%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEV631+1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 : Tue May 5 06:56:02 PM UTC 2026
% Result : Theorem 3.24s 3.44s
% Output : Proof 3.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV631+1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.11 % Command : run_E %s %d THM
% 0.15/0.32 % Computer : n004.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 06:28:49 EDT 2026
% 0.15/0.32 % CPUTime :
% 3.24/3.44 % SZS status Theorem
% 3.24/3.44 % SZS output start Proof
% 3.24/3.44 tff(tptp_fun_V4__c_2068_type, type, (
% 3.24/3.44 tptp_fun_V4__c_2068: $i)).
% 3.24/3.44 tff(tptp_fun_V2__a_2066_type, type, (
% 3.24/3.44 tptp_fun_V2__a_2066: $i)).
% 3.24/3.44 tff(tptp_fun_V5__d_2069_type, type, (
% 3.24/3.44 tptp_fun_V5__d_2069: $i)).
% 3.24/3.44 tff(tptp_fun_V3__b_2067_type, type, (
% 3.24/3.44 tptp_fun_V3__b_2067: $i)).
% 3.24/3.44 tff(cHList_2ehlist_2eHcons___24a4_type, type, (
% 3.24/3.44 cHList_2ehlist_2eHcons___24a4: ( $i * $i * $i * $i ) > $i)).
% 3.24/3.44 tff(tptp_fun_V1__ls_2065_type, type, (
% 3.24/3.44 tptp_fun_V1__ls_2065: $i)).
% 3.24/3.44 tff(tptp_fun_V0__l_2064_type, type, (
% 3.24/3.44 tptp_fun_V0__l_2064: $i)).
% 3.24/3.44 tff(cHList_2ehlist_2ehlist___24t_type, type, (
% 3.24/3.44 cHList_2ehlist_2ehlist___24t: ( $i * $i ) > $o)).
% 3.24/3.44 tff(cF___24t_type, type, (
% 3.24/3.44 cF___24t: ( $i * $i ) > $o)).
% 3.24/3.44 tff(cCoq_2eInit_2eDatatypes_2elist___24t_type, type, (
% 3.24/3.44 cCoq_2eInit_2eDatatypes_2elist___24t: ( $i * $i ) > $o)).
% 3.24/3.44 tff(ciT_type, type, (
% 3.24/3.44 ciT: $i)).
% 3.24/3.44 tff(ciT___24t_type, type, (
% 3.24/3.44 ciT___24t: $i > $o)).
% 3.24/3.44 tff(1,plain,
% 3.24/3.44 ((ciT___24t(V0__l!2064) & (cCoq_2eInit_2eDatatypes_2elist___24t(ciT, V1__ls!2065) & cF___24t(V0__l!2064, V2__a!2066) & cHList_2ehlist_2ehlist___24t(V1__ls!2065, V3__b!2067) & cF___24t(V0__l!2064, V4__c!2068) & (~(((V2__a!2066 = V4__c!2068) & (V3__b!2067 = V5__d!2069)) | (~cHList_2ehlist_2ehlist___24t(V1__ls!2065, V5__d!2069)) | (~(cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V2__a!2066, V3__b!2067) = cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V4__c!2068, V5__d!2069))))))) <=> (ciT___24t(V0__l!2064) & cCoq_2eInit_2eDatatypes_2elist___24t(ciT, V1__ls!2065) & cF___24t(V0__l!2064, V2__a!2066) & cHList_2ehlist_2ehlist___24t(V1__ls!2065, V3__b!2067) & cF___24t(V0__l!2064, V4__c!2068) & (~(((V2__a!2066 = V4__c!2068) & (V3__b!2067 = V5__d!2069)) | (~cHList_2ehlist_2ehlist___24t(V1__ls!2065, V5__d!2069)) | (~(cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V2__a!2066, V3__b!2067) = cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V4__c!2068, V5__d!2069))))))),
% 3.24/3.44 inference(rewrite,[status(thm)],[])).
% 3.24/3.44 tff(2,plain,
% 3.24/3.44 ((cCoq_2eInit_2eDatatypes_2elist___24t(ciT, V1__ls!2065) & (cF___24t(V0__l!2064, V2__a!2066) & cHList_2ehlist_2ehlist___24t(V1__ls!2065, V3__b!2067) & cF___24t(V0__l!2064, V4__c!2068) & (~(((V2__a!2066 = V4__c!2068) & (V3__b!2067 = V5__d!2069)) | (~cHList_2ehlist_2ehlist___24t(V1__ls!2065, V5__d!2069)) | (~(cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V2__a!2066, V3__b!2067) = cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V4__c!2068, V5__d!2069))))))) <=> (cCoq_2eInit_2eDatatypes_2elist___24t(ciT, V1__ls!2065) & cF___24t(V0__l!2064, V2__a!2066) & cHList_2ehlist_2ehlist___24t(V1__ls!2065, V3__b!2067) & cF___24t(V0__l!2064, V4__c!2068) & (~(((V2__a!2066 = V4__c!2068) & (V3__b!2067 = V5__d!2069)) | (~cHList_2ehlist_2ehlist___24t(V1__ls!2065, V5__d!2069)) | (~(cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V2__a!2066, V3__b!2067) = cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V4__c!2068, V5__d!2069))))))),
% 3.24/3.44 inference(rewrite,[status(thm)],[])).
% 3.24/3.44 tff(3,plain,
% 3.24/3.44 ((cF___24t(V0__l!2064, V2__a!2066) & (cHList_2ehlist_2ehlist___24t(V1__ls!2065, V3__b!2067) & cF___24t(V0__l!2064, V4__c!2068) & (~(((V2__a!2066 = V4__c!2068) & (V3__b!2067 = V5__d!2069)) | (~cHList_2ehlist_2ehlist___24t(V1__ls!2065, V5__d!2069)) | (~(cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V2__a!2066, V3__b!2067) = cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V4__c!2068, V5__d!2069))))))) <=> (cF___24t(V0__l!2064, V2__a!2066) & cHList_2ehlist_2ehlist___24t(V1__ls!2065, V3__b!2067) & cF___24t(V0__l!2064, V4__c!2068) & (~(((V2__a!2066 = V4__c!2068) & (V3__b!2067 = V5__d!2069)) | (~cHList_2ehlist_2ehlist___24t(V1__ls!2065, V5__d!2069)) | (~(cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V2__a!2066, V3__b!2067) = cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V4__c!2068, V5__d!2069))))))),
% 3.24/3.44 inference(rewrite,[status(thm)],[])).
% 3.24/3.44 tff(4,plain,
% 3.24/3.44 ((cHList_2ehlist_2ehlist___24t(V1__ls!2065, V3__b!2067) & (cF___24t(V0__l!2064, V4__c!2068) & (~(((V2__a!2066 = V4__c!2068) & (V3__b!2067 = V5__d!2069)) | (~cHList_2ehlist_2ehlist___24t(V1__ls!2065, V5__d!2069)) | (~(cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V2__a!2066, V3__b!2067) = cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V4__c!2068, V5__d!2069))))))) <=> (cHList_2ehlist_2ehlist___24t(V1__ls!2065, V3__b!2067) & cF___24t(V0__l!2064, V4__c!2068) & (~(((V2__a!2066 = V4__c!2068) & (V3__b!2067 = V5__d!2069)) | (~cHList_2ehlist_2ehlist___24t(V1__ls!2065, V5__d!2069)) | (~(cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V2__a!2066, V3__b!2067) = cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V4__c!2068, V5__d!2069))))))),
% 3.24/3.44 inference(rewrite,[status(thm)],[])).
% 3.24/3.44 tff(5,plain,
% 3.24/3.44 ((~(((V2__a!2066 = V4__c!2068) & (V3__b!2067 = V5__d!2069)) | (~cHList_2ehlist_2ehlist___24t(V1__ls!2065, V5__d!2069)) | (~(cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V2__a!2066, V3__b!2067) = cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V4__c!2068, V5__d!2069))))) <=> (~(((V2__a!2066 = V4__c!2068) & (V3__b!2067 = V5__d!2069)) | (~cHList_2ehlist_2ehlist___24t(V1__ls!2065, V5__d!2069)) | (~(cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V2__a!2066, V3__b!2067) = cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V4__c!2068, V5__d!2069)))))),
% 3.24/3.44 inference(rewrite,[status(thm)],[])).
% 3.24/3.44 tff(6,plain,
% 3.24/3.44 ((cF___24t(V0__l!2064, V4__c!2068) & (~(((V2__a!2066 = V4__c!2068) & (V3__b!2067 = V5__d!2069)) | (~cHList_2ehlist_2ehlist___24t(V1__ls!2065, V5__d!2069)) | (~(cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V2__a!2066, V3__b!2067) = cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V4__c!2068, V5__d!2069)))))) <=> (cF___24t(V0__l!2064, V4__c!2068) & (~(((V2__a!2066 = V4__c!2068) & (V3__b!2067 = V5__d!2069)) | (~cHList_2ehlist_2ehlist___24t(V1__ls!2065, V5__d!2069)) | (~(cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V2__a!2066, V3__b!2067) = cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V4__c!2068, V5__d!2069))))))),
% 3.24/3.44 inference(monotonicity,[status(thm)],[5])).
