%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COM195^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 07:46:26 AM UTC 2026
% Result : Theorem 0.65s 0.45s
% Output : Refutation 0.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM195^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 % Computer : n020.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 17:51:50 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
% 0.22/0.29 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
% 0.65/0.45 % (1384165)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.65/0.45 % (1384174)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3912846209:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.65/0.45 % (1384176)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.65/0.45 % (1384176)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
% 0.65/0.45 % (1384171)lrs+10_16_si=on:nwc=1.5:random_seed=2421648948:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.65/0.45 % (1384172)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=351715940:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.65/0.45 % (1384174)Instruction limit reached!
% 0.65/0.45 % (1384174)------------------------------
% 0.65/0.45 % (1384174)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.45 % (1384174)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.45 % (1384174)CaDiCaL version: 2.1.3
% 0.65/0.45 % (1384174)Termination reason: Instruction limit
% 0.65/0.45 % (1384174)Termination phase: Property scanning
% 0.65/0.45 % (1384174)Time elapsed: 0.007 s
% 0.65/0.45 % (1384174)Peak memory usage: 10 MB
% 0.65/0.45 % (1384174)Instructions burned: 29 (million)
% 0.65/0.45 % (1384173)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=877757215: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)
% 0.65/0.45 % (1384175)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1028390897:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.65/0.45 % (1384176)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=28492380:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.65/0.45 % (1384172)Instruction limit reached!
% 0.65/0.45 % (1384172)------------------------------
% 0.65/0.45 % (1384172)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.45 % (1384172)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.45 % (1384172)CaDiCaL version: 2.1.3
% 0.65/0.45 % (1384172)Termination reason: Instruction limit
% 0.65/0.45 % (1384172)Termination phase: shuffling
% 0.65/0.45 % (1384172)Time elapsed: 0.003 s
% 0.65/0.45 % (1384172)Peak memory usage: 10 MB
% 0.65/0.45 % (1384172)Instructions burned: 4 (million)
% 0.65/0.45 % (1384171)Instruction limit reached!
% 0.65/0.45 % (1384171)------------------------------
% 0.65/0.45 % (1384171)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.45 % (1384171)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.45 % (1384171)CaDiCaL version: 2.1.3
% 0.65/0.45 % (1384171)Termination reason: Instruction limit
% 0.65/0.45 % (1384171)Termination phase: Property scanning
% 0.65/0.45 % (1384171)Time elapsed: 0.010 s
% 0.65/0.45 % (1384171)Peak memory usage: 10 MB
% 0.65/0.45 % (1384171)Instructions burned: 20 (million)
% 0.65/0.45 % (1384183)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1491023906:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.65/0.45 % (1384183)Instruction limit reached!
% 0.65/0.45 % (1384183)------------------------------
% 0.65/0.45 % (1384183)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.45 % (1384183)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.45 % (1384183)CaDiCaL version: 2.1.3
% 0.65/0.45 % (1384183)Termination reason: Instruction limit
% 0.65/0.45 % (1384183)Termination phase: shuffling
% 0.65/0.45 % (1384183)Time elapsed: 0.001 s
% 0.65/0.45 % (1384183)Peak memory usage: 10 MB
% 0.65/0.45 % (1384183)Instructions burned: 5 (million)
% 0.65/0.45 % (1384170)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3753580205:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.65/0.45 % (1384184)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=4022812662:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.65/0.45 % (1384185)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.65/0.45 % (1384187)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=4060508414:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.65/0.45 % (1384184)Instruction limit reached!
% 0.65/0.45 % (1384184)------------------------------
% 0.65/0.45 % (1384184)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.45 % (1384184)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.45 % (1384184)CaDiCaL version: 2.1.3
% 0.65/0.45 % (1384184)Termination reason: Instruction limit
% 0.65/0.45 % (1384184)Termination phase: shuffling
% 0.65/0.45 % (1384184)Time elapsed: 0.005 s
% 0.65/0.45 % (1384184)Peak memory usage: 10 MB
% 0.65/0.45 % (1384184)Instructions burned: 5 (million)
% 0.65/0.45 % (1384185)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=4041053047:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.65/0.45 % (1384187)Instruction limit reached!
