%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP139^2 : 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 : n004.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 08:08:31 AM UTC 2026
% Result : Theorem 0.63s 0.38s
% Output : Refutation 0.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP139^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n004.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 19:59:22 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.22/0.27 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
% 0.63/0.38 % (1769676)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.63/0.38 % (1769684)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=3867596303: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)
% 0.63/0.38 % (1769687)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.63/0.38 % (1769687)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
% 0.63/0.38 % (1769682)lrs+10_16_si=on:nwc=1.5:random_seed=2320020616:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.63/0.38 % (1769681)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=389213373:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.63/0.38 % (1769683)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3950519724:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.63/0.38 % (1769685)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=201042754:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.63/0.38 % (1769686)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1858384826:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.63/0.38 % (1769687)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=3441740098:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.63/0.38 % (1769683)Instruction limit reached!
% 0.63/0.38 % (1769683)------------------------------
% 0.63/0.38 % (1769683)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.38 % (1769683)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.38 % (1769683)CaDiCaL version: 2.1.3
% 0.63/0.38 % (1769683)Termination reason: Instruction limit
% 0.63/0.38 % (1769683)Termination phase: shuffling
% 0.63/0.38 % (1769683)Time elapsed: 0.002 s
% 0.63/0.38 % (1769683)Peak memory usage: 10 MB
% 0.63/0.38 % (1769683)Instructions burned: 3 (million)
% 0.63/0.38 % (1769682)Instruction limit reached!
% 0.63/0.38 % (1769682)------------------------------
% 0.63/0.38 % (1769682)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.38 % (1769682)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.38 % (1769682)CaDiCaL version: 2.1.3
% 0.63/0.38 % (1769682)Termination reason: Instruction limit
% 0.63/0.38 % (1769682)Termination phase: Property scanning
% 0.63/0.38 % (1769682)Time elapsed: 0.009 s
% 0.63/0.38 % (1769682)Peak memory usage: 10 MB
% 0.63/0.38 % (1769682)Instructions burned: 20 (million)
% 0.63/0.38 % (1769685)Instruction limit reached!
% 0.63/0.38 % (1769685)------------------------------
% 0.63/0.38 % (1769685)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.38 % (1769685)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.38 % (1769685)CaDiCaL version: 2.1.3
% 0.63/0.38 % (1769685)Termination reason: Instruction limit
% 0.63/0.38 % (1769685)Termination phase: Property scanning
% 0.63/0.38 % (1769685)Time elapsed: 0.011 s
% 0.63/0.38 % (1769685)Peak memory usage: 10 MB
% 0.63/0.38 % (1769685)Instructions burned: 24 (million)
% 0.63/0.38 % (1769695)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=4070305667:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.63/0.38 % (1769695)Instruction limit reached!
% 0.63/0.38 % (1769695)------------------------------
% 0.63/0.38 % (1769695)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.38 % (1769695)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.38 % (1769695)CaDiCaL version: 2.1.3
% 0.63/0.38 % (1769695)Termination reason: Instruction limit
% 0.63/0.38 % (1769695)Termination phase: shuffling
% 0.63/0.38 % (1769695)Time elapsed: 0.003 s
% 0.63/0.38 % (1769695)Peak memory usage: 10 MB
% 0.63/0.38 % (1769695)Instructions burned: 6 (million)
% 0.63/0.38 % (1769697)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.63/0.38 % (1769696)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=90497099:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.63/0.38 % (1769697)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=4129597720:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.63/0.38 % (1769696)Instruction limit reached!
% 0.63/0.38 % (1769696)------------------------------
% 0.63/0.38 % (1769696)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.38 % (1769696)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.38 % (1769696)CaDiCaL version: 2.1.3
% 0.63/0.38 % (1769696)Termination reason: Instruction limit
% 0.63/0.38 % (1769696)Termination phase: shuffling
% 0.63/0.38 % (1769696)Time elapsed: 0.004 s
% 0.63/0.38 % (1769696)Peak memory usage: 10 MB
% 0.63/0.38 % (1769696)Instructions burned: 7 (million)
% 0.63/0.38 % (1769697)Instruction limit reached!