% 3.24/3.44 tff(7,plain,
% 3.24/3.44 ((cHList_2ehlist_2ehlist___24t(V1__ls!2065, V3__b!2067) & (cF___24t(V0__l!2064, V4__c!2068) & (~(((V2__a!2066 = V4__c!2068) & (V3__b!2067 = V5__d!2069)) | (~cHList_2ehlist_2ehlist___24t(V1__ls!2065, V5__d!2069)) | (~(cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V2__a!2066, V3__b!2067) = cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V4__c!2068, V5__d!2069))))))) <=> (cHList_2ehlist_2ehlist___24t(V1__ls!2065, V3__b!2067) & (cF___24t(V0__l!2064, V4__c!2068) & (~(((V2__a!2066 = V4__c!2068) & (V3__b!2067 = V5__d!2069)) | (~cHList_2ehlist_2ehlist___24t(V1__ls!2065, V5__d!2069)) | (~(cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V2__a!2066, V3__b!2067) = cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V4__c!2068, V5__d!2069)))))))),
% 3.24/3.44 inference(monotonicity,[status(thm)],[6])).
% 3.24/3.44 tff(8,plain,
% 3.24/3.44 ((cHList_2ehlist_2ehlist___24t(V1__ls!2065, V3__b!2067) & (cF___24t(V0__l!2064, V4__c!2068) & (~(((V2__a!2066 = V4__c!2068) & (V3__b!2067 = V5__d!2069)) | (~cHList_2ehlist_2ehlist___24t(V1__ls!2065, V5__d!2069)) | (~(cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V2__a!2066, V3__b!2067) = cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V4__c!2068, V5__d!2069))))))) <=> (cHList_2ehlist_2ehlist___24t(V1__ls!2065, V3__b!2067) & cF___24t(V0__l!2064, V4__c!2068) & (~(((V2__a!2066 = V4__c!2068) & (V3__b!2067 = V5__d!2069)) | (~cHList_2ehlist_2ehlist___24t(V1__ls!2065, V5__d!2069)) | (~(cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V2__a!2066, V3__b!2067) = cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V4__c!2068, V5__d!2069))))))),
% 3.24/3.44 inference(transitivity,[status(thm)],[7, 4])).
% 3.24/3.44 tff(9,plain,
% 3.24/3.44 ((cF___24t(V0__l!2064, V2__a!2066) & (cHList_2ehlist_2ehlist___24t(V1__ls!2065, V3__b!2067) & (cF___24t(V0__l!2064, V4__c!2068) & (~(((V2__a!2066 = V4__c!2068) & (V3__b!2067 = V5__d!2069)) | (~cHList_2ehlist_2ehlist___24t(V1__ls!2065, V5__d!2069)) | (~(cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V2__a!2066, V3__b!2067) = cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V4__c!2068, V5__d!2069)))))))) <=> (cF___24t(V0__l!2064, V2__a!2066) & (cHList_2ehlist_2ehlist___24t(V1__ls!2065, V3__b!2067) & cF___24t(V0__l!2064, V4__c!2068) & (~(((V2__a!2066 = V4__c!2068) & (V3__b!2067 = V5__d!2069)) | (~cHList_2ehlist_2ehlist___24t(V1__ls!2065, V5__d!2069)) | (~(cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V2__a!2066, V3__b!2067) = cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V4__c!2068, V5__d!2069)))))))),
% 3.24/3.44 inference(monotonicity,[status(thm)],[8])).
% 3.24/3.44 tff(10,plain,
% 3.24/3.44 ((cF___24t(V0__l!2064, V2__a!2066) & (cHList_2ehlist_2ehlist___24t(V1__ls!2065, V3__b!2067) & (cF___24t(V0__l!2064, V4__c!2068) & (~(((V2__a!2066 = V4__c!2068) & (V3__b!2067 = V5__d!2069)) | (~cHList_2ehlist_2ehlist___24t(V1__ls!2065, V5__d!2069)) | (~(cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V2__a!2066, V3__b!2067) = cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V4__c!2068, V5__d!2069)))))))) <=> (cF___24t(V0__l!2064, V2__a!2066) & cHList_2ehlist_2ehlist___24t(V1__ls!2065, V3__b!2067) & cF___24t(V0__l!2064, V4__c!2068) & (~(((V2__a!2066 = V4__c!2068) & (V3__b!2067 = V5__d!2069)) | (~cHList_2ehlist_2ehlist___24t(V1__ls!2065, V5__d!2069)) | (~(cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V2__a!2066, V3__b!2067) = cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V4__c!2068, V5__d!2069))))))),
% 3.24/3.44 inference(transitivity,[status(thm)],[9, 3])).
% 3.24/3.44 tff(11,plain,
% 3.24/3.44 ((cCoq_2eInit_2eDatatypes_2elist___24t(ciT, V1__ls!2065) & (cF___24t(V0__l!2064, V2__a!2066) & (cHList_2ehlist_2ehlist___24t(V1__ls!2065, V3__b!2067) & (cF___24t(V0__l!2064, V4__c!2068) & (~(((V2__a!2066 = V4__c!2068) & (V3__b!2067 = V5__d!2069)) | (~cHList_2ehlist_2ehlist___24t(V1__ls!2065, V5__d!2069)) | (~(cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V2__a!2066, V3__b!2067) = cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V4__c!2068, V5__d!2069))))))))) <=> (cCoq_2eInit_2eDatatypes_2elist___24t(ciT, V1__ls!2065) & (cF___24t(V0__l!2064, V2__a!2066) & cHList_2ehlist_2ehlist___24t(V1__ls!2065, V3__b!2067) & cF___24t(V0__l!2064, V4__c!2068) & (~(((V2__a!2066 = V4__c!2068) & (V3__b!2067 = V5__d!2069)) | (~cHList_2ehlist_2ehlist___24t(V1__ls!2065, V5__d!2069)) | (~(cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V2__a!2066, V3__b!2067) = cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V4__c!2068, V5__d!2069)))))))),
% 3.24/3.44 inference(monotonicity,[status(thm)],[10])).
% 3.24/3.44 tff(12,plain,
% 3.24/3.44 ((cCoq_2eInit_2eDatatypes_2elist___24t(ciT, V1__ls!2065) & (cF___24t(V0__l!2064, V2__a!2066) & (cHList_2ehlist_2ehlist___24t(V1__ls!2065, V3__b!2067) & (cF___24t(V0__l!2064, V4__c!2068) & (~(((V2__a!2066 = V4__c!2068) & (V3__b!2067 = V5__d!2069)) | (~cHList_2ehlist_2ehlist___24t(V1__ls!2065, V5__d!2069)) | (~(cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V2__a!2066, V3__b!2067) = cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V4__c!2068, V5__d!2069))))))))) <=> (cCoq_2eInit_2eDatatypes_2elist___24t(ciT, V1__ls!2065) & cF___24t(V0__l!2064, V2__a!2066) & cHList_2ehlist_2ehlist___24t(V1__ls!2065, V3__b!2067) & cF___24t(V0__l!2064, V4__c!2068) & (~(((V2__a!2066 = V4__c!2068) & (V3__b!2067 = V5__d!2069)) | (~cHList_2ehlist_2ehlist___24t(V1__ls!2065, V5__d!2069)) | (~(cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V2__a!2066, V3__b!2067) = cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V4__c!2068, V5__d!2069))))))),
% 3.24/3.44 inference(transitivity,[status(thm)],[11, 2])).
% 3.24/3.44 tff(13,plain,
% 3.24/3.44 ((ciT___24t(V0__l!2064) & (cCoq_2eInit_2eDatatypes_2elist___24t(ciT, V1__ls!2065) & (cF___24t(V0__l!2064, V2__a!2066) & (cHList_2ehlist_2ehlist___24t(V1__ls!2065, V3__b!2067) & (cF___24t(V0__l!2064, V4__c!2068) & (~(((V2__a!2066 = V4__c!2068) & (V3__b!2067 = V5__d!2069)) | (~cHList_2ehlist_2ehlist___24t(V1__ls!2065, V5__d!2069)) | (~(cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V2__a!2066, V3__b!2067) = cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V4__c!2068, V5__d!2069)))))))))) <=> (ciT___24t(V0__l!2064) & (cCoq_2eInit_2eDatatypes_2elist___24t(ciT, V1__ls!2065) & cF___24t(V0__l!2064, V2__a!2066) & cHList_2ehlist_2ehlist___24t(V1__ls!2065, V3__b!2067) & cF___24t(V0__l!2064, V4__c!2068) & (~(((V2__a!2066 = V4__c!2068) & (V3__b!2067 = V5__d!2069)) | (~cHList_2ehlist_2ehlist___24t(V1__ls!2065, V5__d!2069)) | (~(cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V2__a!2066, V3__b!2067) = cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V4__c!2068, V5__d!2069)))))))),
% 3.24/3.44 inference(monotonicity,[status(thm)],[12])).
