%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP010^1 : 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 : n003.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 08:07:42 AM UTC 2026
% Result : Theorem 0.33s 0.45s
% Output : Refutation 0.33s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ITP010^1 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.28 % Computer : n003.cluster.edu
% 0.11/0.28 % Model : x86_64 x86_64
% 0.11/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.28 % Memory : 8046.5625MB
% 0.11/0.28 % OS : Linux 6.8.0-71-generic
% 0.11/0.28 % CPULimit : 300
% 0.11/0.28 % WCLimit : 300
% 0.11/0.28 % DateTime : Tue Sep 29 19:27:14 UTC 2026
% 0.11/0.28 % CPUTime :
% 0.11/0.28 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.27/0.34 Running higher-order theorem proving
% 0.27/0.37 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
% 0.33/0.45 % (2947703)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.33/0.45 % (2947711)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=3157711872:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.33/0.45 % (2947714)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.33/0.45 % (2947714)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
% 0.33/0.45 % (2947710)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2663264540:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.33/0.45 % (2947708)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3821686228:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.33/0.45 % (2947709)lrs+10_16_si=on:nwc=1.5:random_seed=791367380:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.33/0.45 % (2947711) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2947703-2947711"...
% 0.33/0.45 % (2947712)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2140204690:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.33/0.45 % (2947714)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=34414362:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.33/0.45 % (2947713)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1791574246:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.33/0.45 % (2947711)...printing done.
% 0.33/0.45 % (2947710)Instruction limit reached!
% 0.33/0.45 % (2947710)------------------------------
% 0.33/0.45 % (2947710)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.33/0.45 % (2947710)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.33/0.45 % (2947710)CaDiCaL version: 2.1.3
% 0.33/0.45 % (2947710)Termination reason: Instruction limit
% 0.33/0.45 % (2947710)Termination phase: shuffling
% 0.33/0.45 % (2947710)Time elapsed: 0.003 s
% 0.33/0.45 % (2947710)Peak memory usage: 9 MB
% 0.33/0.45 % (2947710)Instructions burned: 4 (million)
% 0.33/0.45 % (2947711)Refutation found. Thanks to Tanya!
% 0.33/0.45 % SZS status Theorem for theBenchmark
% 0.33/0.45 % SZS output start Proof for theBenchmark
% 0.33/0.45 thf(type_def_5, type, u: $tType).
% 0.33/0.45 thf(type_def_6, type, d: $tType).
% 0.33/0.45 thf(type_def_7, type, du: $tType).
% 0.33/0.45 thf(type_def_8, type, sTfun: ($tType * $tType) > $tType).
% 0.33/0.45 thf(func_def_0, type, tyop_2Emin_2Ebool: d).
% 0.33/0.45 thf(func_def_1, type, tyop_2Emin_2Efun: (d > d > d)).
% 0.33/0.45 thf(func_def_2, type, s: (d > u > du)).
% 0.33/0.45 thf(func_def_3, type, app_2E2: (du > du > u)).
% 0.33/0.45 thf(func_def_4, type, combin_i_2E0: u).
% 0.33/0.45 thf(func_def_5, type, combin_k_2E0: u).
% 0.33/0.45 thf(func_def_6, type, combin_s_2E0: u).
% 0.33/0.45 thf(func_def_7, type, c_2Ebool_2E_21_2E0: u).
% 0.33/0.45 thf(func_def_8, type, c_2Ebool_2E_21_2E1: (du > u)).
% 0.33/0.45 thf(func_def_9, type, c_2Ebool_2E_2F_5C_2E0: u).
% 0.33/0.45 thf(func_def_10, type, c_2Ebool_2E_2F_5C_2E2: (du > du > u)).
% 0.33/0.45 thf(func_def_11, type, c_2Emin_2E_3D_2E0: u).
% 0.33/0.45 thf(func_def_12, type, c_2Emin_2E_3D_2E2: (du > du > u)).
% 0.33/0.45 thf(func_def_13, type, c_2Emin_2E_3D_3D_3E_2E0: u).