% 0.63/0.38 % (1769697)------------------------------
% 0.63/0.38 % (1769697)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.38 % (1769697)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.38 % (1769697)CaDiCaL version: 2.1.3
% 0.63/0.38 % (1769697)Termination reason: Instruction limit
% 0.63/0.38 % (1769697)Termination phase: shuffling
% 0.63/0.38 % (1769697)Time elapsed: 0.004 s
% 0.63/0.38 % (1769697)Peak memory usage: 10 MB
% 0.63/0.38 % (1769697)Instructions burned: 9 (million)
% 0.63/0.38 % (1769686)Instruction limit reached!
% 0.63/0.38 % (1769686)------------------------------
% 0.63/0.38 % (1769686)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.38 % (1769686)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.38 % (1769686)CaDiCaL version: 2.1.3
% 0.63/0.38 % (1769686)Termination reason: Instruction limit
% 0.63/0.38 % (1769686)Termination phase: Property scanning
% 0.63/0.38 % (1769686)Time elapsed: 0.037 s
% 0.63/0.38 % (1769686)Peak memory usage: 12 MB
% 0.63/0.38 % (1769686)Instructions burned: 77 (million)
% 0.63/0.38 % (1769684) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1769676-1769684"...
% 0.63/0.38 % (1769684)...printing done.
% 0.63/0.38 % (1769699)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=3425249617:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.63/0.38 % (1769684)Refutation found. Thanks to Tanya!
% 0.63/0.38 % SZS status Theorem for theBenchmark
% 0.63/0.38 % SZS output start Proof for theBenchmark
% 0.63/0.38 thf(type_def_5, type, paraco415392788lle_tv: $tType).
% 0.63/0.38 thf(type_def_6, type, product_prod: ($tType * $tType) > $tType).
% 0.63/0.38 thf(type_def_7, type, set: $tType > $tType).
% 0.63/0.38 thf(type_def_8, type, nat: $tType).
% 0.63/0.38 thf(type_def_9, type, sTfun: ($tType * $tType) > $tType).
% 0.63/0.38 thf(func_def_0, type, type: !>[X0: $tType]:($o)).
% 0.63/0.38 thf(func_def_1, type, ord: !>[X0: $tType]:($o)).
% 0.63/0.38 thf(func_def_2, type, top: !>[X0: $tType]:($o)).
% 0.63/0.38 thf(func_def_3, type, order: !>[X0: $tType]:($o)).
% 0.63/0.38 thf(func_def_4, type, group_add: !>[X0: $tType]:($o)).
% 0.63/0.38 thf(func_def_5, type, no_bot: !>[X0: $tType]:($o)).
% 0.63/0.38 thf(func_def_6, type, no_top: !>[X0: $tType]:($o)).
% 0.63/0.38 thf(func_def_7, type, linorder: !>[X0: $tType]:($o)).
% 0.63/0.38 thf(func_def_8, type, preorder: !>[X0: $tType]:($o)).
% 0.63/0.38 thf(func_def_9, type, ab_group_add: !>[X0: $tType]:($o)).
% 0.63/0.38 thf(func_def_10, type, order_top: !>[X0: $tType]:($o)).
% 0.63/0.38 thf(func_def_11, type, wellorder: !>[X0: $tType]:($o)).
% 0.63/0.38 thf(func_def_12, type, semigroup_add: !>[X0: $tType]:($o)).
% 0.63/0.38 thf(func_def_13, type, dense_order: !>[X0: $tType]:($o)).
% 0.63/0.38 thf(func_def_14, type, comm_monoid_add: !>[X0: $tType]:($o)).
% 0.63/0.38 thf(func_def_15, type, ab_semigroup_add: !>[X0: $tType]:($o)).
% 0.63/0.38 thf(func_def_16, type, dense_linorder: !>[X0: $tType]:($o)).
% 0.63/0.38 thf(func_def_17, type, cancel_semigroup_add: !>[X0: $tType]:($o)).
% 0.63/0.38 thf(func_def_18, type, ordere779506340up_add: !>[X0: $tType]:($o)).
% 0.63/0.38 thf(func_def_19, type, canoni770627133id_add: !>[X0: $tType]:($o)).
% 0.63/0.38 thf(func_def_20, type, ordere236663937imp_le: !>[X0: $tType]:($o)).
% 0.63/0.38 thf(func_def_21, type, ordere223160158up_add: !>[X0: $tType]:($o)).
% 0.63/0.38 thf(func_def_22, type, strict2144017051up_add: !>[X0: $tType]:($o)).