% 3.24/3.44 tff(14,plain,
% 3.24/3.44 ((ciT___24t(V0__l!2064) & (cCoq_2eInit_2eDatatypes_2elist___24t(ciT, V1__ls!2065) & (cF___24t(V0__l!2064, V2__a!2066) & (cHList_2ehlist_2ehlist___24t(V1__ls!2065, V3__b!2067) & (cF___24t(V0__l!2064, V4__c!2068) & (~(((V2__a!2066 = V4__c!2068) & (V3__b!2067 = V5__d!2069)) | (~cHList_2ehlist_2ehlist___24t(V1__ls!2065, V5__d!2069)) | (~(cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V2__a!2066, V3__b!2067) = cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V4__c!2068, V5__d!2069)))))))))) <=> (ciT___24t(V0__l!2064) & cCoq_2eInit_2eDatatypes_2elist___24t(ciT, V1__ls!2065) & cF___24t(V0__l!2064, V2__a!2066) & cHList_2ehlist_2ehlist___24t(V1__ls!2065, V3__b!2067) & cF___24t(V0__l!2064, V4__c!2068) & (~(((V2__a!2066 = V4__c!2068) & (V3__b!2067 = V5__d!2069)) | (~cHList_2ehlist_2ehlist___24t(V1__ls!2065, V5__d!2069)) | (~(cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V2__a!2066, V3__b!2067) = cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V4__c!2068, V5__d!2069))))))),
% 3.24/3.44 inference(transitivity,[status(thm)],[13, 1])).
% 3.24/3.44 tff(15,plain,
% 3.24/3.44 ((~![V0__l: $i] : ((~ciT___24t(V0__l)) | ![V1__ls: $i] : ((~cCoq_2eInit_2eDatatypes_2elist___24t(ciT, V1__ls)) | ![V2__a: $i] : ((~cF___24t(V0__l, V2__a)) | ![V3__b: $i] : ((~cHList_2ehlist_2ehlist___24t(V1__ls, V3__b)) | ![V4__c: $i] : ((~cF___24t(V0__l, V4__c)) | ![V5__d: $i] : (((V2__a = V4__c) & (V3__b = V5__d)) | (~cHList_2ehlist_2ehlist___24t(V1__ls, V5__d)) | (~(cHList_2ehlist_2eHcons___24a4(V0__l, V1__ls, V2__a, V3__b) = cHList_2ehlist_2eHcons___24a4(V0__l, V1__ls, V4__c, V5__d)))))))))) <=> (~![V0__l: $i] : ((~ciT___24t(V0__l)) | ![V1__ls: $i] : ((~cCoq_2eInit_2eDatatypes_2elist___24t(ciT, V1__ls)) | ![V2__a: $i] : ((~cF___24t(V0__l, V2__a)) | ![V3__b: $i] : ((~cHList_2ehlist_2ehlist___24t(V1__ls, V3__b)) | ![V4__c: $i] : ((~cF___24t(V0__l, V4__c)) | ![V5__d: $i] : (((V2__a = V4__c) & (V3__b = V5__d)) | (~cHList_2ehlist_2ehlist___24t(V1__ls, V5__d)) | (~(cHList_2ehlist_2eHcons___24a4(V0__l, V1__ls, V2__a, V3__b) = cHList_2ehlist_2eHcons___24a4(V0__l, V1__ls, V4__c, V5__d))))))))))),
% 3.24/3.44 inference(rewrite,[status(thm)],[])).
% 3.24/3.44 tff(16,plain,
% 3.24/3.44 ((~![V0__l: $i] : (ciT___24t(V0__l) => ![V1__ls: $i] : (cCoq_2eInit_2eDatatypes_2elist___24t(ciT, V1__ls) => ![V2__a: $i] : (cF___24t(V0__l, V2__a) => ![V3__b: $i] : (cHList_2ehlist_2ehlist___24t(V1__ls, V3__b) => ![V4__c: $i] : (cF___24t(V0__l, V4__c) => ![V5__d: $i] : (cHList_2ehlist_2ehlist___24t(V1__ls, V5__d) => ((cHList_2ehlist_2eHcons___24a4(V0__l, V1__ls, V2__a, V3__b) = cHList_2ehlist_2eHcons___24a4(V0__l, V1__ls, V4__c, V5__d)) => ((V2__a = V4__c) & (V3__b = V5__d)))))))))) <=> (~![V0__l: $i] : ((~ciT___24t(V0__l)) | ![V1__ls: $i] : ((~cCoq_2eInit_2eDatatypes_2elist___24t(ciT, V1__ls)) | ![V2__a: $i] : ((~cF___24t(V0__l, V2__a)) | ![V3__b: $i] : ((~cHList_2ehlist_2ehlist___24t(V1__ls, V3__b)) | ![V4__c: $i] : ((~cF___24t(V0__l, V4__c)) | ![V5__d: $i] : (((V2__a = V4__c) & (V3__b = V5__d)) | (~cHList_2ehlist_2ehlist___24t(V1__ls, V5__d)) | (~(cHList_2ehlist_2eHcons___24a4(V0__l, V1__ls, V2__a, V3__b) = cHList_2ehlist_2eHcons___24a4(V0__l, V1__ls, V4__c, V5__d))))))))))),
% 3.24/3.44 inference(rewrite,[status(thm)],[])).
% 3.24/3.44 tff(17,axiom,(~![V0__l: $i] : (ciT___24t(V0__l) => ![V1__ls: $i] : (cCoq_2eInit_2eDatatypes_2elist___24t(ciT, V1__ls) => ![V2__a: $i] : (cF___24t(V0__l, V2__a) => ![V3__b: $i] : (cHList_2ehlist_2ehlist___24t(V1__ls, V3__b) => ![V4__c: $i] : (cF___24t(V0__l, V4__c) => ![V5__d: $i] : (cHList_2ehlist_2ehlist___24t(V1__ls, V5__d) => ((cHList_2ehlist_2eHcons___24a4(V0__l, V1__ls, V2__a, V3__b) = cHList_2ehlist_2eHcons___24a4(V0__l, V1__ls, V4__c, V5__d)) => ((V2__a = V4__c) & (V3__b = V5__d)))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''_HAMMER_GOAL'')).
% 3.24/3.44 tff(18,plain,
% 3.24/3.44 (~![V0__l: $i] : ((~ciT___24t(V0__l)) | ![V1__ls: $i] : ((~cCoq_2eInit_2eDatatypes_2elist___24t(ciT, V1__ls)) | ![V2__a: $i] : ((~cF___24t(V0__l, V2__a)) | ![V3__b: $i] : ((~cHList_2ehlist_2ehlist___24t(V1__ls, V3__b)) | ![V4__c: $i] : ((~cF___24t(V0__l, V4__c)) | ![V5__d: $i] : (((V2__a = V4__c) & (V3__b = V5__d)) | (~cHList_2ehlist_2ehlist___24t(V1__ls, V5__d)) | (~(cHList_2ehlist_2eHcons___24a4(V0__l, V1__ls, V2__a, V3__b) = cHList_2ehlist_2eHcons___24a4(V0__l, V1__ls, V4__c, V5__d)))))))))),
% 3.24/3.44 inference(modus_ponens,[status(thm)],[17, 16])).
% 3.24/3.44 tff(19,plain,
% 3.24/3.44 (~![V0__l: $i] : ((~ciT___24t(V0__l)) | ![V1__ls: $i] : ((~cCoq_2eInit_2eDatatypes_2elist___24t(ciT, V1__ls)) | ![V2__a: $i] : ((~cF___24t(V0__l, V2__a)) | ![V3__b: $i] : ((~cHList_2ehlist_2ehlist___24t(V1__ls, V3__b)) | ![V4__c: $i] : ((~cF___24t(V0__l, V4__c)) | ![V5__d: $i] : (((V2__a = V4__c) & (V3__b = V5__d)) | (~cHList_2ehlist_2ehlist___24t(V1__ls, V5__d)) | (~(cHList_2ehlist_2eHcons___24a4(V0__l, V1__ls, V2__a, V3__b) = cHList_2ehlist_2eHcons___24a4(V0__l, V1__ls, V4__c, V5__d)))))))))),
% 3.24/3.44 inference(modus_ponens,[status(thm)],[18, 15])).
% 3.24/3.44 tff(20,plain,
% 3.24/3.44 (~![V0__l: $i] : ((~ciT___24t(V0__l)) | ![V1__ls: $i] : ((~cCoq_2eInit_2eDatatypes_2elist___24t(ciT, V1__ls)) | ![V2__a: $i] : ((~cF___24t(V0__l, V2__a)) | ![V3__b: $i] : ((~cHList_2ehlist_2ehlist___24t(V1__ls, V3__b)) | ![V4__c: $i] : ((~cF___24t(V0__l, V4__c)) | ![V5__d: $i] : (((V2__a = V4__c) & (V3__b = V5__d)) | (~cHList_2ehlist_2ehlist___24t(V1__ls, V5__d)) | (~(cHList_2ehlist_2eHcons___24a4(V0__l, V1__ls, V2__a, V3__b) = cHList_2ehlist_2eHcons___24a4(V0__l, V1__ls, V4__c, V5__d)))))))))),
% 3.24/3.44 inference(modus_ponens,[status(thm)],[19, 15])).
% 3.24/3.44 tff(21,plain,
% 3.24/3.44 (~![V0__l: $i] : ((~ciT___24t(V0__l)) | ![V1__ls: $i] : ((~cCoq_2eInit_2eDatatypes_2elist___24t(ciT, V1__ls)) | ![V2__a: $i] : ((~cF___24t(V0__l, V2__a)) | ![V3__b: $i] : ((~cHList_2ehlist_2ehlist___24t(V1__ls, V3__b)) | ![V4__c: $i] : ((~cF___24t(V0__l, V4__c)) | ![V5__d: $i] : (((V2__a = V4__c) & (V3__b = V5__d)) | (~cHList_2ehlist_2ehlist___24t(V1__ls, V5__d)) | (~(cHList_2ehlist_2eHcons___24a4(V0__l, V1__ls, V2__a, V3__b) = cHList_2ehlist_2eHcons___24a4(V0__l, V1__ls, V4__c, V5__d)))))))))),
% 3.24/3.44 inference(modus_ponens,[status(thm)],[20, 15])).