% 0.65/0.45 % (1384187)------------------------------
% 0.65/0.45 % (1384187)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.45 % (1384187)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.45 % (1384187)CaDiCaL version: 2.1.3
% 0.65/0.45 % (1384187)Termination reason: Instruction limit
% 0.65/0.45 % (1384187)Termination phase: shuffling
% 0.65/0.45 % (1384187)Time elapsed: 0.006 s
% 0.65/0.45 % (1384187)Peak memory usage: 10 MB
% 0.65/0.45 % (1384187)Instructions burned: 13 (million)
% 0.65/0.45 % (1384185)Instruction limit reached!
% 0.65/0.45 % (1384185)------------------------------
% 0.65/0.45 % (1384185)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.45 % (1384185)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.45 % (1384185)CaDiCaL version: 2.1.3
% 0.65/0.45 % (1384185)Termination reason: Instruction limit
% 0.65/0.45 % (1384185)Termination phase: shuffling
% 0.65/0.45 % (1384185)Time elapsed: 0.007 s
% 0.65/0.45 % (1384185)Peak memory usage: 10 MB
% 0.65/0.45 % (1384185)Instructions burned: 7 (million)
% 0.65/0.45 % (1384175)Instruction limit reached!
% 0.65/0.45 % (1384175)------------------------------
% 0.65/0.45 % (1384175)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.45 % (1384175)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.45 % (1384175)CaDiCaL version: 2.1.3
% 0.65/0.45 % (1384175)Termination reason: Instruction limit
% 0.65/0.45 % (1384175)Termination phase: Function definition elimination
% 0.65/0.45 % (1384175)Time elapsed: 0.046 s
% 0.65/0.45 % (1384175)Peak memory usage: 12 MB
% 0.65/0.45 % (1384175)Instructions burned: 75 (million)
% 0.65/0.45 % (1384193)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=856164309:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.65/0.45 % (1384191)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
% 0.65/0.45 % (1384191)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.65/0.45 % (1384191)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2200667058:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.65/0.45 % (1384194)lrs+10_1_si=on:cs=on:random_seed=2856592367:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.65/0.45 % (1384193)Instruction limit reached!
% 0.65/0.45 % (1384193)------------------------------
% 0.65/0.45 % (1384193)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.45 % (1384193)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.45 % (1384193)CaDiCaL version: 2.1.3
% 0.65/0.45 % (1384193)Termination reason: Instruction limit
% 0.65/0.45 % (1384193)Termination phase: Property scanning
% 0.65/0.45 % (1384193)Time elapsed: 0.027 s
% 0.65/0.45 % (1384193)Peak memory usage: 11 MB
% 0.65/0.45 % (1384193)Instructions burned: 88 (million)
% 0.65/0.45 % (1384191)Instruction limit reached!
% 0.65/0.45 % (1384191)------------------------------
% 0.65/0.45 % (1384191)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.45 % (1384191)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.45 % (1384191)CaDiCaL version: 2.1.3
% 0.65/0.45 % (1384191)Termination reason: Instruction limit
% 0.65/0.45 % (1384191)Termination phase: shuffling
% 0.65/0.45 % (1384191)Time elapsed: 0.015 s
% 0.65/0.45 % (1384191)Peak memory usage: 10 MB
% 0.65/0.45 % (1384191)Instructions burned: 29 (million)
% 0.65/0.45 % (1384194)Instruction limit reached!
% 0.65/0.45 % (1384194)------------------------------
% 0.65/0.45 % (1384194)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.45 % (1384194)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.45 % (1384194)CaDiCaL version: 2.1.3
% 0.65/0.45 % (1384194)Termination reason: Instruction limit
% 0.65/0.45 % (1384194)Termination phase: shuffling
% 0.65/0.45 % (1384194)Time elapsed: 0.005 s
% 0.65/0.45 % (1384194)Peak memory usage: 10 MB
% 0.65/0.45 % (1384194)Instructions burned: 10 (million)
% 0.65/0.45 % (1384195)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.65/0.45 % (1384199)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=798322941:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 0.65/0.45 % (1384195)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=4173285284:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.65/0.45 % (1384195)Instruction limit reached!