% 0.63/0.38 thf(func_def_23, type, inj_on: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X0 > $o))).
% 0.63/0.38 thf(func_def_24, type, strict_mono_on: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X0 > $o))).
% 0.63/0.38 thf(func_def_25, type, the_inv_into: !>[X0: $tType, X1: $tType]:((set @ X0 > (X0 > X1) > X1 > X0))).
% 0.63/0.38 thf(func_def_26, type, plus_plus: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.63/0.38 thf(func_def_27, type, ord_less: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.63/0.38 thf(func_def_28, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.63/0.38 thf(func_def_29, type, order_strict_mono: !>[X0: $tType, X1: $tType]:(((X0 > X1) > $o))).
% 0.63/0.38 thf(func_def_30, type, top_top: !>[X0: $tType]:(X0)).
% 0.63/0.38 thf(func_def_31, type, paraco1920534163nge_tv: ((nat > nat) > paraco415392788lle_tv > paraco415392788lle_tv)).
% 0.63/0.38 thf(func_def_32, type, paraco676387099_Indet: (nat > paraco415392788lle_tv)).
% 0.63/0.38 thf(func_def_33, type, paraco152590079rec_tv: !>[X0: $tType]:((($o > X0) > (nat > X0) > paraco415392788lle_tv > X0))).
% 0.63/0.38 thf(func_def_34, type, product_apfst: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1) > product_prod @ X0 @ X2 > product_prod @ X1 @ X2))).
% 0.63/0.38 thf(func_def_35, type, product_apsnd: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1) > product_prod @ X2 @ X0 > product_prod @ X2 @ X1))).
% 0.63/0.38 thf(func_def_36, type, product_map_prod: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((X0 > X1) > (X2 > X3) > product_prod @ X0 @ X2 > product_prod @ X1 @ X3))).
% 0.63/0.38 thf(func_def_37, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.63/0.38 thf(func_def_38, type, image: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X0 > set @ X1))).
% 0.63/0.38 thf(func_def_39, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.63/0.38 thf(func_def_40, type, f: (nat > nat)).
% 0.63/0.38 thf(func_def_44, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.63/0.38 thf(func_def_45, type, vIMP: ($o > $o > $o)).
% 0.63/0.38 thf(func_def_46, type, db0: !>[X0: $tType]:(X0)).
% 0.63/0.38 thf(func_def_47, type, db2: !>[X0: $tType]:(X0)).
% 0.63/0.38 thf(func_def_48, type, db1: !>[X0: $tType]:(X0)).
% 0.63/0.38 thf(func_def_49, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.63/0.38 thf(func_def_50, type, vOR: ($o > $o > $o)).
% 0.63/0.38 thf(func_def_51, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.63/0.38 thf(func_def_52, type, vAND: ($o > $o > $o)).
% 0.63/0.38 thf(func_def_53, type, vNOT: ($o > $o)).
% 0.63/0.38 thf(func_def_54, type, db3: !>[X0: $tType]:(X0)).
% 0.63/0.38 thf(func_def_55, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.63/0.38 thf(func_def_56, type, sP0: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.63/0.38 thf(func_def_57, type, sP1: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.63/0.38 thf(func_def_58, type, sK2: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X0 > X1) > X1))).
% 0.63/0.38 thf(func_def_59, type, sK3: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.63/0.38 thf(func_def_60, type, sK4: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.63/0.38 thf(func_def_61, type, sK5: !>[X0: $tType, X1: $tType]:((X1 > (X0 > X1) > X0))).
% 0.63/0.38 thf(func_def_62, type, sK6: !>[X0: $tType, X1: $tType]:((X0 > X1 > (X0 > X1) > X0))).
% 0.63/0.38 thf(func_def_63, type, sK7: !>[X0: $tType, X1: $tType]:((set @ X0 > set @ X1 > (X0 > X1) > set @ X0))).
% 0.63/0.38 thf(func_def_64, type, sK8: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > (X1 > X0) > X1))).
% 0.63/0.38 thf(func_def_65, type, sK9: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.63/0.38 thf(func_def_66, type, sK10: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.63/0.38 thf(func_def_67, type, sK11: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.63/0.38 thf(func_def_68, type, sK12: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.63/0.38 thf(func_def_69, type, sK13: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > set @ X0 > X1))).
