%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP029^2 : TPTP v9.3.1. Released 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 08:08:02 AM UTC 2026
% Result : ContradictoryAxioms 0.22s 0.35s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP029^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.18 % Computer : n003.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Tue Sep 29 19:40:29 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.22 Running higher-order theorem proving
% 0.10/0.24 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
% 0.22/0.35 % (2967842)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.35 % (2967872)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.35 % (2967872)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
% 0.22/0.35 % (2967872)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=3089194085:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.35 % (2967867)lrs+10_16_si=on:nwc=1.5:random_seed=1182819027:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.35 % (2967866)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1891721329:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.35 % (2967870)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3281185095:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.35 % (2967868)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3714802867:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.35 % (2967869)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=261542882: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)
% 0.22/0.35 % (2967871)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2174535950:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.35 % (2967868)Instruction limit reached!
% 0.22/0.35 % (2967868)------------------------------
% 0.22/0.35 % (2967868)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.35 % (2967868)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.35 % (2967868)CaDiCaL version: 2.1.3
% 0.22/0.35 % (2967868)Termination reason: Instruction limit
% 0.22/0.35 % (2967868)Termination phase: shuffling
% 0.22/0.35 % (2967868)Time elapsed: 0.002 s
% 0.22/0.35 % (2967868)Peak memory usage: 10 MB
% 0.22/0.35 % (2967868)Instructions burned: 3 (million)
% 0.22/0.35 % (2967867)Instruction limit reached!
% 0.22/0.35 % (2967867)------------------------------
% 0.22/0.35 % (2967867)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.35 % (2967867)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.35 % (2967867)CaDiCaL version: 2.1.3
% 0.22/0.35 % (2967867)Termination reason: Instruction limit
% 0.22/0.35 % (2967867)Termination phase: Property scanning
% 0.22/0.35 % (2967867)Time elapsed: 0.010 s
% 0.22/0.35 % (2967867)Peak memory usage: 10 MB
% 0.22/0.35 % (2967867)Instructions burned: 19 (million)
% 0.22/0.35 % (2967870)Instruction limit reached!
% 0.22/0.35 % (2967870)------------------------------
% 0.22/0.35 % (2967870)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.35 % (2967870)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.35 % (2967870)CaDiCaL version: 2.1.3
% 0.22/0.35 % (2967870)Termination reason: Instruction limit
% 0.22/0.35 % (2967870)Termination phase: Property scanning
% 0.22/0.35 % (2967870)Time elapsed: 0.012 s
% 0.22/0.35 % (2967870)Peak memory usage: 10 MB
% 0.22/0.35 % (2967870)Instructions burned: 24 (million)
% 0.22/0.35 % (2967881)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=947499564:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.22/0.35 % (2967881)Instruction limit reached!
% 0.22/0.35 % (2967881)------------------------------
% 0.22/0.35 % (2967881)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.35 % (2967881)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.35 % (2967881)CaDiCaL version: 2.1.3
% 0.22/0.35 % (2967881)Termination reason: Instruction limit
% 0.22/0.35 % (2967881)Termination phase: shuffling
% 0.22/0.35 % (2967881)Time elapsed: 0.003 s
% 0.22/0.35 % (2967881)Peak memory usage: 10 MB
% 0.22/0.35 % (2967881)Instructions burned: 6 (million)
% 0.22/0.35 % (2967886)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.22/0.35 % (2967885)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=4025483498:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.22/0.35 % (2967886)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=4044587750:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.22/0.35 % (2967872) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2967842-2967872"...
% 0.22/0.35 % (2967885)Instruction limit reached!
% 0.22/0.35 % (2967885)------------------------------
% 0.22/0.35 % (2967885)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.35 % (2967885)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.35 % (2967885)CaDiCaL version: 2.1.3
% 0.22/0.35 % (2967885)Termination reason: Instruction limit
% 0.22/0.35 % (2967885)Termination phase: shuffling
% 0.22/0.35 % (2967885)Time elapsed: 0.003 s
% 0.22/0.35 % (2967885)Peak memory usage: 10 MB
% 0.22/0.35 % (2967885)Instructions burned: 5 (million)
% 0.22/0.35 % (2967872)...printing done.
% 0.22/0.35 % (2967872)Refutation found. Thanks to Tanya!