% 3.24/3.44 tff(22,plain,
% 3.24/3.44 (ciT___24t(V0__l!2064) & cCoq_2eInit_2eDatatypes_2elist___24t(ciT, V1__ls!2065) & cF___24t(V0__l!2064, V2__a!2066) & cHList_2ehlist_2ehlist___24t(V1__ls!2065, V3__b!2067) & cF___24t(V0__l!2064, V4__c!2068) & (~(((V2__a!2066 = V4__c!2068) & (V3__b!2067 = V5__d!2069)) | (~cHList_2ehlist_2ehlist___24t(V1__ls!2065, V5__d!2069)) | (~(cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V2__a!2066, V3__b!2067) = cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V4__c!2068, V5__d!2069)))))),
% 3.24/3.44 inference(modus_ponens,[status(thm)],[21, 14])).
% 3.24/3.44 tff(23,plain,
% 3.24/3.44 (~(((V2__a!2066 = V4__c!2068) & (V3__b!2067 = V5__d!2069)) | (~cHList_2ehlist_2ehlist___24t(V1__ls!2065, V5__d!2069)) | (~(cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V2__a!2066, V3__b!2067) = cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V4__c!2068, V5__d!2069))))),
% 3.24/3.44 inference(and_elim,[status(thm)],[22])).
% 3.24/3.44 tff(24,plain,
% 3.24/3.44 (cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V2__a!2066, V3__b!2067) = cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V4__c!2068, V5__d!2069)),
% 3.24/3.44 inference(or_elim,[status(thm)],[23])).
% 3.24/3.44 tff(25,plain,
% 3.24/3.44 (^[Vvar__0__l__46672: $i, Vvar__0__l__46673: $i, Vvar__1__ls__46674: $i, Vvar__1__ls__46675: $i, Vvar__2___24Anonymous__46676: $i, Vvar__2___24Anonymous__46677: $i, Vvar__3___24Anonymous__46678: $i, Vvar__3___24Anonymous__46679: $i] : refl(((~(cHList_2ehlist_2eHcons___24a4(Vvar__0__l__46672, Vvar__1__ls__46674, Vvar__2___24Anonymous__46676, Vvar__3___24Anonymous__46678) = cHList_2ehlist_2eHcons___24a4(Vvar__0__l__46673, Vvar__1__ls__46675, Vvar__2___24Anonymous__46677, Vvar__3___24Anonymous__46679))) | (~((~(Vvar__3___24Anonymous__46678 = Vvar__3___24Anonymous__46679)) | (~(Vvar__2___24Anonymous__46676 = Vvar__2___24Anonymous__46677)) | (~(Vvar__1__ls__46674 = Vvar__1__ls__46675)) | (~(Vvar__0__l__46672 = Vvar__0__l__46673))))) <=> ((~(cHList_2ehlist_2eHcons___24a4(Vvar__0__l__46672, Vvar__1__ls__46674, Vvar__2___24Anonymous__46676, Vvar__3___24Anonymous__46678) = cHList_2ehlist_2eHcons___24a4(Vvar__0__l__46673, Vvar__1__ls__46675, Vvar__2___24Anonymous__46677, Vvar__3___24Anonymous__46679))) | (~((~(Vvar__3___24Anonymous__46678 = Vvar__3___24Anonymous__46679)) | (~(Vvar__2___24Anonymous__46676 = Vvar__2___24Anonymous__46677)) | (~(Vvar__1__ls__46674 = Vvar__1__ls__46675)) | (~(Vvar__0__l__46672 = Vvar__0__l__46673))))))),
% 3.24/3.44 inference(bind,[status(th)],[])).
% 3.24/3.44 tff(26,plain,
% 3.24/3.44 (![Vvar__0__l__46672: $i, Vvar__0__l__46673: $i, Vvar__1__ls__46674: $i, Vvar__1__ls__46675: $i, Vvar__2___24Anonymous__46676: $i, Vvar__2___24Anonymous__46677: $i, Vvar__3___24Anonymous__46678: $i, Vvar__3___24Anonymous__46679: $i] : ((~(cHList_2ehlist_2eHcons___24a4(Vvar__0__l__46672, Vvar__1__ls__46674, Vvar__2___24Anonymous__46676, Vvar__3___24Anonymous__46678) = cHList_2ehlist_2eHcons___24a4(Vvar__0__l__46673, Vvar__1__ls__46675, Vvar__2___24Anonymous__46677, Vvar__3___24Anonymous__46679))) | (~((~(Vvar__3___24Anonymous__46678 = Vvar__3___24Anonymous__46679)) | (~(Vvar__2___24Anonymous__46676 = Vvar__2___24Anonymous__46677)) | (~(Vvar__1__ls__46674 = Vvar__1__ls__46675)) | (~(Vvar__0__l__46672 = Vvar__0__l__46673))))) <=> ![Vvar__0__l__46672: $i, Vvar__0__l__46673: $i, Vvar__1__ls__46674: $i, Vvar__1__ls__46675: $i, Vvar__2___24Anonymous__46676: $i, Vvar__2___24Anonymous__46677: $i, Vvar__3___24Anonymous__46678: $i, Vvar__3___24Anonymous__46679: $i] : ((~(cHList_2ehlist_2eHcons___24a4(Vvar__0__l__46672, Vvar__1__ls__46674, Vvar__2___24Anonymous__46676, Vvar__3___24Anonymous__46678) = cHList_2ehlist_2eHcons___24a4(Vvar__0__l__46673, Vvar__1__ls__46675, Vvar__2___24Anonymous__46677, Vvar__3___24Anonymous__46679))) | (~((~(Vvar__3___24Anonymous__46678 = Vvar__3___24Anonymous__46679)) | (~(Vvar__2___24Anonymous__46676 = Vvar__2___24Anonymous__46677)) | (~(Vvar__1__ls__46674 = Vvar__1__ls__46675)) | (~(Vvar__0__l__46672 = Vvar__0__l__46673)))))),
% 3.24/3.44 inference(quant_intro,[status(thm)],[25])).
% 3.24/3.44 tff(27,plain,
% 3.24/3.44 (^[Vvar__0__l__46672: $i, Vvar__0__l__46673: $i, Vvar__1__ls__46674: $i, Vvar__1__ls__46675: $i, Vvar__2___24Anonymous__46676: $i, Vvar__2___24Anonymous__46677: $i, Vvar__3___24Anonymous__46678: $i, Vvar__3___24Anonymous__46679: $i] : rewrite(((~(cHList_2ehlist_2eHcons___24a4(Vvar__0__l__46672, Vvar__1__ls__46674, Vvar__2___24Anonymous__46676, Vvar__3___24Anonymous__46678) = cHList_2ehlist_2eHcons___24a4(Vvar__0__l__46673, Vvar__1__ls__46675, Vvar__2___24Anonymous__46677, Vvar__3___24Anonymous__46679))) | ((Vvar__3___24Anonymous__46678 = Vvar__3___24Anonymous__46679) & (Vvar__2___24Anonymous__46676 = Vvar__2___24Anonymous__46677) & (Vvar__1__ls__46674 = Vvar__1__ls__46675) & (Vvar__0__l__46672 = Vvar__0__l__46673))) <=> ((~(cHList_2ehlist_2eHcons___24a4(Vvar__0__l__46672, Vvar__1__ls__46674, Vvar__2___24Anonymous__46676, Vvar__3___24Anonymous__46678) = cHList_2ehlist_2eHcons___24a4(Vvar__0__l__46673, Vvar__1__ls__46675, Vvar__2___24Anonymous__46677, Vvar__3___24Anonymous__46679))) | (~((~(Vvar__3___24Anonymous__46678 = Vvar__3___24Anonymous__46679)) | (~(Vvar__2___24Anonymous__46676 = Vvar__2___24Anonymous__46677)) | (~(Vvar__1__ls__46674 = Vvar__1__ls__46675)) | (~(Vvar__0__l__46672 = Vvar__0__l__46673))))))),
% 3.24/3.44 inference(bind,[status(th)],[])).