% 0.33/0.45 thf(func_def_14, type, c_2Emin_2E_3D_3D_3E_2E2: (du > du > u)).
% 0.33/0.45 thf(func_def_15, type, c_2Ebool_2E_3F_2E0: u).
% 0.33/0.45 thf(func_def_16, type, c_2Ebool_2E_3F_2E1: (du > u)).
% 0.33/0.45 thf(func_def_17, type, c_2Ebool_2EF_2E0: u).
% 0.33/0.45 thf(func_def_18, type, c_2Ebool_2ET_2E0: u).
% 0.33/0.45 thf(func_def_19, type, c_2Ebool_2E_5C_2F_2E0: u).
% 0.33/0.45 thf(func_def_20, type, c_2Ebool_2E_5C_2F_2E2: (du > du > u)).
% 0.33/0.45 thf(func_def_21, type, c_2Ecardinal_2Ecardleq_2E0: u).
% 0.33/0.45 thf(func_def_22, type, c_2Ecardinal_2Ecardleq_2E2: (du > du > u)).
% 0.33/0.45 thf(func_def_23, type, c_2Ebool_2E_7E_2E0: u).
% 0.33/0.45 thf(func_def_24, type, c_2Ebool_2E_7E_2E1: (du > u)).
% 0.33/0.45 thf(func_def_25, type, mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: (($o > $o) > $o > $o)).
% 0.33/0.45 thf(func_def_26, type, mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: (($o > $o > $o) > $o > $o > $o)).
% 0.33/0.45 thf(func_def_27, type, mono_2Ec_2Ebool_2E_2F_5C: ($o > $o > $o)).
% 0.33/0.45 thf(func_def_28, type, mono_2Ec_2Emin_2E_3D_3D_3E: ($o > $o > $o)).
% 0.33/0.45 thf(func_def_29, type, mono_2Ec_2Ebool_2EF: $o).
% 0.33/0.45 thf(func_def_30, type, mono_2Ec_2Ebool_2ET: $o).
% 0.33/0.45 thf(func_def_31, type, mono_2Ec_2Ebool_2E_5C_2F: ($o > $o > $o)).
% 0.33/0.45 thf(func_def_32, type, mono_2Ec_2Ebool_2E_7E: ($o > $o)).
% 0.33/0.45 thf(func_def_33, type, i_mono_2Etyop_2Emin_2Ebool: ($o > u)).
% 0.33/0.45 thf(func_def_34, type, i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: (($o > $o) > u)).
% 0.33/0.45 thf(func_def_35, type, i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: (($o > $o > $o) > u)).
% 0.33/0.45 thf(func_def_36, type, j_mono_2Etyop_2Emin_2Ebool: (du > $o)).
% 0.33/0.45 thf(func_def_37, type, j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: (du > $o > $o)).
% 0.33/0.45 thf(func_def_38, type, j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: (du > $o > $o > $o)).
% 0.33/0.45 thf(func_def_40, type, vNOT: ($o > $o)).
% 0.33/0.45 thf(func_def_43, type, vOR: ($o > $o > $o)).
% 0.33/0.45 thf(func_def_44, type, sP0: ($o > $o > $o > $o)).
% 0.33/0.45 thf(func_def_45, type, sP1: ($o > $o > $o > $o)).
% 0.33/0.45 thf(func_def_46, type, sP2: ($o > $o > $o > $o)).
% 0.33/0.45 thf(func_def_47, type, sK3: (u > d > u)).
% 0.33/0.45 thf(func_def_48, type, sK4: (u > d > u)).
% 0.33/0.45 thf(func_def_49, type, sK5: (d > d > u > u > u)).
% 0.33/0.45 thf(func_def_50, type, sK6: u).
% 0.33/0.45 thf(func_def_51, type, sK7: d).
% 0.33/0.45 thf(func_def_52, type, sK8: d).
% 0.33/0.45 thf(func_def_53, type, sK9: u).