% 0.22/0.35 % SZS status ContradictoryAxioms for theBenchmark
% 0.22/0.35 % SZS output start Proof for theBenchmark
% 0.22/0.35 thf(type_def_5, type, binary1291135688e_Tree: $tType > $tType).
% 0.22/0.35 thf(type_def_6, type, set: $tType > $tType).
% 0.22/0.35 thf(type_def_7, type, int: $tType).
% 0.22/0.35 thf(type_def_8, type, a: $tType).
% 0.22/0.35 thf(type_def_9, type, sTfun: ($tType * $tType) > $tType).
% 0.22/0.35 thf(func_def_0, type, bounded_lattice: !>[X0: $tType]:($o)).
% 0.22/0.35 thf(func_def_1, type, type: !>[X0: $tType]:($o)).
% 0.22/0.35 thf(func_def_2, type, bot: !>[X0: $tType]:($o)).
% 0.22/0.35 thf(func_def_3, type, ord: !>[X0: $tType]:($o)).
% 0.22/0.35 thf(func_def_4, type, order: !>[X0: $tType]:($o)).
% 0.22/0.35 thf(func_def_5, type, no_bot: !>[X0: $tType]:($o)).
% 0.22/0.35 thf(func_def_6, type, no_top: !>[X0: $tType]:($o)).
% 0.22/0.35 thf(func_def_7, type, linorder: !>[X0: $tType]:($o)).
% 0.22/0.35 thf(func_def_8, type, preorder: !>[X0: $tType]:($o)).
% 0.22/0.35 thf(func_def_9, type, order_bot: !>[X0: $tType]:($o)).
% 0.22/0.35 thf(func_def_10, type, wellorder: !>[X0: $tType]:($o)).
% 0.22/0.35 thf(func_def_11, type, dense_order: !>[X0: $tType]:($o)).
% 0.22/0.35 thf(func_def_12, type, linordered_idom: !>[X0: $tType]:($o)).
% 0.22/0.35 thf(func_def_13, type, linordered_field: !>[X0: $tType]:($o)).
% 0.22/0.35 thf(func_def_14, type, semilattice_sup: !>[X0: $tType]:($o)).
% 0.22/0.35 thf(func_def_15, type, bounde1808546759up_bot: !>[X0: $tType]:($o)).
% 0.22/0.35 thf(func_def_16, type, condit1656338222tinuum: !>[X0: $tType]:($o)).
% 0.22/0.35 thf(func_def_17, type, binary210054475elle_T: !>[X0: $tType]:((binary1291135688e_Tree @ X0 > X0 > binary1291135688e_Tree @ X0 > binary1291135688e_Tree @ X0))).
% 0.22/0.35 thf(func_def_18, type, binary1746293266le_Tip: !>[X0: $tType]:(binary1291135688e_Tree @ X0)).
% 0.22/0.35 thf(func_def_19, type, binary536355927e_Tree: !>[X0: $tType, X1: $tType]:((X0 > (binary1291135688e_Tree @ X1 > X1 > binary1291135688e_Tree @ X1 > X0) > binary1291135688e_Tree @ X1 > X0))).
% 0.22/0.35 thf(func_def_20, type, binary1929596613c_Tree: !>[X0: $tType, X1: $tType]:((X0 > (binary1291135688e_Tree @ X1 > X1 > binary1291135688e_Tree @ X1 > X0 > X0 > X0) > binary1291135688e_Tree @ X1 > X0))).
% 0.22/0.35 thf(func_def_21, type, binary2130109271t_Tree: !>[X0: $tType]:((binary1291135688e_Tree @ X0 > set @ X0))).
% 0.22/0.35 thf(func_def_22, type, binary64540844le_eqs: !>[X0: $tType]:(((X0 > int) > X0 > set @ X0))).
% 0.22/0.35 thf(func_def_23, type, binary1653327646_setOf: !>[X0: $tType]:((binary1291135688e_Tree @ X0 > set @ X0))).
% 0.22/0.35 thf(func_def_24, type, binary1610619414edTree: !>[X0: $tType]:(((X0 > int) > binary1291135688e_Tree @ X0 > $o))).
% 0.22/0.35 thf(func_def_25, type, binary231205461t_pred: !>[X0: $tType]:(((X0 > int) > X0 > X0 > binary1291135688e_Tree @ X0 > $o))).