% 3.24/3.44 tff(28,plain,
% 3.24/3.44 (![Vvar__0__l__46672: $i, Vvar__0__l__46673: $i, Vvar__1__ls__46674: $i, Vvar__1__ls__46675: $i, Vvar__2___24Anonymous__46676: $i, Vvar__2___24Anonymous__46677: $i, Vvar__3___24Anonymous__46678: $i, Vvar__3___24Anonymous__46679: $i] : ((~(cHList_2ehlist_2eHcons___24a4(Vvar__0__l__46672, Vvar__1__ls__46674, Vvar__2___24Anonymous__46676, Vvar__3___24Anonymous__46678) = cHList_2ehlist_2eHcons___24a4(Vvar__0__l__46673, Vvar__1__ls__46675, Vvar__2___24Anonymous__46677, Vvar__3___24Anonymous__46679))) | ((Vvar__3___24Anonymous__46678 = Vvar__3___24Anonymous__46679) & (Vvar__2___24Anonymous__46676 = Vvar__2___24Anonymous__46677) & (Vvar__1__ls__46674 = Vvar__1__ls__46675) & (Vvar__0__l__46672 = Vvar__0__l__46673))) <=> ![Vvar__0__l__46672: $i, Vvar__0__l__46673: $i, Vvar__1__ls__46674: $i, Vvar__1__ls__46675: $i, Vvar__2___24Anonymous__46676: $i, Vvar__2___24Anonymous__46677: $i, Vvar__3___24Anonymous__46678: $i, Vvar__3___24Anonymous__46679: $i] : ((~(cHList_2ehlist_2eHcons___24a4(Vvar__0__l__46672, Vvar__1__ls__46674, Vvar__2___24Anonymous__46676, Vvar__3___24Anonymous__46678) = cHList_2ehlist_2eHcons___24a4(Vvar__0__l__46673, Vvar__1__ls__46675, Vvar__2___24Anonymous__46677, Vvar__3___24Anonymous__46679))) | (~((~(Vvar__3___24Anonymous__46678 = Vvar__3___24Anonymous__46679)) | (~(Vvar__2___24Anonymous__46676 = Vvar__2___24Anonymous__46677)) | (~(Vvar__1__ls__46674 = Vvar__1__ls__46675)) | (~(Vvar__0__l__46672 = Vvar__0__l__46673)))))),
% 3.24/3.44 inference(quant_intro,[status(thm)],[27])).
% 3.24/3.44 tff(29,plain,
% 3.24/3.44 (![Vvar__0__l__46672: $i, Vvar__0__l__46673: $i, Vvar__1__ls__46674: $i, Vvar__1__ls__46675: $i, Vvar__2___24Anonymous__46676: $i, Vvar__2___24Anonymous__46677: $i, Vvar__3___24Anonymous__46678: $i, Vvar__3___24Anonymous__46679: $i] : ((~(cHList_2ehlist_2eHcons___24a4(Vvar__0__l__46672, Vvar__1__ls__46674, Vvar__2___24Anonymous__46676, Vvar__3___24Anonymous__46678) = cHList_2ehlist_2eHcons___24a4(Vvar__0__l__46673, Vvar__1__ls__46675, Vvar__2___24Anonymous__46677, Vvar__3___24Anonymous__46679))) | ((Vvar__3___24Anonymous__46678 = Vvar__3___24Anonymous__46679) & (Vvar__2___24Anonymous__46676 = Vvar__2___24Anonymous__46677) & (Vvar__1__ls__46674 = Vvar__1__ls__46675) & (Vvar__0__l__46672 = Vvar__0__l__46673))) <=> ![Vvar__0__l__46672: $i, Vvar__0__l__46673: $i, Vvar__1__ls__46674: $i, Vvar__1__ls__46675: $i, Vvar__2___24Anonymous__46676: $i, Vvar__2___24Anonymous__46677: $i, Vvar__3___24Anonymous__46678: $i, Vvar__3___24Anonymous__46679: $i] : ((~(cHList_2ehlist_2eHcons___24a4(Vvar__0__l__46672, Vvar__1__ls__46674, Vvar__2___24Anonymous__46676, Vvar__3___24Anonymous__46678) = cHList_2ehlist_2eHcons___24a4(Vvar__0__l__46673, Vvar__1__ls__46675, Vvar__2___24Anonymous__46677, Vvar__3___24Anonymous__46679))) | ((Vvar__3___24Anonymous__46678 = Vvar__3___24Anonymous__46679) & (Vvar__2___24Anonymous__46676 = Vvar__2___24Anonymous__46677) & (Vvar__1__ls__46674 = Vvar__1__ls__46675) & (Vvar__0__l__46672 = Vvar__0__l__46673)))),
% 3.24/3.44 inference(rewrite,[status(thm)],[])).
% 3.24/3.44 tff(30,plain,
% 3.24/3.44 (^[Vvar__0__l__46672: $i, Vvar__0__l__46673: $i, Vvar__1__ls__46674: $i, Vvar__1__ls__46675: $i, Vvar__2___24Anonymous__46676: $i, Vvar__2___24Anonymous__46677: $i, Vvar__3___24Anonymous__46678: $i, Vvar__3___24Anonymous__46679: $i] : trans(monotonicity(trans(monotonicity(rewrite((((Vvar__3___24Anonymous__46678 = Vvar__3___24Anonymous__46679) & (Vvar__2___24Anonymous__46676 = Vvar__2___24Anonymous__46677)) & (Vvar__1__ls__46674 = Vvar__1__ls__46675)) <=> ((Vvar__3___24Anonymous__46678 = Vvar__3___24Anonymous__46679) & (Vvar__2___24Anonymous__46676 = Vvar__2___24Anonymous__46677) & (Vvar__1__ls__46674 = Vvar__1__ls__46675))), (((((Vvar__3___24Anonymous__46678 = Vvar__3___24Anonymous__46679) & (Vvar__2___24Anonymous__46676 = Vvar__2___24Anonymous__46677)) & (Vvar__1__ls__46674 = Vvar__1__ls__46675)) & (Vvar__0__l__46672 = Vvar__0__l__46673)) <=> (((Vvar__3___24Anonymous__46678 = Vvar__3___24Anonymous__46679) & (Vvar__2___24Anonymous__46676 = Vvar__2___24Anonymous__46677) & (Vvar__1__ls__46674 = Vvar__1__ls__46675)) & (Vvar__0__l__46672 = Vvar__0__l__46673)))), rewrite((((Vvar__3___24Anonymous__46678 = Vvar__3___24Anonymous__46679) & (Vvar__2___24Anonymous__46676 = Vvar__2___24Anonymous__46677) & (Vvar__1__ls__46674 = Vvar__1__ls__46675)) & (Vvar__0__l__46672 = Vvar__0__l__46673)) <=> ((Vvar__3___24Anonymous__46678 = Vvar__3___24Anonymous__46679) & (Vvar__2___24Anonymous__46676 = Vvar__2___24Anonymous__46677) & (Vvar__1__ls__46674 = Vvar__1__ls__46675) & (Vvar__0__l__46672 = Vvar__0__l__46673))), (((((Vvar__3___24Anonymous__46678 = Vvar__3___24Anonymous__46679) & (Vvar__2___24Anonymous__46676 = Vvar__2___24Anonymous__46677)) & (Vvar__1__ls__46674 = Vvar__1__ls__46675)) & (Vvar__0__l__46672 = Vvar__0__l__46673)) <=> ((Vvar__3___24Anonymous__46678 = Vvar__3___24Anonymous__46679) & (Vvar__2___24Anonymous__46676 = Vvar__2___24Anonymous__46677) & (Vvar__1__ls__46674 = Vvar__1__ls__46675) & (Vvar__0__l__46672 = Vvar__0__l__46673)))), (((cHList_2ehlist_2eHcons___24a4(Vvar__0__l__46672, Vvar__1__ls__46674, Vvar__2___24Anonymous__46676, Vvar__3___24Anonymous__46678) = cHList_2ehlist_2eHcons___24a4(Vvar__0__l__46673, Vvar__1__ls__46675, Vvar__2___24Anonymous__46677, Vvar__3___24Anonymous__46679)) => ((((Vvar__3___24Anonymous__46678 = Vvar__3___24Anonymous__46679) & (Vvar__2___24Anonymous__46676 = Vvar__2___24Anonymous__46677)) & (Vvar__1__ls__46674 = Vvar__1__ls__46675)) & (Vvar__0__l__46672 = Vvar__0__l__46673))) <=> ((cHList_2ehlist_2eHcons___24a4(Vvar__0__l__46672, Vvar__1__ls__46674, Vvar__2___24Anonymous__46676, Vvar__3___24Anonymous__46678) = cHList_2ehlist_2eHcons___24a4(Vvar__0__l__46673, Vvar__1__ls__46675, Vvar__2___24Anonymous__46677, Vvar__3___24Anonymous__46679)) => ((Vvar__3___24Anonymous__46678 = Vvar__3___24Anonymous__46679) & (Vvar__2___24Anonymous__46676 = Vvar__2___24Anonymous__46677) & (Vvar__1__ls__46674 = Vvar__1__ls__46675) & (Vvar__0__l__46672 = Vvar__0__l__46673))))), rewrite(((cHList_2ehlist_2eHcons___24a4(Vvar__0__l__46672, Vvar__1__ls__46674, Vvar__2___24Anonymous__46676, Vvar__3___24Anonymous__46678) = cHList_2ehlist_2eHcons___24a4(Vvar__0__l__46673, Vvar__1__ls__46675, Vvar__2___24Anonymous__46677, Vvar__3___24Anonymous__46679)) => ((Vvar__3___24Anonymous__46678 = Vvar__3___24Anonymous__46679) & (Vvar__2___24Anonymous__46676 = Vvar__2___24Anonymous__46677) & (Vvar__1__ls__46674 = Vvar__1__ls__46675) & (Vvar__0__l__46672 = Vvar__0__l__46673))) <=> ((~(cHList_2ehlist_2eHcons___24a4(Vvar__0__l__46672, Vvar__1__ls__46674, Vvar__2___24Anonymous__46676, Vvar__3___24Anonymous__46678) = cHList_2ehlist_2eHcons___24a4(Vvar__0__l__46673, Vvar__1__ls__46675, Vvar__2___24Anonymous__46677, Vvar__3___24Anonymous__46679))) | ((Vvar__3___24Anonymous__46678 = Vvar__3___24Anonymous__46679) & (Vvar__2___24Anonymous__46676 = Vvar__2___24Anonymous__46677) & (Vvar__1__ls__46674 = Vvar__1__ls__46675) & (Vvar__0__l__46672 = Vvar__0__l__46673)))), (((cHList_2ehlist_2eHcons___24a4(Vvar__0__l__46672, Vvar__1__ls__46674, Vvar__2___24Anonymous__46676, Vvar__3___24Anonymous__46678) = cHList_2ehlist_2eHcons___24a4(Vvar__0__l__46673, Vvar__1__ls__46675, Vvar__2___24Anonymous__46677, Vvar__3___24Anonymous__46679)) => ((((Vvar__3___24Anonymous__46678 = Vvar__3___24Anonymous__46679) & (Vvar__2___24Anonymous__46676 = Vvar__2___24Anonymous__46677)) & (Vvar__1__ls__46674 = Vvar__1__ls__46675)) & (Vvar__0__l__46672 = Vvar__0__l__46673))) <=> ((~(cHList_2ehlist_2eHcons___24a4(Vvar__0__l__46672, Vvar__1__ls__46674, Vvar__2___24Anonymous__46676, Vvar__3___24Anonymous__46678) = cHList_2ehlist_2eHcons___24a4(Vvar__0__l__46673, Vvar__1__ls__46675, Vvar__2___24Anonymous__46677, Vvar__3___24Anonymous__46679))) | ((Vvar__3___24Anonymous__46678 = Vvar__3___24Anonymous__46679) & (Vvar__2___24Anonymous__46676 = Vvar__2___24Anonymous__46677) & (Vvar__1__ls__46674 = Vvar__1__ls__46675) & (Vvar__0__l__46672 = Vvar__0__l__46673)))))),
% 3.24/3.44 inference(bind,[status(th)],[])).