% 0.63/0.38 thf(func_def_70, type, sK14: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.63/0.38 thf(func_def_71, type, sK15: !>[X0: $tType]:((X0 > X0 > X0 > X0))).
% 0.63/0.38 thf(func_def_72, type, sK16: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.63/0.38 thf(func_def_73, type, sK17: !>[X0: $tType, X1: $tType]:((set @ X0 > (X1 > $o) > (X0 > X1) > X0))).
% 0.63/0.38 thf(func_def_74, type, sK18: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X0 > (X1 > $o) > X1))).
% 0.63/0.38 thf(func_def_75, type, sK19: !>[X0: $tType]:((set @ X0 > X0))).
% 0.63/0.38 thf(func_def_76, type, sK20: !>[X0: $tType]:((set @ X0 > X0))).
% 0.63/0.38 thf(func_def_77, type, sK21: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X1))).
% 0.63/0.38 thf(func_def_78, type, sK22: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X1))).
% 0.63/0.38 thf(func_def_79, type, sK23: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.63/0.38 thf(func_def_80, type, sK24: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.63/0.38 thf(func_def_81, type, sK25: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.63/0.38 thf(func_def_82, type, sK26: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.63/0.38 thf(func_def_83, type, sK27: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.63/0.38 thf(func_def_84, type, sK28: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X1 > X0) > set @ X0 > X0))).
% 0.63/0.38 thf(func_def_85, type, sK29: !>[X0: $tType, X1: $tType]:((set @ X0 > (X0 > X1) > X0))).
% 0.63/0.38 thf(func_def_86, type, sK30: !>[X0: $tType, X1: $tType]:((set @ X0 > (X0 > X1) > X0))).
% 0.63/0.38 thf(func_def_87, type, sK31: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.63/0.38 thf(func_def_88, type, sK32: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.63/0.38 thf(func_def_89, type, sK33: !>[X0: $tType]:((X0 > X0))).
% 0.63/0.38 thf(func_def_90, type, sK34: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > X1))).
% 0.63/0.38 thf(func_def_91, type, sK35: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > X1))).
% 0.63/0.38 thf(func_def_92, type, sK36: !>[X0: $tType]:((set @ X0 > X0))).
% 0.63/0.38 thf(func_def_93, type, sK37: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.63/0.38 thf(func_def_94, type, sK38: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.63/0.38 thf(func_def_95, type, sK39: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.63/0.38 thf(func_def_96, type, sK40: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.63/0.38 thf(func_def_97, type, sK41: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.63/0.38 thf(func_def_98, type, sK42: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.63/0.38 thf(func_def_99, type, sK43: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.63/0.38 thf(func_def_100, type, sK44: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.63/0.38 thf(func_def_101, type, sK45: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.63/0.38 thf(func_def_102, type, sK46: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.63/0.38 thf(func_def_103, type, sK47: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.63/0.38 thf(func_def_104, type, sK48: !>[X0: $tType, X1: $tType]:((set @ X0 > set @ X1 > (X0 > X1) > set @ X0))).
% 0.63/0.38 thf(func_def_105, type, sK49: !>[X0: $tType]:((X0 > X0))).
% 0.63/0.38 thf(func_def_106, type, sK50: !>[X0: $tType, X1: $tType]:((set @ X0 > (X0 > X1) > (X0 > X1) > X0))).
% 0.63/0.38 thf(func_def_107, type, sK51: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.63/0.38 thf(func_def_108, type, sK52: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X1 > X0))).
% 0.63/0.38 thf(func_def_109, type, sK53: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X0 > X1))).
% 0.63/0.38 thf(func_def_110, type, sK54: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.63/0.38 thf(func_def_111, type, sK55: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.63/0.38 thf(func_def_112, type, sK56: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.63/0.38 thf(func_def_113, type, sK57: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.63/0.38 thf(func_def_114, type, sK58: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 0.63/0.38 thf(func_def_115, type, sK59: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.63/0.38 thf(func_def_116, type, sK60: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.63/0.38 thf(func_def_117, type, sK61: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.63/0.38 thf(func_def_118, type, sK62: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.63/0.38 thf(func_def_119, type, sK63: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.63/0.38 thf(func_def_120, type, sK64: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.63/0.38 thf(func_def_121, type, sK65: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.63/0.38 thf(func_def_122, type, sK66: !>[X0: $tType]:(X0)).
