%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP019^3 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:07:51 AM UTC 2026
% Result : Theorem 0.22s 0.30s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP019^3 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 % Computer : n019.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 19:33:18 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.24 Running higher-order theorem proving
% 0.10/0.25 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.30 % (1244756)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.30 % (1244766)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1524343211:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.30 % (1244766) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1244756-1244766"...
% 0.22/0.30 % (1244766)...printing done.
% 0.22/0.30 % (1244763)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3026530692:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.30 % (1244767)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.30 % (1244761)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2066657109:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.30 % (1244767)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.22/0.30 % (1244762)lrs+10_16_si=on:nwc=1.5:random_seed=973825089:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.30 % (1244766)Refutation found. Thanks to Tanya!
% 0.22/0.30 % SZS status Theorem for theBenchmark
% 0.22/0.30 % SZS output start Proof for theBenchmark
% 0.22/0.30 thf(type_def_5, type, tyop_2Emin_2Ebool: $tType).
% 0.22/0.30 thf(type_def_6, type, tyop_2Emin_2Efun: ($tType * $tType) > $tType).
% 0.22/0.30 thf(type_def_7, type, tyop_2Enum_2Enum: $tType).
% 0.22/0.30 thf(type_def_8, type, tyop_2Epair_2Eprod: ($tType * $tType) > $tType).
% 0.22/0.30 thf(type_def_9, type, tyop_2Erealax_2Ereal: $tType).
% 0.22/0.30 thf(type_def_10, type, sTfun: ($tType * $tType) > $tType).
% 0.22/0.30 thf(func_def_0, type, c_2Ebool_2E_21: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.22/0.30 thf(func_def_1, type, c_2Ebool_2E_2F_5C: ($o > $o > $o)).
% 0.22/0.30 thf(func_def_2, type, c_2Enum_2E0: tyop_2Enum_2Enum).
% 0.22/0.30 thf(func_def_3, type, c_2Emin_2E_3D: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.22/0.30 thf(func_def_4, type, c_2Emin_2E_3D_3D_3E: ($o > $o > $o)).
% 0.22/0.30 thf(func_def_5, type, c_2Ebool_2E_3F: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.22/0.30 thf(func_def_6, type, c_2Ebool_2EF: $o).
% 0.22/0.30 thf(func_def_7, type, c_2Ebool_2ET: $o).
% 0.22/0.30 thf(func_def_8, type, c_2Ebool_2E_5C_2F: ($o > $o > $o)).
% 0.22/0.30 thf(func_def_9, type, c_2Ecomplex_2Ecomplex__inv: (tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal > tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal)).
% 0.22/0.30 thf(func_def_10, type, c_2Ecomplex_2Ecomplex__of__num: (tyop_2Enum_2Enum > tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal)).
% 0.22/0.30 thf(func_def_11, type, c_2Ebool_2E_7E: ($o > $o)).
% 0.22/0.30 thf(func_def_13, type, vNOT: ($o > $o)).
% 0.22/0.30 thf(func_def_16, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.22/0.30 thf(func_def_17, type, sK0: tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal).
% 0.22/0.30 thf(func_def_18, type, sK1: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.22/0.30 thf(func_def_19, type, sK2: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.22/0.30 thf(f11,axiom,(
% 0.22/0.30 ! [X0 : tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal] : ((X0 = ((c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0))) <=> (((c_2Ecomplex_2Ecomplex__inv @ X0)) = ((c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0))))),
% 0.22/0.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__INV__EQ__0)).
% 0.22/0.30 thf(f12,conjecture,(
% 0.22/0.30 ! [X0 : tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal] : ((~ (X0 = ((c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0)))) => (~ (((c_2Ecomplex_2Ecomplex__inv @ X0)) = ((c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0)))))),
% 0.22/0.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__INV__NZ)).
% 0.22/0.30 thf(f13,negated_conjecture,(
% 0.22/0.30 ~ ! [X0 : tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal] : ((~ (X0 = ((c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0)))) => (~ (((c_2Ecomplex_2Ecomplex__inv @ X0)) = ((c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0)))))),
% 0.22/0.30 inference(negated_conjecture,[status(cth)],[f12])).
% 0.22/0.30 thf(f26,plain,(
% 0.22/0.30 ~ ! [X0 : tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal] : ((~ (X0 = ((c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0)))) => (~ (((c_2Ecomplex_2Ecomplex__inv @ X0)) = ((c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0)))))),
% 0.22/0.30 inference(rectify,[],[f13])).