% 3.24/3.44 tff(31,plain,
% 3.24/3.44 (![Vvar__0__l__46672: $i, Vvar__0__l__46673: $i, Vvar__1__ls__46674: $i, Vvar__1__ls__46675: $i, Vvar__2___24Anonymous__46676: $i, Vvar__2___24Anonymous__46677: $i, Vvar__3___24Anonymous__46678: $i, Vvar__3___24Anonymous__46679: $i] : ((cHList_2ehlist_2eHcons___24a4(Vvar__0__l__46672, Vvar__1__ls__46674, Vvar__2___24Anonymous__46676, Vvar__3___24Anonymous__46678) = cHList_2ehlist_2eHcons___24a4(Vvar__0__l__46673, Vvar__1__ls__46675, Vvar__2___24Anonymous__46677, Vvar__3___24Anonymous__46679)) => ((((Vvar__3___24Anonymous__46678 = Vvar__3___24Anonymous__46679) & (Vvar__2___24Anonymous__46676 = Vvar__2___24Anonymous__46677)) & (Vvar__1__ls__46674 = Vvar__1__ls__46675)) & (Vvar__0__l__46672 = Vvar__0__l__46673))) <=> ![Vvar__0__l__46672: $i, Vvar__0__l__46673: $i, Vvar__1__ls__46674: $i, Vvar__1__ls__46675: $i, Vvar__2___24Anonymous__46676: $i, Vvar__2___24Anonymous__46677: $i, Vvar__3___24Anonymous__46678: $i, Vvar__3___24Anonymous__46679: $i] : ((~(cHList_2ehlist_2eHcons___24a4(Vvar__0__l__46672, Vvar__1__ls__46674, Vvar__2___24Anonymous__46676, Vvar__3___24Anonymous__46678) = cHList_2ehlist_2eHcons___24a4(Vvar__0__l__46673, Vvar__1__ls__46675, Vvar__2___24Anonymous__46677, Vvar__3___24Anonymous__46679))) | ((Vvar__3___24Anonymous__46678 = Vvar__3___24Anonymous__46679) & (Vvar__2___24Anonymous__46676 = Vvar__2___24Anonymous__46677) & (Vvar__1__ls__46674 = Vvar__1__ls__46675) & (Vvar__0__l__46672 = Vvar__0__l__46673)))),
% 3.24/3.44 inference(quant_intro,[status(thm)],[30])).
% 3.24/3.44 tff(32,axiom,(![Vvar__0__l__46672: $i, Vvar__0__l__46673: $i, Vvar__1__ls__46674: $i, Vvar__1__ls__46675: $i, Vvar__2___24Anonymous__46676: $i, Vvar__2___24Anonymous__46677: $i, Vvar__3___24Anonymous__46678: $i, Vvar__3___24Anonymous__46679: $i] : ((cHList_2ehlist_2eHcons___24a4(Vvar__0__l__46672, Vvar__1__ls__46674, Vvar__2___24Anonymous__46676, Vvar__3___24Anonymous__46678) = cHList_2ehlist_2eHcons___24a4(Vvar__0__l__46673, Vvar__1__ls__46675, Vvar__2___24Anonymous__46677, Vvar__3___24Anonymous__46679)) => ((((Vvar__3___24Anonymous__46678 = Vvar__3___24Anonymous__46679) & (Vvar__2___24Anonymous__46676 = Vvar__2___24Anonymous__46677)) & (Vvar__1__ls__46674 = Vvar__1__ls__46675)) & (Vvar__0__l__46672 = Vvar__0__l__46673)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''$_inj_HList.hlist.Hcons'')).
% 3.24/3.44 tff(33,plain,
% 3.24/3.44 (![Vvar__0__l__46672: $i, Vvar__0__l__46673: $i, Vvar__1__ls__46674: $i, Vvar__1__ls__46675: $i, Vvar__2___24Anonymous__46676: $i, Vvar__2___24Anonymous__46677: $i, Vvar__3___24Anonymous__46678: $i, Vvar__3___24Anonymous__46679: $i] : ((~(cHList_2ehlist_2eHcons___24a4(Vvar__0__l__46672, Vvar__1__ls__46674, Vvar__2___24Anonymous__46676, Vvar__3___24Anonymous__46678) = cHList_2ehlist_2eHcons___24a4(Vvar__0__l__46673, Vvar__1__ls__46675, Vvar__2___24Anonymous__46677, Vvar__3___24Anonymous__46679))) | ((Vvar__3___24Anonymous__46678 = Vvar__3___24Anonymous__46679) & (Vvar__2___24Anonymous__46676 = Vvar__2___24Anonymous__46677) & (Vvar__1__ls__46674 = Vvar__1__ls__46675) & (Vvar__0__l__46672 = Vvar__0__l__46673)))),
% 3.24/3.44 inference(modus_ponens,[status(thm)],[32, 31])).
% 3.24/3.44 tff(34,plain,
% 3.24/3.44 (![Vvar__0__l__46672: $i, Vvar__0__l__46673: $i, Vvar__1__ls__46674: $i, Vvar__1__ls__46675: $i, Vvar__2___24Anonymous__46676: $i, Vvar__2___24Anonymous__46677: $i, Vvar__3___24Anonymous__46678: $i, Vvar__3___24Anonymous__46679: $i] : ((~(cHList_2ehlist_2eHcons___24a4(Vvar__0__l__46672, Vvar__1__ls__46674, Vvar__2___24Anonymous__46676, Vvar__3___24Anonymous__46678) = cHList_2ehlist_2eHcons___24a4(Vvar__0__l__46673, Vvar__1__ls__46675, Vvar__2___24Anonymous__46677, Vvar__3___24Anonymous__46679))) | ((Vvar__3___24Anonymous__46678 = Vvar__3___24Anonymous__46679) & (Vvar__2___24Anonymous__46676 = Vvar__2___24Anonymous__46677) & (Vvar__1__ls__46674 = Vvar__1__ls__46675) & (Vvar__0__l__46672 = Vvar__0__l__46673)))),
% 3.24/3.44 inference(modus_ponens,[status(thm)],[33, 29])).
% 3.24/3.44 tff(35,plain,(
% 3.24/3.44 ![Vvar__0__l__46672: $i, Vvar__0__l__46673: $i, Vvar__1__ls__46674: $i, Vvar__1__ls__46675: $i, Vvar__2___24Anonymous__46676: $i, Vvar__2___24Anonymous__46677: $i, Vvar__3___24Anonymous__46678: $i, Vvar__3___24Anonymous__46679: $i] : ((~(cHList_2ehlist_2eHcons___24a4(Vvar__0__l__46672, Vvar__1__ls__46674, Vvar__2___24Anonymous__46676, Vvar__3___24Anonymous__46678) = cHList_2ehlist_2eHcons___24a4(Vvar__0__l__46673, Vvar__1__ls__46675, Vvar__2___24Anonymous__46677, Vvar__3___24Anonymous__46679))) | ((Vvar__3___24Anonymous__46678 = Vvar__3___24Anonymous__46679) & (Vvar__2___24Anonymous__46676 = Vvar__2___24Anonymous__46677) & (Vvar__1__ls__46674 = Vvar__1__ls__46675) & (Vvar__0__l__46672 = Vvar__0__l__46673)))),
% 3.24/3.44 inference(skolemize,[status(sab)],[34])).