% 0.63/0.38 thf(func_def_123, type, sK67: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.63/0.38 thf(func_def_124, type, sK68: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.63/0.38 thf(func_def_125, type, sK69: !>[X0: $tType, X1: $tType]:(((X1 > X1) > set @ X1 > (X1 > X0) > X1))).
% 0.63/0.38 thf(func_def_126, type, sK70: !>[X0: $tType, X1: $tType]:(((X1 > X1) > set @ X1 > (X1 > X0) > X1))).
% 0.63/0.38 thf(func_def_127, type, sK71: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.63/0.38 thf(func_def_128, type, sK72: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.63/0.38 thf(func_def_129, type, sK73: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.63/0.38 thf(func_def_130, type, sK74: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.63/0.38 thf(func_def_131, type, sK75: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > X1) > X0))).
% 0.63/0.38 thf(func_def_132, type, sK76: !>[X0: $tType, X1: $tType]:((X0 > (X1 > X0) > X1))).
% 0.63/0.38 thf(func_def_133, type, sK77: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X0))).
% 0.63/0.38 thf(func_def_134, type, sK78: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.63/0.38 thf(func_def_135, type, sK79: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.63/0.38 thf(func_def_136, type, sK80: !>[X0: $tType, X1: $tType]:((set @ X0 > set @ X1 > (X0 > X1) > set @ X0))).
% 0.63/0.38 thf(func_def_137, type, sK81: !>[X0: $tType, X1: $tType]:((set @ X1 > set @ X0 > (X0 > X1) > X0))).
% 0.63/0.38 thf(func_def_138, type, sK82: !>[X0: $tType]:((X0 > X0 > X0 > X0))).
% 0.63/0.38 thf(func_def_139, type, sK83: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.63/0.38 thf(func_def_140, type, sK84: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.63/0.38 thf(func_def_141, type, sK85: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X1 > X0) > X0))).
% 0.63/0.38 thf(func_def_142, type, sK86: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.63/0.38 thf(func_def_143, type, sK87: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.63/0.38 thf(func_def_144, type, sK88: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X0 > X1))).
% 0.63/0.38 thf(func_def_146, type, inv_paraco676387099_Indet_90: (paraco415392788lle_tv > nat)).
% 0.63/0.38 thf(func_def_147, type, inv_f_91: (nat > nat)).
% 0.63/0.38 thf(f1,axiom,(
% 0.63/0.38 ! [X5 : paraco415392788lle_tv,X4 : paraco415392788lle_tv] : ((((paraco1920534163nge_tv @ f @ X4)) = ((paraco1920534163nge_tv @ f @ X5))) => (X4 = X5))),
% 0.63/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__092_060open_062_092_060And_062tv2_Atv1_O_Achange__tv_Af_Atv1_A_061_Achange__tv_Af_Atv2_A_092_060Longrightarrow_062_Atv1_A_061_Atv2_092_060close_062)).
% 0.63/0.38 thf(f6,axiom,(
% 0.63/0.38 ! [X1 : $tType,X0 : $tType,X2 : (X1 > X0)] : (! [X3 : X1,X4 : X1] : ((((X2 @ X3)) = ((X2 @ X4))) => (X3 = X4)) => (inj_on @ X1 @ X0 @ X2 @ top_top @ set @ X1))),
% 0.63/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_injI)).
% 0.63/0.38 thf(f288,conjecture,(
% 0.63/0.38 (inj_on @ paraco415392788lle_tv @ paraco415392788lle_tv @ (paraco1920534163nge_tv @ f) @ top_top @ set @ paraco415392788lle_tv)),
% 0.63/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 0.63/0.38 thf(f289,negated_conjecture,(
% 0.63/0.38 ~(inj_on @ paraco415392788lle_tv @ paraco415392788lle_tv @ (paraco1920534163nge_tv @ f) @ top_top @ set @ paraco415392788lle_tv)),
% 0.63/0.38 inference(negated_conjecture,[status(cth)],[f288])).
% 0.63/0.38 thf(f513,plain,(
% 0.63/0.38 ! [X0 : $tType,X1 : $tType,X2 : (X0 > X1)] : (! [X3 : X0,X4 : X0] : ((((X2 @ X4)) = ((X2 @ X3))) => (X3 = X4)) => (inj_on @ X0 @ X1 @ X2 @ top_top @ set @ X0))),
% 0.63/0.38 inference(rectify,[],[f6])).