% 0.22/0.35 thf(func_def_26, type, the: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.22/0.35 thf(func_def_27, type, if: !>[X0: $tType]:(($o > X0 > X0 > X0))).
% 0.22/0.35 thf(func_def_28, type, semilattice_neutr: !>[X0: $tType]:(((X0 > X0 > X0) > X0 > $o))).
% 0.22/0.35 thf(func_def_29, type, sup_sup: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.22/0.35 thf(func_def_30, type, bot_bot: !>[X0: $tType]:(X0)).
% 0.22/0.35 thf(func_def_31, type, ord_less: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.22/0.35 thf(func_def_32, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.22/0.35 thf(func_def_33, type, powp: !>[X0: $tType]:(((X0 > $o) > set @ X0 > $o))).
% 0.22/0.35 thf(func_def_34, type, inv_imagep: !>[X0: $tType, X1: $tType]:(((X0 > X0 > $o) > (X1 > X0) > X1 > X1 > $o))).
% 0.22/0.35 thf(func_def_35, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.22/0.35 thf(func_def_36, type, pow: !>[X0: $tType]:((set @ X0 > set @ set @ X0))).
% 0.22/0.35 thf(func_def_37, type, insert: !>[X0: $tType]:((X0 > set @ X0 > set @ X0))).
% 0.22/0.35 thf(func_def_38, type, is_empty: !>[X0: $tType]:((set @ X0 > $o))).
% 0.22/0.35 thf(func_def_39, type, is_singleton: !>[X0: $tType]:((set @ X0 > $o))).
% 0.22/0.35 thf(func_def_40, type, the_elem: !>[X0: $tType]:((set @ X0 > X0))).
% 0.22/0.35 thf(func_def_41, type, chains: !>[X0: $tType]:((set @ set @ X0 > set @ set @ set @ X0))).
% 0.22/0.35 thf(func_def_42, type, pred_chain: !>[X0: $tType]:((set @ X0 > (X0 > X0 > $o) > set @ X0 > $o))).
% 0.22/0.35 thf(func_def_43, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.22/0.35 thf(func_def_44, type, a2: a).
% 0.22/0.35 thf(func_def_45, type, b: a).
% 0.22/0.35 thf(func_def_46, type, h: (a > int)).
% 0.22/0.35 thf(func_def_47, type, t1: binary1291135688e_Tree @ a).
% 0.22/0.35 thf(func_def_48, type, t2: binary1291135688e_Tree @ a).
% 0.22/0.35 thf(func_def_49, type, x: a).
% 0.22/0.35 thf(func_def_53, type, vIMP: ($o > $o > $o)).
% 0.22/0.35 thf(func_def_54, type, db0: !>[X0: $tType]:(X0)).
% 0.22/0.35 thf(func_def_55, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.22/0.35 thf(func_def_56, type, vNOT: ($o > $o)).
% 0.22/0.35 thf(func_def_57, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.22/0.35 thf(func_def_58, type, vAND: ($o > $o > $o)).
% 0.22/0.35 thf(func_def_59, type, vOR: ($o > $o > $o)).
% 0.22/0.35 thf(func_def_60, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.22/0.35 thf(func_def_61, type, db1: !>[X0: $tType]:(X0)).
% 0.22/0.35 thf(func_def_62, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.22/0.35 thf(func_def_63, type, db2: !>[X0: $tType]:(X0)).
% 0.22/0.35 thf(func_def_64, type, db3: !>[X0: $tType]:(X0)).
% 0.22/0.35 thf(func_def_65, type, sP0: !>[X0: $tType]:(((X0 > X0 > $o) > $o))).
% 0.22/0.35 thf(func_def_66, type, sP1: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > $o))).
% 0.22/0.35 thf(func_def_67, type, sP2: !>[X0: $tType]:((X0 > binary1291135688e_Tree @ X0 > $o))).
% 0.22/0.35 thf(func_def_68, type, sP3: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.22/0.35 thf(func_def_69, type, sP4: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.22/0.35 thf(func_def_70, type, sP5: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.22/0.35 thf(func_def_71, type, sP6: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.22/0.35 thf(func_def_72, type, sP7: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.22/0.35 thf(func_def_73, type, sP8: !>[X0: $tType]:(((X0 > X0 > $o) > $o))).