% 3.24/3.44 tff(36,plain,
% 3.24/3.44 (![Vvar__0__l__46672: $i, Vvar__0__l__46673: $i, Vvar__1__ls__46674: $i, Vvar__1__ls__46675: $i, Vvar__2___24Anonymous__46676: $i, Vvar__2___24Anonymous__46677: $i, Vvar__3___24Anonymous__46678: $i, Vvar__3___24Anonymous__46679: $i] : ((~(cHList_2ehlist_2eHcons___24a4(Vvar__0__l__46672, Vvar__1__ls__46674, Vvar__2___24Anonymous__46676, Vvar__3___24Anonymous__46678) = cHList_2ehlist_2eHcons___24a4(Vvar__0__l__46673, Vvar__1__ls__46675, Vvar__2___24Anonymous__46677, Vvar__3___24Anonymous__46679))) | (~((~(Vvar__3___24Anonymous__46678 = Vvar__3___24Anonymous__46679)) | (~(Vvar__2___24Anonymous__46676 = Vvar__2___24Anonymous__46677)) | (~(Vvar__1__ls__46674 = Vvar__1__ls__46675)) | (~(Vvar__0__l__46672 = Vvar__0__l__46673)))))),
% 3.24/3.44 inference(modus_ponens,[status(thm)],[35, 28])).
% 3.24/3.44 tff(37,plain,
% 3.24/3.44 (![Vvar__0__l__46672: $i, Vvar__0__l__46673: $i, Vvar__1__ls__46674: $i, Vvar__1__ls__46675: $i, Vvar__2___24Anonymous__46676: $i, Vvar__2___24Anonymous__46677: $i, Vvar__3___24Anonymous__46678: $i, Vvar__3___24Anonymous__46679: $i] : ((~(cHList_2ehlist_2eHcons___24a4(Vvar__0__l__46672, Vvar__1__ls__46674, Vvar__2___24Anonymous__46676, Vvar__3___24Anonymous__46678) = cHList_2ehlist_2eHcons___24a4(Vvar__0__l__46673, Vvar__1__ls__46675, Vvar__2___24Anonymous__46677, Vvar__3___24Anonymous__46679))) | (~((~(Vvar__3___24Anonymous__46678 = Vvar__3___24Anonymous__46679)) | (~(Vvar__2___24Anonymous__46676 = Vvar__2___24Anonymous__46677)) | (~(Vvar__1__ls__46674 = Vvar__1__ls__46675)) | (~(Vvar__0__l__46672 = Vvar__0__l__46673)))))),
% 3.24/3.44 inference(modus_ponens,[status(thm)],[36, 26])).
% 3.24/3.44 tff(38,plain,
% 3.24/3.44 (((~![Vvar__0__l__46672: $i, Vvar__0__l__46673: $i, Vvar__1__ls__46674: $i, Vvar__1__ls__46675: $i, Vvar__2___24Anonymous__46676: $i, Vvar__2___24Anonymous__46677: $i, Vvar__3___24Anonymous__46678: $i, Vvar__3___24Anonymous__46679: $i] : ((~(cHList_2ehlist_2eHcons___24a4(Vvar__0__l__46672, Vvar__1__ls__46674, Vvar__2___24Anonymous__46676, Vvar__3___24Anonymous__46678) = cHList_2ehlist_2eHcons___24a4(Vvar__0__l__46673, Vvar__1__ls__46675, Vvar__2___24Anonymous__46677, Vvar__3___24Anonymous__46679))) | (~((~(Vvar__3___24Anonymous__46678 = Vvar__3___24Anonymous__46679)) | (~(Vvar__2___24Anonymous__46676 = Vvar__2___24Anonymous__46677)) | (~(Vvar__1__ls__46674 = Vvar__1__ls__46675)) | (~(Vvar__0__l__46672 = Vvar__0__l__46673)))))) | ((~(cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V2__a!2066, V3__b!2067) = cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V4__c!2068, V5__d!2069))) | (~((~(V2__a!2066 = V4__c!2068)) | (~(V3__b!2067 = V5__d!2069)))))) <=> ((~![Vvar__0__l__46672: $i, Vvar__0__l__46673: $i, Vvar__1__ls__46674: $i, Vvar__1__ls__46675: $i, Vvar__2___24Anonymous__46676: $i, Vvar__2___24Anonymous__46677: $i, Vvar__3___24Anonymous__46678: $i, Vvar__3___24Anonymous__46679: $i] : ((~(cHList_2ehlist_2eHcons___24a4(Vvar__0__l__46672, Vvar__1__ls__46674, Vvar__2___24Anonymous__46676, Vvar__3___24Anonymous__46678) = cHList_2ehlist_2eHcons___24a4(Vvar__0__l__46673, Vvar__1__ls__46675, Vvar__2___24Anonymous__46677, Vvar__3___24Anonymous__46679))) | (~((~(Vvar__3___24Anonymous__46678 = Vvar__3___24Anonymous__46679)) | (~(Vvar__2___24Anonymous__46676 = Vvar__2___24Anonymous__46677)) | (~(Vvar__1__ls__46674 = Vvar__1__ls__46675)) | (~(Vvar__0__l__46672 = Vvar__0__l__46673)))))) | (~(cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V2__a!2066, V3__b!2067) = cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V4__c!2068, V5__d!2069))) | (~((~(V2__a!2066 = V4__c!2068)) | (~(V3__b!2067 = V5__d!2069)))))),
% 3.24/3.44 inference(rewrite,[status(thm)],[])).
% 3.24/3.44 tff(39,plain,
% 3.24/3.44 (((~(cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V2__a!2066, V3__b!2067) = cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V4__c!2068, V5__d!2069))) | (~((~(V3__b!2067 = V5__d!2069)) | (~(V2__a!2066 = V4__c!2068)) | (~(V1__ls!2065 = V1__ls!2065)) | (~(V0__l!2064 = V0__l!2064))))) <=> ((~(cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V2__a!2066, V3__b!2067) = cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V4__c!2068, V5__d!2069))) | (~((~(V2__a!2066 = V4__c!2068)) | (~(V3__b!2067 = V5__d!2069)))))),
% 3.24/3.44 inference(rewrite,[status(thm)],[])).
% 3.24/3.44 tff(40,plain,
% 3.24/3.44 (((~![Vvar__0__l__46672: $i, Vvar__0__l__46673: $i, Vvar__1__ls__46674: $i, Vvar__1__ls__46675: $i, Vvar__2___24Anonymous__46676: $i, Vvar__2___24Anonymous__46677: $i, Vvar__3___24Anonymous__46678: $i, Vvar__3___24Anonymous__46679: $i] : ((~(cHList_2ehlist_2eHcons___24a4(Vvar__0__l__46672, Vvar__1__ls__46674, Vvar__2___24Anonymous__46676, Vvar__3___24Anonymous__46678) = cHList_2ehlist_2eHcons___24a4(Vvar__0__l__46673, Vvar__1__ls__46675, Vvar__2___24Anonymous__46677, Vvar__3___24Anonymous__46679))) | (~((~(Vvar__3___24Anonymous__46678 = Vvar__3___24Anonymous__46679)) | (~(Vvar__2___24Anonymous__46676 = Vvar__2___24Anonymous__46677)) | (~(Vvar__1__ls__46674 = Vvar__1__ls__46675)) | (~(Vvar__0__l__46672 = Vvar__0__l__46673)))))) | ((~(cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V2__a!2066, V3__b!2067) = cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V4__c!2068, V5__d!2069))) | (~((~(V3__b!2067 = V5__d!2069)) | (~(V2__a!2066 = V4__c!2068)) | (~(V1__ls!2065 = V1__ls!2065)) | (~(V0__l!2064 = V0__l!2064)))))) <=> ((~![Vvar__0__l__46672: $i, Vvar__0__l__46673: $i, Vvar__1__ls__46674: $i, Vvar__1__ls__46675: $i, Vvar__2___24Anonymous__46676: $i, Vvar__2___24Anonymous__46677: $i, Vvar__3___24Anonymous__46678: $i, Vvar__3___24Anonymous__46679: $i] : ((~(cHList_2ehlist_2eHcons___24a4(Vvar__0__l__46672, Vvar__1__ls__46674, Vvar__2___24Anonymous__46676, Vvar__3___24Anonymous__46678) = cHList_2ehlist_2eHcons___24a4(Vvar__0__l__46673, Vvar__1__ls__46675, Vvar__2___24Anonymous__46677, Vvar__3___24Anonymous__46679))) | (~((~(Vvar__3___24Anonymous__46678 = Vvar__3___24Anonymous__46679)) | (~(Vvar__2___24Anonymous__46676 = Vvar__2___24Anonymous__46677)) | (~(Vvar__1__ls__46674 = Vvar__1__ls__46675)) | (~(Vvar__0__l__46672 = Vvar__0__l__46673)))))) | ((~(cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V2__a!2066, V3__b!2067) = cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V4__c!2068, V5__d!2069))) | (~((~(V2__a!2066 = V4__c!2068)) | (~(V3__b!2067 = V5__d!2069))))))),
% 3.24/3.44 inference(monotonicity,[status(thm)],[39])).