% 0.65/0.45 % (1384195)------------------------------
% 0.65/0.45 % (1384195)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.45 % (1384195)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.45 % (1384195)CaDiCaL version: 2.1.3
% 0.65/0.45 % (1384195)Termination reason: Instruction limit
% 0.65/0.45 % (1384195)Termination phase: shuffling
% 0.65/0.45 % (1384195)Time elapsed: 0.002 s
% 0.65/0.45 % (1384195)Peak memory usage: 10 MB
% 0.65/0.45 % (1384195)Instructions burned: 2 (million)
% 0.65/0.45 % (1384173) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1384165-1384173"...
% 0.65/0.45 % (1384173)...printing done.
% 0.65/0.45 % (1384173)Refutation found. Thanks to Tanya!
% 0.65/0.45 % SZS status Theorem for theBenchmark
% 0.65/0.45 % SZS output start Proof for theBenchmark
% 0.65/0.45 thf(type_def_5, type, set: $tType > $tType).
% 0.65/0.45 thf(type_def_6, type, itself: $tType > $tType).
% 0.65/0.45 thf(type_def_7, type, a: $tType).
% 0.65/0.45 thf(type_def_8, type, sTfun: ($tType * $tType) > $tType).
% 0.65/0.45 thf(func_def_0, type, type: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.65/0.45 thf(func_def_1, type, uminus: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.65/0.45 thf(func_def_2, type, ord: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.65/0.45 thf(func_def_3, type, order: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.65/0.45 thf(func_def_4, type, group_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.65/0.45 thf(func_def_5, type, no_bot: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.65/0.45 thf(func_def_6, type, no_top: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.65/0.45 thf(func_def_7, type, linorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.65/0.45 thf(func_def_8, type, preorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.65/0.45 thf(func_def_9, type, wellorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.65/0.45 thf(func_def_10, type, dense_order: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.65/0.45 thf(func_def_11, type, boolean_algebra: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.65/0.45 thf(func_def_12, type, semilattice_sup: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.65/0.45 thf(func_def_13, type, dense_linorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.65/0.45 thf(func_def_14, type, ordered_ab_group_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.65/0.45 thf(func_def_15, type, condit1656338222tinuum: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.65/0.45 thf(func_def_16, type, condit1037483654norder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.65/0.45 thf(func_def_17, type, gram_L1456083582e_leqv: !>[X0: $tType]:((set @ set @ X0 > set @ set @ X0 > $o))).
% 0.65/0.45 thf(func_def_18, type, gram_L608943123e_subs: !>[X0: $tType]:((set @ set @ X0 > set @ set @ X0 > $o))).
% 0.65/0.45 thf(func_def_19, type, uminus_uminus: !>[X0: $tType]:((X0 > X0))).
% 0.65/0.45 thf(func_def_20, type, sup_sup: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.65/0.45 thf(func_def_21, type, ord_less: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.65/0.45 thf(func_def_22, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.65/0.45 thf(func_def_23, type, order_antimono: !>[X0: $tType, X1: $tType]:(((X0 > X1) > $o))).
% 0.65/0.45 thf(func_def_24, type, order_strict_mono: !>[X0: $tType, X1: $tType]:(((X0 > X1) > $o))).
% 0.65/0.45 thf(func_def_25, type, type2: !>[X0: $tType]:(itself @ X0)).
% 0.65/0.45 thf(func_def_26, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.65/0.45 thf(func_def_27, type, pow: !>[X0: $tType]:((set @ X0 > set @ set @ X0))).
% 0.65/0.45 thf(func_def_28, type, pairwise: !>[X0: $tType]:(((X0 > X0 > $o) > set @ X0 > $o))).
% 0.65/0.45 thf(func_def_29, type, set_ord_atLeast: !>[X0: $tType]:((X0 > set @ X0))).
% 0.65/0.45 thf(func_def_30, type, set_or331188842AtMost: !>[X0: $tType]:((X0 > X0 > set @ X0))).
% 0.65/0.45 thf(func_def_31, type, set_or1433837966ssThan: !>[X0: $tType]:((X0 > X0 > set @ X0))).
% 0.65/0.45 thf(func_def_32, type, set_ord_atMost: !>[X0: $tType]:((X0 > set @ X0))).
% 0.65/0.45 thf(func_def_33, type, set_ord_greaterThan: !>[X0: $tType]:((X0 > set @ X0))).
% 0.65/0.45 thf(func_def_34, type, set_or1361889807AtMost: !>[X0: $tType]:((X0 > X0 > set @ X0))).