% 0.22/0.35 thf(func_def_74, type, sP9: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > $o))).
% 0.22/0.35 thf(func_def_75, type, sP10: !>[X0: $tType]:((X0 > (X0 > $o) > $o))).
% 0.22/0.35 thf(func_def_76, type, sP11: !>[X0: $tType]:(((X0 > X0 > $o) > (X0 > X0 > $o) > set @ X0 > $o))).
% 0.22/0.35 thf(func_def_77, type, sP12: !>[X0: $tType]:(((binary1291135688e_Tree @ X0 > $o) > $o))).
% 0.22/0.35 thf(func_def_78, type, sP13: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > $o))).
% 0.22/0.35 thf(func_def_79, type, sP14: !>[X0: $tType]:((set @ X0 > $o))).
% 0.22/0.35 thf(func_def_80, type, sP15: !>[X0: $tType]:((set @ set @ X0 > set @ set @ X0 > $o))).
% 0.22/0.35 thf(func_def_81, type, sP16: !>[X0: $tType]:((set @ set @ X0 > $o))).
% 0.22/0.35 thf(func_def_82, type, sP17: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > $o))).
% 0.22/0.35 thf(func_def_83, type, sP18: !>[X0: $tType, X1: $tType]:((((X1 > X0) > X1 > X0 > $o) > $o))).
% 0.22/0.35 thf(func_def_84, type, sP19: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > $o))).
% 0.22/0.35 thf(func_def_85, type, sK20: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.22/0.35 thf(func_def_86, type, sK21: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.22/0.35 thf(func_def_87, type, sK22: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.22/0.35 thf(func_def_88, type, sK23: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.22/0.35 thf(func_def_89, type, sK24: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.22/0.35 thf(func_def_90, type, sK25: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.22/0.35 thf(func_def_91, type, sK26: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.22/0.35 thf(func_def_92, type, sK27: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0))).
% 0.22/0.35 thf(func_def_93, type, sK28: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.22/0.35 thf(func_def_94, type, sK29: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.22/0.35 thf(func_def_95, type, sK30: !>[X0: $tType]:((X0 > binary1291135688e_Tree @ X0 > binary1291135688e_Tree @ X0))).
% 0.22/0.35 thf(func_def_96, type, sK31: !>[X0: $tType]:((X0 > binary1291135688e_Tree @ X0 > X0))).
% 0.22/0.35 thf(func_def_97, type, sK32: !>[X0: $tType]:((X0 > binary1291135688e_Tree @ X0 > binary1291135688e_Tree @ X0))).
% 0.22/0.35 thf(func_def_98, type, sK33: !>[X0: $tType]:((X0 > binary1291135688e_Tree @ X0 > binary1291135688e_Tree @ X0))).
% 0.22/0.35 thf(func_def_99, type, sK34: !>[X0: $tType]:((X0 > binary1291135688e_Tree @ X0 > binary1291135688e_Tree @ X0))).
% 0.22/0.35 thf(func_def_100, type, sK35: !>[X0: $tType]:((X0 > binary1291135688e_Tree @ X0 > X0))).
% 0.22/0.35 thf(func_def_101, type, sK36: !>[X0: $tType]:((X0 > binary1291135688e_Tree @ X0 > binary1291135688e_Tree @ X0))).
% 0.22/0.35 thf(func_def_102, type, sK37: !>[X0: $tType]:((X0 > binary1291135688e_Tree @ X0 > binary1291135688e_Tree @ X0))).
% 0.22/0.35 thf(func_def_103, type, sK38: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.22/0.35 thf(func_def_104, type, sK39: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.22/0.35 thf(func_def_105, type, sK40: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 0.22/0.35 thf(func_def_106, type, sK41: !>[X0: $tType, X1: $tType]:(((X1 > $o) > (X1 > X0) > X1))).
% 0.22/0.35 thf(func_def_107, type, sK42: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > $o) > X0))).
% 0.22/0.35 thf(func_def_108, type, sK43: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.22/0.35 thf(func_def_109, type, sK44: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.22/0.35 thf(func_def_110, type, sK45: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.22/0.35 thf(func_def_111, type, sK46: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.22/0.35 thf(func_def_112, type, sK47: !>[X0: $tType]:((set @ X0 > set @ set @ X0 > set @ X0))).