% 3.24/3.44 tff(41,plain,
% 3.24/3.44 (((~![Vvar__0__l__46672: $i, Vvar__0__l__46673: $i, Vvar__1__ls__46674: $i, Vvar__1__ls__46675: $i, Vvar__2___24Anonymous__46676: $i, Vvar__2___24Anonymous__46677: $i, Vvar__3___24Anonymous__46678: $i, Vvar__3___24Anonymous__46679: $i] : ((~(cHList_2ehlist_2eHcons___24a4(Vvar__0__l__46672, Vvar__1__ls__46674, Vvar__2___24Anonymous__46676, Vvar__3___24Anonymous__46678) = cHList_2ehlist_2eHcons___24a4(Vvar__0__l__46673, Vvar__1__ls__46675, Vvar__2___24Anonymous__46677, Vvar__3___24Anonymous__46679))) | (~((~(Vvar__3___24Anonymous__46678 = Vvar__3___24Anonymous__46679)) | (~(Vvar__2___24Anonymous__46676 = Vvar__2___24Anonymous__46677)) | (~(Vvar__1__ls__46674 = Vvar__1__ls__46675)) | (~(Vvar__0__l__46672 = Vvar__0__l__46673)))))) | ((~(cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V2__a!2066, V3__b!2067) = cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V4__c!2068, V5__d!2069))) | (~((~(V3__b!2067 = V5__d!2069)) | (~(V2__a!2066 = V4__c!2068)) | (~(V1__ls!2065 = V1__ls!2065)) | (~(V0__l!2064 = V0__l!2064)))))) <=> ((~![Vvar__0__l__46672: $i, Vvar__0__l__46673: $i, Vvar__1__ls__46674: $i, Vvar__1__ls__46675: $i, Vvar__2___24Anonymous__46676: $i, Vvar__2___24Anonymous__46677: $i, Vvar__3___24Anonymous__46678: $i, Vvar__3___24Anonymous__46679: $i] : ((~(cHList_2ehlist_2eHcons___24a4(Vvar__0__l__46672, Vvar__1__ls__46674, Vvar__2___24Anonymous__46676, Vvar__3___24Anonymous__46678) = cHList_2ehlist_2eHcons___24a4(Vvar__0__l__46673, Vvar__1__ls__46675, Vvar__2___24Anonymous__46677, Vvar__3___24Anonymous__46679))) | (~((~(Vvar__3___24Anonymous__46678 = Vvar__3___24Anonymous__46679)) | (~(Vvar__2___24Anonymous__46676 = Vvar__2___24Anonymous__46677)) | (~(Vvar__1__ls__46674 = Vvar__1__ls__46675)) | (~(Vvar__0__l__46672 = Vvar__0__l__46673)))))) | (~(cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V2__a!2066, V3__b!2067) = cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V4__c!2068, V5__d!2069))) | (~((~(V2__a!2066 = V4__c!2068)) | (~(V3__b!2067 = V5__d!2069)))))),
% 3.24/3.44 inference(transitivity,[status(thm)],[40, 38])).
% 3.45/3.63 tff(42,plain,
% 3.45/3.63 ((~![Vvar__0__l__46672: $i, Vvar__0__l__46673: $i, Vvar__1__ls__46674: $i, Vvar__1__ls__46675: $i, Vvar__2___24Anonymous__46676: $i, Vvar__2___24Anonymous__46677: $i, Vvar__3___24Anonymous__46678: $i, Vvar__3___24Anonymous__46679: $i] : ((~(cHList_2ehlist_2eHcons___24a4(Vvar__0__l__46672, Vvar__1__ls__46674, Vvar__2___24Anonymous__46676, Vvar__3___24Anonymous__46678) = cHList_2ehlist_2eHcons___24a4(Vvar__0__l__46673, Vvar__1__ls__46675, Vvar__2___24Anonymous__46677, Vvar__3___24Anonymous__46679))) | (~((~(Vvar__3___24Anonymous__46678 = Vvar__3___24Anonymous__46679)) | (~(Vvar__2___24Anonymous__46676 = Vvar__2___24Anonymous__46677)) | (~(Vvar__1__ls__46674 = Vvar__1__ls__46675)) | (~(Vvar__0__l__46672 = Vvar__0__l__46673)))))) | ((~(cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V2__a!2066, V3__b!2067) = cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V4__c!2068, V5__d!2069))) | (~((~(V3__b!2067 = V5__d!2069)) | (~(V2__a!2066 = V4__c!2068)) | (~(V1__ls!2065 = V1__ls!2065)) | (~(V0__l!2064 = V0__l!2064)))))),
% 3.45/3.63 inference(quant_inst,[status(thm)],[])).
% 3.45/3.63 tff(43,plain,
% 3.45/3.63 ((~![Vvar__0__l__46672: $i, Vvar__0__l__46673: $i, Vvar__1__ls__46674: $i, Vvar__1__ls__46675: $i, Vvar__2___24Anonymous__46676: $i, Vvar__2___24Anonymous__46677: $i, Vvar__3___24Anonymous__46678: $i, Vvar__3___24Anonymous__46679: $i] : ((~(cHList_2ehlist_2eHcons___24a4(Vvar__0__l__46672, Vvar__1__ls__46674, Vvar__2___24Anonymous__46676, Vvar__3___24Anonymous__46678) = cHList_2ehlist_2eHcons___24a4(Vvar__0__l__46673, Vvar__1__ls__46675, Vvar__2___24Anonymous__46677, Vvar__3___24Anonymous__46679))) | (~((~(Vvar__3___24Anonymous__46678 = Vvar__3___24Anonymous__46679)) | (~(Vvar__2___24Anonymous__46676 = Vvar__2___24Anonymous__46677)) | (~(Vvar__1__ls__46674 = Vvar__1__ls__46675)) | (~(Vvar__0__l__46672 = Vvar__0__l__46673)))))) | (~(cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V2__a!2066, V3__b!2067) = cHList_2ehlist_2eHcons___24a4(V0__l!2064, V1__ls!2065, V4__c!2068, V5__d!2069))) | (~((~(V2__a!2066 = V4__c!2068)) | (~(V3__b!2067 = V5__d!2069))))),
% 3.45/3.63 inference(modus_ponens,[status(thm)],[42, 41])).
% 3.45/3.63 tff(44,plain,
% 3.45/3.63 (~((~(V2__a!2066 = V4__c!2068)) | (~(V3__b!2067 = V5__d!2069)))),
% 3.45/3.63 inference(unit_resolution,[status(thm)],[43, 37, 24])).
% 3.45/3.63 tff(45,plain,
% 3.45/3.63 (((~(V2__a!2066 = V4__c!2068)) | (~(V3__b!2067 = V5__d!2069))) | (V2__a!2066 = V4__c!2068)),
% 3.45/3.63 inference(tautology,[status(thm)],[])).
% 3.45/3.63 tff(46,plain,
% 3.45/3.63 (V2__a!2066 = V4__c!2068),
% 3.45/3.63 inference(unit_resolution,[status(thm)],[45, 44])).
% 3.45/3.63 tff(47,plain,
% 3.45/3.63 (((~(V2__a!2066 = V4__c!2068)) | (~(V3__b!2067 = V5__d!2069))) | (V3__b!2067 = V5__d!2069)),
% 3.45/3.63 inference(tautology,[status(thm)],[])).
% 3.45/3.63 tff(48,plain,
% 3.45/3.63 (V3__b!2067 = V5__d!2069),
% 3.45/3.63 inference(unit_resolution,[status(thm)],[47, 44])).
% 3.45/3.63 tff(49,plain,
% 3.45/3.63 ((~(~((~(V2__a!2066 = V4__c!2068)) | (~(V3__b!2067 = V5__d!2069))))) <=> ((~(V2__a!2066 = V4__c!2068)) | (~(V3__b!2067 = V5__d!2069)))),
% 3.45/3.63 inference(rewrite,[status(thm)],[])).
% 3.45/3.63 tff(50,plain,
% 3.45/3.63 (((V2__a!2066 = V4__c!2068) & (V3__b!2067 = V5__d!2069)) <=> (~((~(V2__a!2066 = V4__c!2068)) | (~(V3__b!2067 = V5__d!2069))))),
% 3.45/3.63 inference(rewrite,[status(thm)],[])).
% 3.45/3.63 tff(51,plain,
% 3.45/3.63 ((~((V2__a!2066 = V4__c!2068) & (V3__b!2067 = V5__d!2069))) <=> (~(~((~(V2__a!2066 = V4__c!2068)) | (~(V3__b!2067 = V5__d!2069)))))),
% 3.45/3.63 inference(monotonicity,[status(thm)],[50])).
% 3.45/3.63 tff(52,plain,
% 3.45/3.63 ((~((V2__a!2066 = V4__c!2068) & (V3__b!2067 = V5__d!2069))) <=> ((~(V2__a!2066 = V4__c!2068)) | (~(V3__b!2067 = V5__d!2069)))),
% 3.45/3.63 inference(transitivity,[status(thm)],[51, 49])).
% 3.45/3.63 tff(53,plain,
% 3.45/3.63 (~((V2__a!2066 = V4__c!2068) & (V3__b!2067 = V5__d!2069))),
% 3.45/3.63 inference(or_elim,[status(thm)],[23])).
% 3.45/3.63 tff(54,plain,
% 3.45/3.63 ((~(V2__a!2066 = V4__c!2068)) | (~(V3__b!2067 = V5__d!2069))),
% 3.45/3.63 inference(modus_ponens,[status(thm)],[53, 52])).
% 3.45/3.63 tff(55,plain,
% 3.45/3.63 ($false),
% 3.45/3.63 inference(unit_resolution,[status(thm)],[54, 48, 46])).
% 3.45/3.63 % SZS output end Proof
% 3.45/3.64 % E exiting
%------------------------------------------------------------------------------