% 0.33/0.45 thf(f33,axiom,(
% 0.33/0.45 ! [X0 : $o] : (((~ X0) <=> (mono_2Ec_2Ebool_2EF = X0)) & ((X0 = mono_2Ec_2Ebool_2EF) <=> (~ X0)) & ((X0 = mono_2Ec_2Ebool_2ET) <=> X0) & ((mono_2Ec_2Ebool_2ET = X0) <=> X0))),
% 0.33/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EEQ__CLAUSES)).
% 0.33/0.45 thf(f42,conjecture,(
% 0.33/0.45 ! [X0 : d,X2 : u,X1 : d,X3 : u] : ((~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ecardinal_2Ecardleq_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X2) @ (s @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool) @ X3))))) <=> (~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ecardinal_2Ecardleq_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X2) @ (s @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool) @ X3))))))),
% 0.33/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ecardinal_2ECARD__NOT__LE)).
% 0.33/0.45 thf(f43,negated_conjecture,(
% 0.33/0.45 ~ ! [X0 : d,X2 : u,X1 : d,X3 : u] : ((~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ecardinal_2Ecardleq_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X2) @ (s @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool) @ X3))))) <=> (~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ecardinal_2Ecardleq_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X2) @ (s @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool) @ X3))))))),
% 0.33/0.45 inference(negated_conjecture,[status(cth)],[f42])).
% 0.33/0.45 thf(f44,plain,(
% 0.33/0.45 ~ ! [X0 : d,X1 : u,X2 : d,X3 : u] : ((~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ecardinal_2Ecardleq_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1) @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ X3))))) <=> (~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ecardinal_2Ecardleq_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1) @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ X3))))))),
% 0.33/0.45 inference(rectify,[],[f43])).
% 0.33/0.45 thf(f45,plain,(
% 0.33/0.45 ~ ! [X2 : d,X3 : u,X1 : u,X0 : d] : (((~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ecardinal_2Ecardleq_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1) @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ X3)))))) = ((~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ecardinal_2Ecardleq_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1) @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ X3)))))))),
% 0.33/0.45 inference(fool_elimination,[],[f44])).
% 0.33/0.45 thf(f48,plain,(
% 0.33/0.45 ! [X0 : $o] : (((~ X0) <=> (mono_2Ec_2Ebool_2EF = X0)) & ((X0 = mono_2Ec_2Ebool_2EF) <=> (~ X0)) & ((X0 = mono_2Ec_2Ebool_2ET) <=> X0) & ((mono_2Ec_2Ebool_2ET = X0) <=> X0))),
% 0.33/0.45 inference(rectify,[],[f33])).
% 0.33/0.45 thf(f49,plain,(
% 0.33/0.45 ! [X0 : $o] : (((($true = X0) <=> (mono_2Ec_2Ebool_2ET = $true)) <=> ($true = X0)) & ((((~ X0)) = $true) <=> (($true = X0) <=> (mono_2Ec_2Ebool_2EF = $true))) & ((($true = X0) <=> (mono_2Ec_2Ebool_2EF = $true)) <=> (((~ X0)) = $true)) & (($true = X0) <=> (($true = X0) <=> (mono_2Ec_2Ebool_2ET = $true))))),
% 0.33/0.45 inference(fool_elimination,[],[f48])).
% 0.33/0.45 thf(f114,plain,(
% 0.33/0.45 ? [X3 : u,X0 : d,X2 : d,X1 : u] : (((~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ecardinal_2Ecardleq_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1) @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ X3)))))) != ((~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ecardinal_2Ecardleq_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ X1) @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ X3)))))))),
% 0.33/0.45 inference(ennf_transformation,[],[f45])).