% 0.22/0.35 thf(func_def_113, type, sK48: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.22/0.35 thf(func_def_114, type, sK49: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0))).
% 0.22/0.35 thf(func_def_115, type, sK50: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.22/0.35 thf(func_def_116, type, sK51: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.22/0.35 thf(func_def_117, type, sK52: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.22/0.35 thf(func_def_118, type, sK53: !>[X0: $tType]:((X0 > X0))).
% 0.22/0.35 thf(func_def_119, type, sK54: !>[X0: $tType]:((X0 > (X0 > $o) > X0))).
% 0.22/0.35 thf(func_def_120, type, sK55: !>[X0: $tType]:((set @ X0 > set @ set @ X0 > set @ X0))).
% 0.22/0.35 thf(func_def_121, type, sK56: !>[X0: $tType]:((X0 > X0))).
% 0.22/0.35 thf(func_def_122, type, sK57: !>[X0: $tType]:((X0 > (X0 > $o) > X0))).
% 0.22/0.35 thf(func_def_123, type, sK58: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.22/0.35 thf(func_def_124, type, sK59: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > X1) > X0))).
% 0.22/0.35 thf(func_def_125, type, sK60: !>[X0: $tType]:((X0 > X0))).
% 0.22/0.35 thf(func_def_126, type, sK61: !>[X0: $tType]:((X0 > X0))).
% 0.22/0.35 thf(func_def_127, type, sK62: !>[X0: $tType]:((X0 > X0))).
% 0.22/0.35 thf(func_def_128, type, sK63: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.22/0.35 thf(func_def_129, type, sK64: !>[X0: $tType]:((X0 > X0))).
% 0.22/0.35 thf(func_def_130, type, sK65: !>[X0: $tType]:((set @ X0 > X0 > set @ X0))).
% 0.22/0.35 thf(func_def_131, type, sK66: !>[X0: $tType]:((X0 > X0))).
% 0.22/0.35 thf(func_def_132, type, sK67: !>[X0: $tType]:((X0 > X0))).
% 0.22/0.35 thf(func_def_133, type, sK68: !>[X0: $tType]:((X0 > (X0 > $o) > X0))).
% 0.22/0.35 thf(func_def_134, type, sK69: !>[X0: $tType]:((X0 > (X0 > $o) > X0))).
% 0.22/0.35 thf(func_def_135, type, sK70: !>[X0: $tType]:((set @ X0 > X0))).
% 0.22/0.35 thf(func_def_136, type, sK71: !>[X0: $tType]:((X0 > X0))).
% 0.22/0.35 thf(func_def_137, type, sK72: !>[X0: $tType]:(((X0 > X0 > $o) > (X0 > X0 > $o) > set @ X0 > X0))).
% 0.22/0.35 thf(func_def_138, type, sK73: !>[X0: $tType]:(((X0 > X0 > $o) > (X0 > X0 > $o) > set @ X0 > X0))).
% 0.22/0.35 thf(func_def_139, type, sK74: !>[X0: $tType]:(((binary1291135688e_Tree @ X0 > $o) > X0))).
% 0.22/0.35 thf(func_def_140, type, sK75: !>[X0: $tType]:(((binary1291135688e_Tree @ X0 > $o) > binary1291135688e_Tree @ X0))).
% 0.22/0.35 thf(func_def_141, type, sK76: !>[X0: $tType]:(((binary1291135688e_Tree @ X0 > $o) > binary1291135688e_Tree @ X0))).
% 0.22/0.35 thf(func_def_142, type, sK77: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.22/0.35 thf(func_def_143, type, sK78: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.22/0.35 thf(func_def_144, type, sK79: !>[X0: $tType]:((X0 > X0))).
% 0.22/0.35 thf(func_def_145, type, sK80: !>[X0: $tType]:(((X0 > X0 > $o) > set @ X0 > X0 > X0))).
% 0.22/0.35 thf(func_def_146, type, sK81: !>[X0: $tType]:((binary1291135688e_Tree @ X0 > X0))).
% 0.22/0.35 thf(func_def_147, type, sK82: !>[X0: $tType]:((binary1291135688e_Tree @ X0 > binary1291135688e_Tree @ X0))).
