (forall @t29 (=> (and @t13 @t6 @t19 (tptp.aReductOfIn0 @t5 @t7 @t1) (tptp.aReductOfIn0 @t18 @t7 @t1)) @t28)))))) % 3.61/3.89 (assume @p12 (forall @t3 (=> @t4 (= @t30 (forall (@list @t7 @t5) (=> (and @t13 @t6) (=> (tptp.sdtmndtplgtdt0 @t7 @t1 @t5) (tptp.iLess0 @t5 @t7)))))))) % 3.61/3.89 (assume @p13 (forall @t12 (=> @t11 (forall @t9 (= (tptp.aNormalFormOfIn0 @t5 @t1 @t7) (and @t6 @t24 (not (exists @t20 (tptp.aReductOfIn0 @t18 @t5 @t7))))))))) % 3.61/3.89 (assume @p14 (forall @t3 (=> (and @t4 @t30) (forall @t31 (=> @t13 (exists @t9 (tptp.aNormalFormOfIn0 @t5 @t7 @t1))))))) % 3.61/3.89 (assume @p15 (tptp.aRewritingSystem0 tptp.xR)) % 3.61/3.89 (assume @p16 (and (forall @t17 (=> (and @t2 @t13 @t6 @t34 @t33) @t36)) (tptp.isLocallyConfluent0 tptp.xR) (forall @t12 (=> @t14 (=> (or @t34 (exists @t9 (and @t6 @t33 (tptp.sdtmndtplgtdt0 @t5 tptp.xR @t7))) @t32) (tptp.iLess0 @t7 @t1)))) (tptp.isTerminating0 tptp.xR))) % 3.61/3.89 (assume @p17 (and @t38 @t37 (tptp.aElement0 tptp.xc))) % 3.61/3.89 (assume @p18 (forall @t17 (=> (and @t2 @t13 @t6 (or (= @t1 @t7) @t34 (exists @t20 (and @t19 @t39 (tptp.sdtmndtplgtdt0 @t18 tptp.xR @t7))) @t32 (tptp.sdtmndtasgtdt0 @t1 tptp.xR @t7)) (or @t23 @t33 (exists @t20 (and @t19 @t39 (tptp.sdtmndtplgtdt0 @t18 tptp.xR @t5))) (tptp.sdtmndtplgtdt0 @t1 tptp.xR @t5) (tptp.sdtmndtasgtdt0 @t1 tptp.xR @t5))) (=> (tptp.iLess0 @t1 tptp.xa) @t36)))) % 3.61/3.89 (assume @p19 (and @t46 @t41 (or (tptp.aReductOfIn0 tptp.xc tptp.xa tptp.xR) (exists @t3 (and @t2 @t40 (tptp.sdtmndtplgtdt0 @t1 tptp.xR tptp.xc)))) (tptp.sdtmndtplgtdt0 tptp.xa tptp.xR tptp.xc))) % 3.61/3.89 (assume @p20 @t56) % 3.61/3.89 (assume @p21 true) % 3.61/3.89 (step @p22 :rule bool-double-not-elim :args (@t67)) % 3.61/3.89 (step @p23 :rule quant-merge-prenex :args ((= (forall @t3 @t69) @t67))) % 3.61/3.89 (step @p24 :rule quant-unused-vars :args ((= @t70 @t57))) % 3.61/3.89 (step @p25 :rule quant-unused-vars :args ((= @t71 @t58))) % 3.61/3.89 (step @p26 :rule alpha_equiv :args (@t72 (@list @t59) (@list @t7))) % 3.61/3.89 (step @p27 :rule quant-unused-vars :args ((= @t73 @t61))) % 3.61/3.89 (step @p28 :rule quant-unused-vars :args ((= @t74 @t62))) % 3.61/3.89 (step @p29 :rule nary_cong :premises (@p28 @p27 @p26 @p25 @p24) :args (@t75)) % 3.61/3.89 (step @p30 :rule quant-miniscope-and :args ((= @t76 @t75))) % 3.61/3.89 (step @p31 :rule trans :premises (@p30 @p29)) % 3.61/3.89 (step @p32 :rule refl :args (@t64)) % 3.61/3.89 (step @p33 :rule refl :args (@t65)) % 3.61/3.89 (step @p34 :rule nary_cong :premises (@p33 @p32 @p31) :args (@t77)) % 3.61/3.89 (step @p35 :rule quant-miniscope-or :args ((= @t69 @t77))) % 3.61/3.89 (step @p36 :rule trans :premises (@p35 @p34)) % 3.61/3.89 (step @p37 :rule symm :premises (@p36)) % 3.61/3.89 (step @p38 :rule cong :premises (@p37) :args ((forall @t3 (or @t65 @t64 (and @t62 @t61 @t82 @t58 @t57))))) % 3.61/3.89 (step @p39 :rule trans :premises (@p38 @p23)) % 3.61/3.89 (step @p40 :rule refl :args (@t57)) % 3.61/3.89 (step @p41 :rule refl :args (@t58)) % 3.61/3.89 (step @p42 :rule bool-double-not-elim :args (@t82)) % 3.61/3.89 (step @p43 :rule refl :args (@t61)) % 3.61/3.89 (step @p44 :rule refl :args (@t62)) % 3.61/3.89 (step @p45 :rule nary_cong :premises (@p44 @p43 @p42 @p41 @p40) :args (@t85)) % 3.61/3.89 (step @p46 :rule aci_norm :args ((= (and @t62 (and @t61 (and @t84 (and @t58 @t57)))) @t85))) % 3.61/3.89 (step @p47 :rule trans :premises (@p46 @p45)) % 3.61/3.89 (step @p48 :rule bool-or-de-morgan :args (@t42 @t47 false)) % 3.61/3.89 (step @p49 :rule refl :args (@t84)) % 3.61/3.89 (step @p50 :rule nary_cong :premises (@p49 @p48) :args ((and @t84 (not (or @t42 @t47))))) % 3.61/3.89 (step @p51 :rule bool-or-de-morgan :args (@t83 @t42 (or @t47))) % 3.61/3.89 (step @p52 :rule trans :premises (@p51 @p50)) % 3.61/3.89 (step @p53 :rule nary_cong :premises (@p43 @p52) :args ((and @t61 (not (or @t83 @t42 @t47))))) % 3.61/3.89 (step @p54 :rule bool-or-de-morgan :args (@t51 @t83 (or @t42 @t47))) % 3.61/3.89 (step @p55 :rule trans :premises (@p54 @p53)) % 3.61/3.89 (step @p56 :rule nary_cong :premises (@p44 @p55) :args ((and @t62 (not (or @t51 @t83 @t42 @t47))))) % 3.61/3.89 (step @p57 :rule bool-or-de-morgan :args (@t52 @t51 (or @t83 @t42 @t47))) % 3.61/3.89 (step @p58 :rule trans :premises (@p57 @p56)) % 3.61/3.89 (step @p59 :rule trans :premises (@p58 @p47)) % 3.61/3.89 (step @p60 :rule nary_cong :premises (@p33 @p32 @p59) :args (@t88)) % 3.61/3.89 (step @p61 :rule aci_norm :args ((= (or @t65 (or @t64 @t87)) @t88))) % 3.61/3.89 (step @p62 :rule bool-and-de-morgan :args (@t40 @t86 true)) % 3.61/3.89 (step @p63 :rule nary_cong :premises (@p33 @p62) :args ((or @t65 (not (and @t40 @t86))))) % 3.61/3.89 (step @p64 :rule bool-and-de-morgan :args (@t2 @t40 (and @t86))) % 3.61/3.89 (step @p65 :rule trans :premises (@p64 @p63)) % 3.61/3.89 (step @p66 :rule trans :premises (@p65 @p61)) % 3.61/3.89 (step @p67 :rule trans :premises (@p66 @p60)) % 3.61/3.89 (step @p68 :rule cong :premises (@p67) :args (@t90)) % 3.61/3.89 (step @p69 :rule trans :premises (@p68 @p39)) % 3.61/3.89 (step @p70 :rule cong :premises (@p69) :args (@t91)) % 3.61/3.89 (step @p71 :rule exists-elim :args ((= (exists @t3 @t89) @t91))) % 3.61/3.89 (step @p72 :rule trans :premises (@p71 @p70)) % 3.61/3.89 (step @p73 :rule refl :args (@t47)) % 3.61/3.89 (step @p74 :rule refl :args (@t42)) % 3.61/3.89 (step @p75 :rule aci_norm :args ((= (or @t80 (or @t79 @t78)) @t81))) % 