% 0.33/0.45 thf(f119,plain,(
% 0.33/0.45 ! [X0 : $o] : (((((($true = X0) | (mono_2Ec_2Ebool_2ET != $true)) & ((mono_2Ec_2Ebool_2ET = $true) | ($true != X0))) | ($true != X0)) & (($true = X0) | (((mono_2Ec_2Ebool_2ET != $true) | ($true != X0)) & ((mono_2Ec_2Ebool_2ET = $true) | ($true = X0))))) & (((((~ X0)) = $true) | (((mono_2Ec_2Ebool_2EF != $true) | ($true != X0)) & ((mono_2Ec_2Ebool_2EF = $true) | ($true = X0)))) & (((($true = X0) | (mono_2Ec_2Ebool_2EF != $true)) & ((mono_2Ec_2Ebool_2EF = $true) | ($true != X0))) | (((~ X0)) != $true))) & ((((($true = X0) | (mono_2Ec_2Ebool_2EF != $true)) & ((mono_2Ec_2Ebool_2EF = $true) | ($true != X0))) | (((~ X0)) != $true)) & ((((~ X0)) = $true) | (((mono_2Ec_2Ebool_2EF != $true) | ($true != X0)) & ((mono_2Ec_2Ebool_2EF = $true) | ($true = X0))))) & ((($true = X0) | (((mono_2Ec_2Ebool_2ET != $true) | ($true != X0)) & ((mono_2Ec_2Ebool_2ET = $true) | ($true = X0)))) & (((($true = X0) | (mono_2Ec_2Ebool_2ET != $true)) & ((mono_2Ec_2Ebool_2ET = $true) | ($true != X0))) | ($true != X0))))),
% 0.33/0.45 inference(nnf_transformation,[],[f49])).
% 0.33/0.45 thf(f120,plain,(
% 0.33/0.45 ! [X0 : $o] : ((((($true = X0) | (mono_2Ec_2Ebool_2ET != $true)) & ((mono_2Ec_2Ebool_2ET = $true) | ($true != X0))) | ($true != X0)) & (($true = X0) | (((mono_2Ec_2Ebool_2ET != $true) | ($true != X0)) & ((mono_2Ec_2Ebool_2ET = $true) | ($true = X0)))) & ((((~ X0)) = $true) | (((mono_2Ec_2Ebool_2EF != $true) | ($true != X0)) & ((mono_2Ec_2Ebool_2EF = $true) | ($true = X0)))) & (((($true = X0) | (mono_2Ec_2Ebool_2EF != $true)) & ((mono_2Ec_2Ebool_2EF = $true) | ($true != X0))) | (((~ X0)) != $true)) & (((($true = X0) | (mono_2Ec_2Ebool_2EF != $true)) & ((mono_2Ec_2Ebool_2EF = $true) | ($true != X0))) | (((~ X0)) != $true)) & ((((~ X0)) = $true) | (((mono_2Ec_2Ebool_2EF != $true) | ($true != X0)) & ((mono_2Ec_2Ebool_2EF = $true) | ($true = X0)))) & (($true = X0) | (((mono_2Ec_2Ebool_2ET != $true) | ($true != X0)) & ((mono_2Ec_2Ebool_2ET = $true) | ($true = X0)))) & (((($true = X0) | (mono_2Ec_2Ebool_2ET != $true)) & ((mono_2Ec_2Ebool_2ET = $true) | ($true != X0))) | ($true != X0)))),
% 0.33/0.45 inference(flattening,[],[f119])).
% 0.33/0.45 thf(f133,plain,(
% 0.33/0.45 ? [X0 : u,X1 : d,X2 : d,X3 : u] : (((~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ecardinal_2Ecardleq_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool) @ X3) @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ X0)))))) != ((~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ecardinal_2Ecardleq_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool) @ X3) @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ X0)))))))),
% 0.33/0.45 inference(rectify,[],[f114])).
% 0.33/0.45 thf(f134,plain,(
% 0.33/0.45 (((~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ecardinal_2Ecardleq_2E2 @ (s @ (tyop_2Emin_2Efun @ sK7 @ tyop_2Emin_2Ebool) @ sK9) @ (s @ (tyop_2Emin_2Efun @ sK8 @ tyop_2Emin_2Ebool) @ sK6)))))) != ((~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ecardinal_2Ecardleq_2E2 @ (s @ (tyop_2Emin_2Efun @ sK7 @ tyop_2Emin_2Ebool) @ sK9) @ (s @ (tyop_2Emin_2Efun @ sK8 @ tyop_2Emin_2Ebool) @ sK6)))))))),
% 0.33/0.45 inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9]),skolemize(X0,sK6),skolemize(X1,sK7),skolemize(X2,sK8),skolemize(X3,sK9)],[f133])).