% 0.63/0.38 thf(f514,plain,(
% 0.63/0.38 ! [X1 : $tType,X0 : $tType,X2 : (X0 > X1)] : (! [X3 : X0,X4 : X0] : ((((X2 @ X4)) = ((X2 @ X3))) => (X3 = X4)) => ($true = ((inj_on @ X0 @ X1 @ X2 @ top_top @ set @ X0))))),
% 0.63/0.38 inference(fool_elimination,[],[f513])).
% 0.63/0.38 thf(f580,plain,(
% 0.63/0.38 ~(inj_on @ paraco415392788lle_tv @ paraco415392788lle_tv @ (paraco1920534163nge_tv @ f) @ top_top @ set @ paraco415392788lle_tv)),
% 0.63/0.38 inference(rectify,[],[f289])).
% 0.63/0.38 thf(f581,plain,(
% 0.63/0.38 ~ (((inj_on @ paraco415392788lle_tv @ paraco415392788lle_tv @ (paraco1920534163nge_tv @ f) @ top_top @ set @ paraco415392788lle_tv)) = $true)),
% 0.63/0.38 inference(fool_elimination,[],[f580])).
% 0.63/0.38 thf(f855,plain,(
% 0.63/0.38 ! [X0 : paraco415392788lle_tv,X1 : paraco415392788lle_tv] : ((((paraco1920534163nge_tv @ f @ X1)) = ((paraco1920534163nge_tv @ f @ X0))) => (X0 = X1))),
% 0.63/0.38 inference(rectify,[],[f1])).
% 0.63/0.38 thf(f856,plain,(
% 0.63/0.38 (((inj_on @ paraco415392788lle_tv @ paraco415392788lle_tv @ (paraco1920534163nge_tv @ f) @ top_top @ set @ paraco415392788lle_tv)) != $true)),
% 0.63/0.38 inference(flattening,[],[f581])).
% 0.63/0.38 thf(f996,plain,(
% 0.63/0.38 ! [X1 : $tType,X0 : $tType,X2 : (X0 > X1)] : (? [X3 : X0,X4 : X0] : ((X3 != X4) & (((X2 @ X4)) = ((X2 @ X3)))) | ($true = ((inj_on @ X0 @ X1 @ X2 @ top_top @ set @ X0))))),
% 0.63/0.38 inference(ennf_transformation,[],[f514])).
% 0.63/0.38 thf(f1163,plain,(
% 0.63/0.38 ! [X1 : paraco415392788lle_tv,X0 : paraco415392788lle_tv] : ((X0 = X1) | (((paraco1920534163nge_tv @ f @ X1)) != ((paraco1920534163nge_tv @ f @ X0))))),
% 0.63/0.38 inference(ennf_transformation,[],[f855])).
% 0.63/0.38 thf(f1271,plain,(
% 0.63/0.38 ! [X0 : $tType,X1 : $tType,X2 : (X1 > X0)] : (? [X3 : X1,X4 : X1] : ((X3 != X4) & (((X2 @ X3)) = ((X2 @ X4)))) | (((inj_on @ X1 @ X0 @ X2 @ top_top @ set @ X1)) = $true))),
% 0.63/0.38 inference(rectify,[],[f996])).
% 0.63/0.38 thf(f1272,plain,(
% 0.63/0.38 ! [X0 : $tType,X1 : $tType,X2 : (X1 > X0)] : (((((sK27 @ X0 @ X1 @ X2)) != ((sK26 @ X0 @ X1 @ X2))) & (((X2 @ (sK26 @ X0 @ X1 @ X2))) = ((X2 @ (sK27 @ X0 @ X1 @ X2))))) | (((inj_on @ X1 @ X0 @ X2 @ top_top @ set @ X1)) = $true))),
% 0.63/0.38 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP]),skolemize(X4,sK2 @ X0 @ X1 @ X3 @ X2),skolemize(X4,sK2 @ X0 @ X1 @ X3 @ X2)],[f1271])).
% 0.63/0.38 thf(f1301,plain,(
% 0.63/0.38 ! [X0 : paraco415392788lle_tv,X1 : paraco415392788lle_tv] : ((X0 = X1) | (((paraco1920534163nge_tv @ f @ X1)) != ((paraco1920534163nge_tv @ f @ X0))))),
% 0.63/0.38 inference(rectify,[],[f1163])).