% 0.22/0.35 thf(func_def_148, type, sK83: !>[X0: $tType]:((binary1291135688e_Tree @ X0 > binary1291135688e_Tree @ X0))).
% 0.22/0.35 thf(func_def_149, type, sK84: !>[X0: $tType]:((X0 > X0))).
% 0.22/0.35 thf(func_def_150, type, sK85: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.22/0.35 thf(func_def_151, type, sK86: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0))).
% 0.22/0.35 thf(func_def_152, type, sK87: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.22/0.35 thf(func_def_153, type, sK88: !>[X0: $tType]:((X0 > (X0 > $o) > X0))).
% 0.22/0.35 thf(func_def_154, type, sK89: !>[X0: $tType]:((set @ X0 > X0))).
% 0.22/0.35 thf(func_def_155, type, sK90: !>[X0: $tType]:((set @ X0 > X0))).
% 0.22/0.35 thf(func_def_156, type, sK91: !>[X0: $tType]:((set @ set @ X0 > set @ set @ X0))).
% 0.22/0.35 thf(func_def_157, type, sK92: !>[X0: $tType]:((set @ X0 > set @ set @ X0 > set @ X0))).
% 0.22/0.35 thf(func_def_158, type, sK93: !>[X0: $tType]:((set @ set @ X0 > set @ X0))).
% 0.22/0.35 thf(func_def_159, type, sK94: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.22/0.35 thf(func_def_160, type, sK95: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.22/0.35 thf(func_def_161, type, sK96: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0))).
% 0.22/0.35 thf(func_def_162, type, sK97: !>[X0: $tType, X1: $tType]:((X0 > X1))).
% 0.22/0.35 thf(func_def_163, type, sK98: !>[X0: $tType]:((X0 > X0))).
% 0.22/0.35 thf(func_def_164, type, sK99: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.22/0.35 thf(func_def_165, type, sK100: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.22/0.35 thf(func_def_166, type, sK101: !>[X0: $tType, X1: $tType]:((((X1 > X0) > X1 > X0 > $o) > X1))).
% 0.22/0.35 thf(func_def_167, type, sK102: !>[X0: $tType, X1: $tType]:((((X1 > X0) > X1 > X0 > $o) > X1 > X0))).
% 0.22/0.35 thf(func_def_168, type, sK103: !>[X0: $tType, X1: $tType]:((((X1 > X0) > X1 > X0 > $o) > X1 > X0))).
% 0.22/0.35 thf(func_def_169, type, sK104: !>[X0: $tType, X1: $tType]:((((X1 > X0) > X1 > X0 > $o) > X1))).
% 0.22/0.35 thf(func_def_170, type, sK105: !>[X0: $tType, X1: $tType]:((((X1 > X0) > X1 > X0 > $o) > X1 > X0))).
% 0.22/0.35 thf(func_def_171, type, sK106: !>[X0: $tType, X1: $tType]:((((X1 > X0) > X1 > X0 > $o) > X1 > X0))).
% 0.22/0.35 thf(func_def_172, type, sK107: !>[X0: $tType, X1: $tType]:((((X1 > X0) > X1 > X0 > $o) > X0))).
% 0.22/0.35 thf(func_def_173, type, sK108: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.22/0.35 thf(func_def_174, type, sK109: !>[X0: $tType]:((X0 > (X0 > $o) > X0))).
% 0.22/0.35 thf(func_def_175, type, sK110: !>[X0: $tType, X1: $tType]:((X0 > X1))).
% 0.22/0.35 thf(func_def_176, type, sK111: !>[X0: $tType]:((set @ X0 > X0 > set @ X0))).
% 0.22/0.35 thf(func_def_177, type, sK112: !>[X0: $tType]:((X0 > X0))).
% 0.22/0.35 thf(func_def_178, type, sK113: !>[X0: $tType]:((set @ X0 > X0))).
% 0.22/0.35 thf(func_def_179, type, sK114: !>[X0: $tType]:((set @ X0 > X0))).
% 0.22/0.35 thf(func_def_180, type, sK115: !>[X0: $tType]:((X0 > X0))).
% 0.22/0.35 thf(func_def_181, type, sK116: !>[X0: $tType]:((binary1291135688e_Tree @ X0 > X0 > (X0 > int) > X0))).