% 0.33/0.45 thf(f185,plain,(
% 0.33/0.45 ( ! [X0 : $o] : ((((~ X0)) = $true) | (mono_2Ec_2Ebool_2EF != $true) | ($true != X0)) )),
% 0.33/0.45 inference(cnf_transformation,[],[f120])).
% 0.33/0.45 thf(f207,plain,(
% 0.33/0.45 (((~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ecardinal_2Ecardleq_2E2 @ (s @ (tyop_2Emin_2Efun @ sK7 @ tyop_2Emin_2Ebool) @ sK9) @ (s @ (tyop_2Emin_2Efun @ sK8 @ tyop_2Emin_2Ebool) @ sK6)))))) != ((~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ecardinal_2Ecardleq_2E2 @ (s @ (tyop_2Emin_2Efun @ sK7 @ tyop_2Emin_2Ebool) @ sK9) @ (s @ (tyop_2Emin_2Efun @ sK8 @ tyop_2Emin_2Ebool) @ sK6)))))))),
% 0.33/0.45 inference(cnf_transformation,[],[f134])).
% 0.33/0.45 thf(f304,plain,(
% 0.33/0.45 (((~ $true)) = $true) | (mono_2Ec_2Ebool_2EF != $true)),
% 0.33/0.45 inference(equality_resolution,[],[f185])).
% 0.33/0.45 thf(f405,plain,(
% 0.33/0.45 (mono_2Ec_2Ebool_2EF != $true) | ($false = $true)),
% 0.33/0.45 inference(not_proxy_clausification,[],[f304])).
% 0.33/0.45 thf(f406,plain,(
% 0.33/0.45 (mono_2Ec_2Ebool_2EF != $true)),
% 0.33/0.45 inference(trivial_inequality_removal,[],[f405])).
% 0.33/0.45 thf(f488,plain,(
% 0.33/0.45 (((~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ecardinal_2Ecardleq_2E2 @ (s @ (tyop_2Emin_2Efun @ sK7 @ tyop_2Emin_2Ebool) @ sK9) @ (s @ (tyop_2Emin_2Efun @ sK8 @ tyop_2Emin_2Ebool) @ sK6)))))) = $true) | (((~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ecardinal_2Ecardleq_2E2 @ (s @ (tyop_2Emin_2Efun @ sK7 @ tyop_2Emin_2Ebool) @ sK9) @ (s @ (tyop_2Emin_2Efun @ sK8 @ tyop_2Emin_2Ebool) @ sK6)))))) = $true)),
% 0.33/0.45 inference(xor_proxy_clausification,[],[f207])).
% 0.33/0.45 thf(f489,plain,(
% 0.33/0.45 ($false = ((~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ecardinal_2Ecardleq_2E2 @ (s @ (tyop_2Emin_2Efun @ sK7 @ tyop_2Emin_2Ebool) @ sK9) @ (s @ (tyop_2Emin_2Efun @ sK8 @ tyop_2Emin_2Ebool) @ sK6))))))) | ($false = ((~ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ecardinal_2Ecardleq_2E2 @ (s @ (tyop_2Emin_2Efun @ sK7 @ tyop_2Emin_2Ebool) @ sK9) @ (s @ (tyop_2Emin_2Efun @ sK8 @ tyop_2Emin_2Ebool) @ sK6)))))))),
% 0.33/0.45 inference(xor_proxy_clausification,[],[f207])).