% 0.63/0.38 thf(f1587,plain,(
% 0.63/0.38 ( ! [X1 : $tType,X0 : $tType,X2 : (X1 > X0)] : ((((X2 @ (sK26 @ X0 @ X1 @ X2))) = ((X2 @ (sK27 @ X0 @ X1 @ X2)))) | (((inj_on @ X1 @ X0 @ X2 @ top_top @ set @ X1)) = $true)) )),
% 0.63/0.38 inference(cnf_transformation,[],[f1272])).
% 0.63/0.38 thf(f1588,plain,(
% 0.63/0.38 ( ! [X1 : $tType,X0 : $tType,X2 : (X1 > X0)] : ((((inj_on @ X1 @ X0 @ X2 @ top_top @ set @ X1)) = $true) | (((sK27 @ X0 @ X1 @ X2)) != ((sK26 @ X0 @ X1 @ X2)))) )),
% 0.63/0.38 inference(cnf_transformation,[],[f1272])).
% 0.63/0.38 thf(f1634,plain,(
% 0.63/0.38 ( ! [X0 : paraco415392788lle_tv,X1 : paraco415392788lle_tv] : ((((paraco1920534163nge_tv @ f @ X1)) != ((paraco1920534163nge_tv @ f @ X0))) | (X0 = X1)) )),
% 0.63/0.38 inference(cnf_transformation,[],[f1301])).
% 0.63/0.38 thf(f1810,plain,(
% 0.63/0.38 (((inj_on @ paraco415392788lle_tv @ paraco415392788lle_tv @ (paraco1920534163nge_tv @ f) @ top_top @ set @ paraco415392788lle_tv)) != $true)),
% 0.63/0.38 inference(cnf_transformation,[],[f856])).
% 0.63/0.38 thf(f2003,definition,(
% 0.63/0.38 spl89_1 <=> (((inj_on @ paraco415392788lle_tv @ paraco415392788lle_tv @ (paraco1920534163nge_tv @ f) @ top_top @ set @ paraco415392788lle_tv)) = $true)),
% 0.63/0.38 introduced(definition,[new_symbols(definition,[spl89_1])],[avatar_definition])).
% 0.63/0.38 thf(f2005,plain,(
% 0.63/0.38 (((inj_on @ paraco415392788lle_tv @ paraco415392788lle_tv @ (paraco1920534163nge_tv @ f) @ top_top @ set @ paraco415392788lle_tv)) != $true) | spl89_1),
% 0.63/0.38 inference(avatar_component_clause,[],[f2003])).
% 0.63/0.38 thf(f2006,plain,(
% 0.63/0.38 ~spl89_1),
% 0.63/0.38 inference(avatar_split_clause,[],[f1810,f2003])).
% 0.63/0.38 thf(f2154,plain,(
% 0.63/0.38 ($true != $true) | (((sK26 @ paraco415392788lle_tv @ paraco415392788lle_tv @ (paraco1920534163nge_tv @ f))) != ((sK27 @ paraco415392788lle_tv @ paraco415392788lle_tv @ (paraco1920534163nge_tv @ f)))) | spl89_1),
% 0.63/0.38 inference(superposition,[],[f2005,f1588])).
% 0.63/0.38 thf(f2155,plain,(
% 0.63/0.38 (((sK26 @ paraco415392788lle_tv @ paraco415392788lle_tv @ (paraco1920534163nge_tv @ f))) != ((sK27 @ paraco415392788lle_tv @ paraco415392788lle_tv @ (paraco1920534163nge_tv @ f)))) | spl89_1),
% 0.63/0.38 inference(trivial_inequality_removal,[],[f2154])).
% 0.63/0.38 thf(f2157,definition,(
% 0.63/0.38 spl89_26 <=> (((sK26 @ paraco415392788lle_tv @ paraco415392788lle_tv @ (paraco1920534163nge_tv @ f))) = ((sK27 @ paraco415392788lle_tv @ paraco415392788lle_tv @ (paraco1920534163nge_tv @ f))))),
% 0.63/0.38 introduced(definition,[new_symbols(definition,[spl89_26])],[avatar_definition])).