% 0.22/0.35 thf(func_def_182, type, sK117: !>[X0: $tType]:((X0 > (X0 > int) > binary1291135688e_Tree @ X0 > X0))).
% 0.22/0.35 thf(func_def_183, type, sK118: !>[X0: $tType]:((set @ X0 > X0 > X0 > set @ X0 > set @ X0))).
% 0.22/0.35 thf(func_def_184, type, sK119: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.22/0.35 thf(func_def_185, type, sK120: !>[X0: $tType]:((set @ X0 > X0))).
% 0.22/0.35 thf(func_def_186, type, sK121: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.22/0.35 thf(func_def_187, type, sK122: !>[X0: $tType]:(((X0 > $o) > set @ X0 > set @ X0 > X0))).
% 0.22/0.35 thf(func_def_188, type, sK123: !>[X0: $tType]:(((X0 > $o) > set @ X0 > X0))).
% 0.22/0.35 thf(func_def_189, type, sK124: !>[X0: $tType]:(((X0 > $o) > set @ X0 > X0))).
% 0.22/0.35 thf(func_def_190, type, sK125: !>[X0: $tType]:((set @ X0 > (X0 > $o) > set @ X0 > X0))).
% 0.22/0.35 thf(func_def_191, type, sK126: !>[X0: $tType]:((set @ X0 > (X0 > $o) > X0))).
% 0.22/0.35 thf(func_def_192, type, sK127: !>[X0: $tType]:((set @ X0 > (X0 > $o) > X0))).
% 0.22/0.35 thf(func_def_193, type, sK128: !>[X0: $tType]:((set @ X0 > X0))).
% 0.22/0.35 thf(f1,axiom,(
% 0.22/0.35 (((h @ a2)) = ((h @ b)))),
% 0.22/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_hahb)).
% 0.22/0.35 thf(f2,axiom,(
% 0.22/0.35 (ord_less @ int @ (h @ b) @ (h @ a2))),
% 0.22/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__092_060open_062h_Ab_A_060_Ah_Aa_092_060close_062)).
% 0.22/0.35 thf(f71,axiom,(
% 0.22/0.35 ! [X0 : $tType] : (preorder @ X0 => ! [X1 : X0] : ~(ord_less @ X0 @ X1 @ X1))),
% 0.22/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_less__irrefl)).
% 0.22/0.35 thf(f269,axiom,(
% 0.22/0.35 preorder @ int),
% 0.22/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Orderings_Opreorder_4)).
% 0.22/0.35 thf(f379,plain,(
% 0.22/0.35 ! [X0 : $tType] : (preorder @ X0 => ! [X1 : X0] : ~(ord_less @ X0 @ X1 @ X1))),
% 0.22/0.35 inference(rectify,[],[f71])).
% 0.22/0.35 thf(f380,plain,(
% 0.22/0.35 ! [X0 : $tType] : ((preorder @ X0 = $true) => ! [X1 : X0] : ~ (((ord_less @ X0 @ X1 @ X1)) = $true))),
% 0.22/0.35 inference(fool_elimination,[],[f379])).
% 0.22/0.35 thf(f570,plain,(
% 0.22/0.35 (ord_less @ int @ (h @ b) @ (h @ a2))),
% 0.22/0.35 inference(rectify,[],[f2])).
% 0.22/0.35 thf(f571,plain,(
% 0.22/0.35 (((ord_less @ int @ (h @ b) @ (h @ a2))) = $true)),
% 0.22/0.35 inference(fool_elimination,[],[f570])).
% 0.22/0.35 thf(f737,plain,(
% 0.22/0.35 preorder @ int),
% 0.22/0.35 inference(rectify,[],[f269])).
% 0.22/0.35 thf(f738,plain,(
% 0.22/0.35 (preorder @ int = $true)),
% 0.22/0.35 inference(fool_elimination,[],[f737])).
% 0.22/0.35 thf(f809,plain,(
% 0.22/0.35 ! [X0 : $tType] : ((preorder @ X0 = $true) => ! [X1 : X0] : (((ord_less @ X0 @ X1 @ X1)) != $true))),
% 0.22/0.35 inference(flattening,[],[f380])).