% 0.33/0.45 thf(f490,plain,(
% 0.33/0.45 (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ecardinal_2Ecardleq_2E2 @ (s @ (tyop_2Emin_2Efun @ sK7 @ tyop_2Emin_2Ebool) @ sK9) @ (s @ (tyop_2Emin_2Efun @ sK8 @ tyop_2Emin_2Ebool) @ sK6))))) = $true) | (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ecardinal_2Ecardleq_2E2 @ (s @ (tyop_2Emin_2Efun @ sK7 @ tyop_2Emin_2Ebool) @ sK9) @ (s @ (tyop_2Emin_2Efun @ sK8 @ tyop_2Emin_2Ebool) @ sK6))))) = $true)),
% 0.33/0.45 inference(not_proxy_clausification,[],[f489])).
% 0.33/0.45 thf(f491,plain,(
% 0.33/0.45 (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ecardinal_2Ecardleq_2E2 @ (s @ (tyop_2Emin_2Efun @ sK7 @ tyop_2Emin_2Ebool) @ sK9) @ (s @ (tyop_2Emin_2Efun @ sK8 @ tyop_2Emin_2Ebool) @ sK6))))) = $true)),
% 0.33/0.45 inference(duplicate_literal_removal,[],[f490])).
% 0.33/0.45 thf(f492,plain,(
% 0.33/0.45 ($false = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ecardinal_2Ecardleq_2E2 @ (s @ (tyop_2Emin_2Efun @ sK7 @ tyop_2Emin_2Ebool) @ sK9) @ (s @ (tyop_2Emin_2Efun @ sK8 @ tyop_2Emin_2Ebool) @ sK6)))))) | ($false = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ecardinal_2Ecardleq_2E2 @ (s @ (tyop_2Emin_2Efun @ sK7 @ tyop_2Emin_2Ebool) @ sK9) @ (s @ (tyop_2Emin_2Efun @ sK8 @ tyop_2Emin_2Ebool) @ sK6))))))),
% 0.33/0.45 inference(not_proxy_clausification,[],[f488])).
% 0.33/0.45 thf(f493,plain,(
% 0.33/0.45 ($false = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ecardinal_2Ecardleq_2E2 @ (s @ (tyop_2Emin_2Efun @ sK7 @ tyop_2Emin_2Ebool) @ sK9) @ (s @ (tyop_2Emin_2Efun @ sK8 @ tyop_2Emin_2Ebool) @ sK6))))))),
% 0.33/0.45 inference(duplicate_literal_removal,[],[f492])).
% 0.33/0.45 thf(f502,definition,(
% 0.33/0.45 spl10_2 <=> (mono_2Ec_2Ebool_2EF = $true)),
% 0.33/0.45 introduced(definition,[new_symbols(definition,[spl10_2])],[avatar_definition])).
% 0.33/0.45 thf(f503,plain,(
% 0.33/0.45 (mono_2Ec_2Ebool_2EF != $true) | spl10_2),
% 0.33/0.45 inference(avatar_component_clause,[],[f502])).
% 0.33/0.45 thf(f516,definition,(
% 0.33/0.45 spl10_5 <=> (mono_2Ec_2Ebool_2EF = $false)),
% 0.33/0.45 introduced(definition,[new_symbols(definition,[spl10_5])],[avatar_definition])).
% 0.33/0.45 thf(f522,plain,(
% 0.33/0.45 ~spl10_2),
% 0.33/0.45 inference(avatar_split_clause,[],[f406,f502])).
% 0.33/0.45 thf(f540,definition,(
% 0.33/0.45 spl10_8 <=> (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ecardinal_2Ecardleq_2E2 @ (s @ (tyop_2Emin_2Efun @ sK7 @ tyop_2Emin_2Ebool) @ sK9) @ (s @ (tyop_2Emin_2Efun @ sK8 @ tyop_2Emin_2Ebool) @ sK6))))) = $true)),
% 0.33/0.45 introduced(definition,[new_symbols(definition,[spl10_8])],[avatar_definition])).
% 0.33/0.45 thf(f543,plain,(
% 0.33/0.45 spl10_8),
% 0.33/0.45 inference(avatar_split_clause,[],[f491,f540])).