% 0.22/0.30 thf(f27,plain,(
% 0.22/0.30 ~ ! [X0 : tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal] : (($true = ((~ ((c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0) = X0)))) => ($true = ((~ ((c_2Ecomplex_2Ecomplex__inv @ X0) = (c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0))))))),
% 0.22/0.30 inference(fool_elimination,[],[f26])).
% 0.22/0.30 thf(f39,plain,(
% 0.22/0.30 ? [X0 : tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal] : (($true != ((~ ((c_2Ecomplex_2Ecomplex__inv @ X0) = (c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0))))) & ($true = ((~ ((c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0) = X0)))))),
% 0.22/0.30 inference(ennf_transformation,[],[f27])).
% 0.22/0.30 thf(f42,plain,(
% 0.22/0.30 ($true != ((~ ((c_2Ecomplex_2Ecomplex__inv @ sK0) = (c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0))))) & ($true = ((~ ((c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0) = sK0))))),
% 0.22/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f39])).
% 0.22/0.30 thf(f56,plain,(
% 0.22/0.30 ! [X0 : tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal] : (((X0 = ((c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0))) | (((c_2Ecomplex_2Ecomplex__inv @ X0)) != ((c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0)))) & ((((c_2Ecomplex_2Ecomplex__inv @ X0)) = ((c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0))) | (((c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0)) != X0)))),
% 0.22/0.30 inference(nnf_transformation,[],[f11])).
% 0.22/0.30 thf(f75,plain,(
% 0.22/0.30 ($true = ((~ ((c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0) = sK0))))),
% 0.22/0.30 inference(cnf_transformation,[],[f42])).
% 0.22/0.30 thf(f76,plain,(
% 0.22/0.30 ($true != ((~ ((c_2Ecomplex_2Ecomplex__inv @ sK0) = (c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0)))))),
% 0.22/0.30 inference(cnf_transformation,[],[f42])).
% 0.22/0.30 thf(f92,plain,(
% 0.22/0.30 ( ! [X0 : tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal] : ((((c_2Ecomplex_2Ecomplex__inv @ X0)) != ((c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0))) | (((c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0)) = X0)) )),
% 0.22/0.30 inference(cnf_transformation,[],[f56])).
% 0.22/0.30 thf(f126,plain,(
% 0.22/0.30 ($true = (((c_2Ecomplex_2Ecomplex__inv @ sK0) = (c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0))))),
% 0.22/0.30 inference(not_proxy_clausification,[],[f76])).
% 0.22/0.30 thf(f127,plain,(
% 0.22/0.30 (((c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0)) = ((c_2Ecomplex_2Ecomplex__inv @ sK0)))),
% 0.22/0.30 inference(equality_proxy_clausification,[],[f126])).
% 0.22/0.30 thf(f128,plain,(
% 0.22/0.30 ((((c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0) = sK0)) = $false)),
% 0.22/0.30 inference(not_proxy_clausification,[],[f75])).
% 0.22/0.30 thf(f129,plain,(
% 0.22/0.30 (((c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0)) != sK0)),
% 0.22/0.30 inference(equality_proxy_clausification,[],[f128])).
% 0.22/0.30 thf(f149,plain,(
% 0.22/0.30 (((c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0)) = sK0) | (((c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0)) != ((c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0)))),
% 0.22/0.30 inference(constrained_superposition,[],[f92,f127])).
% 0.22/0.30 thf(f150,plain,(
% 0.22/0.30 (((c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0)) = sK0)),
% 0.22/0.30 inference(trivial_inequality_removal,[],[f149])).
% 0.22/0.30 thf(f151,plain,(
% 0.22/0.30 $false),
% 0.22/0.30 inference(forward_subsumption_resolution,[],[f150,f129])).
% 0.22/0.30 % SZS output end Proof for theBenchmark
% 0.22/0.30 % (1244766)------------------------------
% 0.22/0.30 % (1244766)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.30 % (1244766)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.30 % (1244766)CaDiCaL version: 2.1.3
% 0.22/0.30 % (1244766)Termination reason: Refutation
% 0.22/0.30 % (1244766)Time elapsed: 0.002 s
% 0.22/0.30 % (1244766)Peak memory usage: 12 MB
% 0.22/0.30 % (1244766)Instructions burned: 5 (million)
% 0.22/0.30 % (1244756)Success in time 0.038 s
% 0.22/0.30 % Vampire exiting
%------------------------------------------------------------------------------