% 0.22/0.35 thf(f859,plain,(
% 0.22/0.35 ! [X0 : $tType] : (! [X1 : X0] : (((ord_less @ X0 @ X1 @ X1)) != $true) | (preorder @ X0 != $true))),
% 0.22/0.35 inference(ennf_transformation,[],[f809])).
% 0.22/0.35 thf(f1332,plain,(
% 0.22/0.35 (preorder @ int = $true)),
% 0.22/0.35 inference(cnf_transformation,[],[f738])).
% 0.22/0.35 thf(f1422,plain,(
% 0.22/0.35 (((ord_less @ int @ (h @ b) @ (h @ a2))) = $true)),
% 0.22/0.35 inference(cnf_transformation,[],[f571])).
% 0.22/0.35 thf(f1539,plain,(
% 0.22/0.35 ( ! [X0 : $tType,X1 : X0] : ((((ord_less @ X0 @ X1 @ X1)) != $true) | (preorder @ X0 != $true)) )),
% 0.22/0.35 inference(cnf_transformation,[],[f859])).
% 0.22/0.35 thf(f1589,plain,(
% 0.22/0.35 (((h @ a2)) = ((h @ b)))),
% 0.22/0.35 inference(cnf_transformation,[],[f1])).
% 0.22/0.35 thf(f2569,definition,(
% 0.22/0.35 spl129_6 <=> (((h @ a2)) = ((h @ b)))),
% 0.22/0.35 introduced(definition,[new_symbols(definition,[spl129_6])],[avatar_definition])).
% 0.22/0.35 thf(f2570,plain,(
% 0.22/0.35 (((h @ a2)) = ((h @ b))) | ~spl129_6),
% 0.22/0.35 inference(avatar_component_clause,[],[f2569])).
% 0.22/0.35 thf(f2631,plain,(
% 0.22/0.35 spl129_6),
% 0.22/0.35 inference(avatar_split_clause,[],[f1589,f2569])).
% 0.22/0.35 thf(f2791,plain,(
% 0.22/0.35 ($true = ((ord_less @ int @ (h @ b) @ (h @ b)))) | ~spl129_6),
% 0.22/0.35 inference(forward_demodulation,[],[f1422,f2570])).
% 0.22/0.35 thf(f2798,plain,(
% 0.22/0.35 ($true != $true) | (preorder @ int != $true) | ~spl129_6),
% 0.22/0.35 inference(constrained_superposition,[],[f1539,f2791])).
% 0.22/0.35 thf(f2808,plain,(
% 0.22/0.35 (preorder @ int != $true) | ~spl129_6),
% 0.22/0.35 inference(trivial_inequality_removal,[],[f2798])).
% 0.22/0.35 thf(f2823,plain,(
% 0.22/0.35 $false | ~spl129_6),
% 0.22/0.35 inference(forward_subsumption_resolution,[],[f2808,f1332])).
% 0.22/0.35 thf(f2824,plain,(
% 0.22/0.35 ~spl129_6),
% 0.22/0.35 inference(avatar_contradiction_clause,[],[f2823])).
% 0.22/0.35 cnf(s11, plain, spl129_6, inference(sat_conversion,[],[f2631])).
% 0.22/0.35 cnf(s24, plain, ~spl129_6, inference(sat_conversion,[],[f2824])).
% 0.22/0.35 cnf(s25, plain, $false, inference(rat,[],[s11,s24])).
% 0.22/0.35 thf(f2825,plain,(
% 0.22/0.35 $false),
% 0.22/0.35 inference(avatar_sat_refutation,[],[s25])).
% 0.22/0.35 % SZS output end Proof for theBenchmark
% 0.22/0.35 % (2967872)------------------------------
% 0.22/0.35 % (2967872)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.35 % (2967872)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.35 % (2967872)CaDiCaL version: 2.1.3
% 0.22/0.35 % (2967872)Termination reason: Refutation
% 0.22/0.35 % (2967872)Time elapsed: 0.040 s
% 0.22/0.35 % (2967872)Peak memory usage: 14 MB
% 0.22/0.35 % (2967872)Instructions burned: 145 (million)
% 0.22/0.35 % (2967842)Success in time 0.093 s
% 0.22/0.35 % Vampire exiting
%------------------------------------------------------------------------------