3.61/3.89 (step @p76 :rule bool-and-de-morgan :args (@t34 @t48 true)) % 3.61/3.89 (step @p77 :rule refl :args (@t80)) % 3.61/3.89 (step @p78 :rule nary_cong :premises (@p77 @p76) :args ((or @t80 (not (and @t34 @t48))))) % 3.61/3.89 (step @p79 :rule bool-and-de-morgan :args (@t13 @t34 (and @t48))) % 3.61/3.89 (step @p80 :rule trans :premises (@p79 @p78)) % 3.61/3.89 (step @p81 :rule trans :premises (@p80 @p75)) % 3.61/3.89 (step @p82 :rule cong :premises (@p81) :args (@t92)) % 3.61/3.89 (step @p83 :rule cong :premises (@p82) :args (@t93)) % 3.61/3.89 (step @p84 :rule exists-elim :args ((= @t50 @t93))) % 3.61/3.89 (step @p85 :rule trans :premises (@p84 @p83)) % 3.61/3.89 (step @p86 :rule refl :args (@t51)) % 3.61/3.89 (step @p87 :rule refl :args (@t52)) % 3.61/3.89 (step @p88 :rule nary_cong :premises (@p87 @p86 @p85 @p74 @p73) :args (@t53)) % 3.61/3.89 (step @p89 :rule refl :args (@t40)) % 3.61/3.89 (step @p90 :rule refl :args (@t2)) % 3.61/3.89 (step @p91 :rule nary_cong :premises (@p90 @p89 @p88) :args (@t54)) % 3.61/3.89 (step @p92 :rule cong :premises (@p91) :args (@t55)) % 3.61/3.89 (step @p93 :rule trans :premises (@p92 @p72)) % 3.61/3.89 (step @p94 :rule cong :premises (@p93) :args (@t56)) % 3.61/3.89 (step @p95 :rule trans :premises (@p94 @p22)) % 3.61/3.89 (step @p96 :rule eq_resolve :premises (@p20 @p95)) % 3.61/3.89 (step @p97 :rule bool-double-not-elim :args (@t97)) % 3.61/3.89 (step @p98 :rule refl :args (@t103)) % 3.61/3.89 (step @p99 :rule nary_cong :premises (@p98 @p97) :args ((or @t103 (not @t102)))) % 3.61/3.89 (step @p100 :rule cnf_or_neg :args (@t103 0)) % 3.61/3.89 (step @p101 :rule eq_resolve :premises (@p100 @p99)) % 3.61/3.89 (step @p102 :rule reordering :premises (@p101) :args ((or @t97 @t103))) % 3.61/3.89 (step @p103 :rule bool-double-not-elim :args (@t100)) % 3.61/3.89 (step @p104 :rule nary_cong :premises (@p98 @p103) :args ((or @t103 (not @t101)))) % 3.61/3.89 (step @p105 :rule cnf_or_neg :args (@t103 1)) % 3.61/3.89 (step @p106 :rule eq_resolve :premises (@p105 @p104)) % 3.61/3.89 (step @p107 :rule reordering :premises (@p106) :args ((or @t100 @t103))) % 3.61/3.89 (step @p108 :rule bool-double-not-elim :args (@t98)) % 3.61/3.89 (step @p109 :rule nary_cong :premises (@p98 @p108) :args ((or @t103 (not @t99)))) % 3.61/3.89 (step @p110 :rule cnf_or_neg :args (@t103 2)) % 3.61/3.89 (step @p111 :rule eq_resolve :premises (@p110 @p109)) % 3.61/3.89 (step @p112 :rule reordering :premises (@p111) :args ((or @t98 @t103))) % 3.61/3.89 (step @p113 :rule refl :args (@t104)) % 3.61/3.89 (step @p114 :rule refl :args (@t99)) % 3.61/3.89 (step @p115 :rule refl :args (@t108)) % 3.61/3.89 (step @p116 :rule refl :args (@t106)) % 3.61/3.89 (step @p117 :rule eq-symm :args (@t96 tptp.xb)) % 3.61/3.89 (step @p118 :rule cong :premises (@p117) :args (@t109)) % 3.61/3.89 (step @p119 :rule nary_cong :premises (@p118 @p116 @p115 @p114 @p113) :args (@t110)) % 3.61/3.89 (step @p120 :rule refl :args (@t101)) % 3.61/3.89 (step @p121 :rule refl :args (@t102)) % 3.61/3.89 (step @p122 :rule nary_cong :premises (@p121 @p120 @p119) :args (@t111)) % 3.61/3.89 (step @p123 :rule refl :args (@t67)) % 3.61/3.89 (step @p124 :rule cong :premises (@p123 @p122) :args ((=> @t67 @t111))) % 3.61/3.89 (assume-push @p190 @t67) % 3.61/3.89 (step @p126 :rule instantiate :premises (@p96) :args ((@list @t96 tptp.xb))) % 3.61/3.89 (step-pop @p191 :rule scope :premises (@p126)) % 3.61/3.89 (step @p127 :rule process_scope :premises (@p191) :args (@t111)) % 3.61/3.89 (step @p129 :rule eq_resolve :premises (@p127 @p124)) % 3.61/3.89 (step @p130 :rule implies_elim :premises (@p129)) % 3.61/3.89 (step @p131 :rule chain_m_resolution :premises (@p130 @p96) :args (@t113 @t114 (@list @t67))) % 3.61/3.89 (step @p132 :rule cnf_or_pos :args (@t113)) % 3.61/3.89 (step @p133 :rule reordering :premises (@p132) :args ((or @t102 @t101 @t112 (not @t113)))) % 3.61/3.89 (step @p134 :rule cnf_and_pos :args (@t112 3)) % 3.61/3.89 (step @p135 :rule reordering :premises (@p134) :args ((or @t99 (not @t112)))) % 3.61/3.89 (step @p136 :rule chain_m_resolution :premises (@p135 @p133 @p131 @p112 @p107 @p102) :args (@t103 (@list false false false false false) (@list @t112 @t113 @t98 @t100 @t97))) % 3.61/3.89 (step @p137 :rule refl :args (@t115)) % 3.61/3.89 (step @p138 :rule bool-double-not-elim :args (@t95)) % 3.61/3.89 (step @p139 :rule nary_cong :premises (@p138 @p137) :args ((or (not @t116) @t115))) % 3.61/3.89 (assume-push @p192 @t116) % 3.61/3.89 (step @p141 :rule skolemize :premises (@p192)) % 3.61/3.89 (step-pop @p193 :rule scope :premises (@p141)) % 3.61/3.89 (step @p142 :rule process_scope :premises (@p193) :args (@t115)) % 3.61/3.89 (step @p144 :rule implies_elim :premises (@p142)) % 3.61/3.89 (step @p145 :rule eq_resolve :premises (@p144 @p139)) % 3.61/3.89 (step @p146 :rule chain_m_resolution :premises (@p145 @p136) :args (@t95 @t114 (@list @t103))) % 0.33/3.90 (step @p147 :rule aci_norm :args ((= (or @t65 (or @t64 @t58)) @t94))) % 0.33/3.90 (step @p148 :rule bool-and-de-morgan :args (@t40 @t42 true)) % 0.33/3.90 (step @p149 :rule nary_cong :premises (@p33 @p148) :args ((or @t65 (not (and @t40 @t42))))) % 0.33/3.90 (step @p150 :rule bool-and-de-morgan :args (@t2 @t40 (and @t42))) % 0.33/3.90 (step @p151 :rule trans :premises (@p150 @p149)) % 0.33/3.90 (step @p152 :rule trans :premises (@p151 @p147)) % 0.33/3.90 (step @p153 :rule cong :premises (@p152) :args (@t117)) % 0.33/3.90 (step @p154 :rule cong :premises (@p153) :args (@t118)) % 0.33/3.90 (step @p155 :rule exists-elim :args ((= @t44 @t118))) % 0.33/3.90 (step @p156 :rule trans :premises (@p155 @p154)) % 0.33/3.90 (step @p157 :rule refl :args (@t45)) % 0.33/3.90 (step @p158 :rule nary_cong :premises (@p157 @p156) :args (@t46)) % 0.33/3.90 (step @p159 :rule and_elim :premises (@p19) :args (0)) % 0.33/3.90 (step @p160 :rule eq_resolve :premises (@p159 @p158)) % 0.33/3.90 (step @p161 :rule chain_m_resolution :premises (@p160 @p146) :args (@t45 @t114 (@list @t95))) % 0.33/3.90 (step @p162 :rule and_elim :premises (@p17) :args (1)) % 0.33/3.90 (step @p163 :rule cnf_or_pos :args (@t120)) % 0.33/3.90 (step @p164 :rule reordering :premises (@p163) :args ((or @t107 @t119 @t121))) % 0.33/3.90 (step @p165 :rule chain_m_resolution :premises (@p164 @p162 @p161) :args (@t121 (@list false false) (@list @t37 @t45))) % 0.33/3.90 (step @p166 :rule aci_norm :args ((= (or @t107 @t119 false) @t120))) % 0.33/3.90 (step @p167 :rule absorb :args ((= (and false @t124 @t123 @t105 @t122) false))) % 0.33/3.90 (step @p168 :rule refl :args (@t122)) % 0.33/3.90 (step @p169 :rule refl :args (@t105)) % 0.33/3.90 (step @p170 :rule refl :args (@t123)) % 0.33/3.90 (step @p171 :rule refl :args (@t124)) % 0.33/3.90 (step @p172 :rule evaluate :args ((not true))) % 0.33/3.90 (step @p173 :rule eq-refl :args (tptp.xb)) % 0.33/3.90 (step @p174 :rule cong :premises (@p173) :args (@t125)) % 0.33/3.90 (step @p175 :rule trans :premises (@p174 @p172)) % 0.33/3.90 (step @p176 :rule nary_cong :premises (@p175 @p171 @p170 @p169 @p168) :args (@t126)) % 0.33/3.90 (step @p177 :rule trans :premises (@p176 @p167)) % 0.33/3.90 (step @p178 :rule refl :args (@t119)) % 0.33/3.90 (step @p179 :rule refl :args (@t107)) % 0.33/3.90 (step @p180 :rule nary_cong :premises (@p179 @p178 @p177) :args (@t127)) % 0.33/3.90 (step @p181 :rule trans :premises (@p180 @p166)) % 0.33/3.90 (step @p182 :rule cong :premises (@p123 @p181) :args ((=> @t67 @t127))) % 0.33/3.90 (assume-push @p194 @t67) % 0.33/3.90 (step @p184 :rule instantiate :premises (@p96) :args ((@list tptp.xb tptp.xa))) % 0.33/3.90 (step-pop @p195 :rule scope :premises (@p184)) % 0.33/3.90 (step @p185 :rule process_scope :premises (@p195) :args (@t127)) % 0.33/3.90 (step @p187 :rule eq_resolve :premises (@p185 @p182)) % 0.33/3.90 (step @p188 :rule implies_elim :premises (@p187)) % 0.33/3.90 (step @p189 false :rule chain_m_resolution :premises (@p188 @p165 @p96) :args (false (@list true false) (@list @t120 @t67))) % 0.33/3.90 ) % 0.33/3.90 % SZS output end Proof % 0.33/3.90 % cvc5 exiting %------------------------------------------------------------------------------