% 0.33/0.45 thf(f545,definition,(
% 0.33/0.45 spl10_9 <=> ($false = ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ecardinal_2Ecardleq_2E2 @ (s @ (tyop_2Emin_2Efun @ sK7 @ tyop_2Emin_2Ebool) @ sK9) @ (s @ (tyop_2Emin_2Efun @ sK8 @ tyop_2Emin_2Ebool) @ sK6))))))),
% 0.33/0.45 introduced(definition,[new_symbols(definition,[spl10_9])],[avatar_definition])).
% 0.33/0.45 thf(f548,plain,(
% 0.33/0.45 spl10_9),
% 0.33/0.45 inference(avatar_split_clause,[],[f493,f545])).
% 0.33/0.45 thf(f551,plain,(
% 0.33/0.45 (mono_2Ec_2Ebool_2EF = $false) | ($true != $true) | spl10_2),
% 0.33/0.45 inference(fool_paramodulation,[],[f503])).
% 0.33/0.45 thf(f552,plain,(
% 0.33/0.45 (mono_2Ec_2Ebool_2EF = $false) | spl10_2),
% 0.33/0.45 inference(trivial_inequality_removal,[],[f551])).
% 0.33/0.45 thf(f553,plain,(
% 0.33/0.45 spl10_5 | spl10_2),
% 0.33/0.45 inference(avatar_split_clause,[],[f552,f502,f516])).
% 0.33/0.45 thf(f555,definition,(
% 0.33/0.45 (mono_2Ec_2Ebool_2EF != $false) | ($false != ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ecardinal_2Ecardleq_2E2 @ (s @ (tyop_2Emin_2Efun @ sK7 @ tyop_2Emin_2Ebool) @ sK9) @ (s @ (tyop_2Emin_2Efun @ sK8 @ tyop_2Emin_2Ebool) @ sK6)))))) | (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Ecardinal_2Ecardleq_2E2 @ (s @ (tyop_2Emin_2Efun @ sK7 @ tyop_2Emin_2Ebool) @ sK9) @ (s @ (tyop_2Emin_2Efun @ sK8 @ tyop_2Emin_2Ebool) @ sK6))))) != $true) | (mono_2Ec_2Ebool_2EF = $true)),
% 0.33/0.45 introduced(theory,[theory_tautology_sat_conflict])).
% 0.33/0.45 cnf(s9, plain, ~spl10_2, inference(sat_conversion,[],[f522])).
% 0.33/0.45 cnf(s24, plain, spl10_8, inference(sat_conversion,[],[f543])).
% 0.33/0.45 cnf(s25, plain, spl10_9, inference(sat_conversion,[],[f548])).
% 0.33/0.45 cnf(s27, plain, spl10_2 | spl10_5, inference(sat_conversion,[],[f553])).
% 0.33/0.45 cnf(s29, plain, spl10_2 | ~spl10_5 | ~spl10_8 | ~spl10_9, inference(sat_conversion,[],[f555])).
% 0.33/0.45 cnf(s31, plain, ~spl10_5, inference(rat,[],[s29,s25,s24,s9])).
% 0.33/0.45 cnf(s33, plain, $false, inference(rat,[],[s27,s31,s9])).
% 0.33/0.45 thf(f557,plain,(
% 0.33/0.45 $false),
% 0.33/0.45 inference(avatar_sat_refutation,[],[s33])).
% 0.33/0.45 % SZS output end Proof for theBenchmark
% 0.33/0.45 % (2947711)------------------------------
% 0.33/0.45 % (2947711)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.33/0.45 % (2947711)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.33/0.45 % (2947711)CaDiCaL version: 2.1.3
% 0.33/0.45 % (2947711)Termination reason: Refutation
% 0.33/0.45 % (2947711)Time elapsed: 0.015 s
% 0.33/0.45 % (2947711)Peak memory usage: 13 MB
% 0.33/0.45 % (2947711)Instructions burned: 31 (million)
% 0.33/0.45 % (2947703)Success in time 0.062 s
% 0.33/0.45 % Vampire exiting
%------------------------------------------------------------------------------