% 0.63/0.38 thf(f2159,plain,(
% 0.63/0.38 (((sK26 @ paraco415392788lle_tv @ paraco415392788lle_tv @ (paraco1920534163nge_tv @ f))) != ((sK27 @ paraco415392788lle_tv @ paraco415392788lle_tv @ (paraco1920534163nge_tv @ f)))) | spl89_26),
% 0.63/0.38 inference(avatar_component_clause,[],[f2157])).
% 0.63/0.38 thf(f2160,plain,(
% 0.63/0.38 ~spl89_26 | spl89_1),
% 0.63/0.38 inference(avatar_split_clause,[],[f2155,f2003,f2157])).
% 0.63/0.38 thf(f2558,plain,(
% 0.63/0.38 ( ! [X0 : paraco415392788lle_tv] : ((((inj_on @ paraco415392788lle_tv @ paraco415392788lle_tv @ (paraco1920534163nge_tv @ f) @ top_top @ set @ paraco415392788lle_tv)) = $true) | (((paraco1920534163nge_tv @ f @ (sK26 @ paraco415392788lle_tv @ paraco415392788lle_tv @ (paraco1920534163nge_tv @ f)))) != ((paraco1920534163nge_tv @ f @ X0))) | (((sK27 @ paraco415392788lle_tv @ paraco415392788lle_tv @ (paraco1920534163nge_tv @ f))) = X0)) )),
% 0.63/0.38 inference(superposition,[],[f1634,f1587])).
% 0.63/0.38 thf(f2598,plain,(
% 0.63/0.38 ( ! [X0 : paraco415392788lle_tv] : ((((paraco1920534163nge_tv @ f @ (sK26 @ paraco415392788lle_tv @ paraco415392788lle_tv @ (paraco1920534163nge_tv @ f)))) != ((paraco1920534163nge_tv @ f @ X0))) | (((sK27 @ paraco415392788lle_tv @ paraco415392788lle_tv @ (paraco1920534163nge_tv @ f))) = X0)) ) | spl89_1),
% 0.63/0.38 inference(forward_subsumption_resolution,[],[f2558,f2005])).
% 0.63/0.38 thf(f2620,plain,(
% 0.63/0.38 (((sK26 @ paraco415392788lle_tv @ paraco415392788lle_tv @ (paraco1920534163nge_tv @ f))) = ((sK27 @ paraco415392788lle_tv @ paraco415392788lle_tv @ (paraco1920534163nge_tv @ f)))) | spl89_1),
% 0.63/0.38 inference(equality_resolution,[],[f2598])).
% 0.63/0.38 thf(f2621,plain,(
% 0.63/0.38 $false | (spl89_1 | spl89_26)),
% 0.63/0.38 inference(forward_subsumption_resolution,[],[f2620,f2159])).
% 0.63/0.38 thf(f2622,plain,(
% 0.63/0.38 spl89_1 | spl89_26),
% 0.63/0.38 inference(avatar_contradiction_clause,[],[f2621])).
% 0.63/0.38 cnf(s1, plain, ~spl89_1, inference(sat_conversion,[],[f2006])).
% 0.63/0.38 cnf(s28, plain, spl89_1 | ~spl89_26, inference(sat_conversion,[],[f2160])).
% 0.63/0.38 cnf(s39, plain, spl89_1 | spl89_26, inference(sat_conversion,[],[f2622])).
% 0.63/0.38 cnf(s40, plain, spl89_26, inference(rat,[],[s39,s1])).
% 0.63/0.38 cnf(s42, plain, $false, inference(rat,[],[s28,s40,s1])).
% 0.63/0.38 thf(f2623,plain,(
% 0.63/0.38 $false),
% 0.63/0.38 inference(avatar_sat_refutation,[],[s42])).
% 0.63/0.38 % SZS output end Proof for theBenchmark
% 0.63/0.38 % (1769684)------------------------------
% 0.63/0.38 % (1769684)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.38 % (1769684)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.38 % (1769684)CaDiCaL version: 2.1.3
% 0.63/0.38 % (1769684)Termination reason: Refutation
% 0.63/0.38 % (1769684)Time elapsed: 0.058 s
% 0.63/0.38 % (1769684)Peak memory usage: 15 MB
% 0.63/0.38 % (1769684)Instructions burned: 205 (million)
% 0.63/0.38 % (1769676)Success in time 0.1 s
% 0.63/0.38 % Vampire exiting
%------------------------------------------------------------------------------