% 0.65/0.45 thf(func_def_35, type, set_or578182835ssThan: !>[X0: $tType]:((X0 > X0 > set @ X0))).
% 0.65/0.45 thf(func_def_36, type, set_ord_lessThan: !>[X0: $tType]:((X0 > set @ X0))).
% 0.65/0.45 thf(func_def_37, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.65/0.45 thf(func_def_38, type, l1: set @ set @ a).
% 0.65/0.45 thf(func_def_39, type, l2: set @ set @ a).
% 0.65/0.45 thf(func_def_43, type, vAND: ($o > $o > $o)).
% 0.65/0.45 thf(func_def_44, type, db1: !>[X0: $tType]:(X0)).
% 0.65/0.45 thf(func_def_45, type, db0: !>[X0: $tType]:(X0)).
% 0.65/0.45 thf(func_def_46, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.65/0.45 thf(func_def_47, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.65/0.45 thf(func_def_48, type, vNOT: ($o > $o)).
% 0.65/0.45 thf(func_def_49, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.65/0.45 thf(func_def_50, type, vIMP: ($o > $o > $o)).
% 0.65/0.45 thf(func_def_51, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.65/0.45 thf(func_def_52, type, db3: !>[X0: $tType]:(X0)).
% 0.65/0.45 thf(func_def_53, type, db2: !>[X0: $tType]:(X0)).
% 0.65/0.45 thf(func_def_54, type, vOR: ($o > $o > $o)).
% 0.65/0.45 thf(func_def_55, type, sP0: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.65/0.45 thf(func_def_56, type, sP1: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.65/0.45 thf(func_def_57, type, sK2: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0))).
% 0.65/0.45 thf(func_def_58, type, sK3: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.65/0.45 thf(func_def_59, type, sK4: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.65/0.45 thf(func_def_60, type, sK5: !>[X0: $tType]:((X0 > X0))).
% 0.65/0.45 thf(func_def_61, type, sK6: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.65/0.45 thf(func_def_62, type, sK7: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.65/0.45 thf(func_def_63, type, sK8: !>[X0: $tType]:((X0 > X0))).
% 0.65/0.45 thf(func_def_64, type, sK9: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.65/0.45 thf(func_def_65, type, sK10: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.65/0.45 thf(func_def_66, type, sK11: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.65/0.45 thf(func_def_67, type, sK12: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.65/0.45 thf(func_def_68, type, sK13: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 0.65/0.45 thf(func_def_69, type, sK14: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.65/0.45 thf(func_def_70, type, sK15: !>[X0: $tType]:((X0 > X0))).
% 0.65/0.45 thf(func_def_71, type, sK16: !>[X0: $tType]:((X0 > X0))).
% 0.65/0.45 thf(func_def_72, type, sK17: !>[X0: $tType]:((X0 > X0))).
% 0.65/0.45 thf(func_def_73, type, sK18: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.65/0.45 thf(func_def_74, type, sK19: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.65/0.45 thf(func_def_75, type, sK20: !>[X0: $tType]:(((X0 > $o) > X0 > X0 > X0))).
% 0.65/0.45 thf(func_def_76, type, sK21: !>[X0: $tType]:((X0 > (X0 > $o) > X0 > X0))).
% 0.65/0.45 thf(func_def_77, type, sK22: !>[X0: $tType]:((X0 > X0))).
% 0.65/0.45 thf(func_def_78, type, sK23: !>[X0: $tType]:((X0 > X0))).
% 0.65/0.45 thf(func_def_79, type, sK24: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.65/0.45 thf(func_def_80, type, sK25: !>[X0: $tType]:((X0 > X0))).
% 0.65/0.45 thf(func_def_81, type, sK26: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.65/0.45 thf(func_def_82, type, sK27: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.65/0.45 thf(func_def_83, type, sK28: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0))).
% 0.65/0.45 thf(func_def_84, type, sK29: !>[X0: $tType]:((X0 > X0))).
% 0.65/0.45 thf(func_def_85, type, sK30: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.65/0.45 thf(func_def_86, type, sK31: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.65/0.45 thf(func_def_87, type, sK32: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.65/0.45 thf(func_def_88, type, sK33: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.65/0.45 thf(func_def_89, type, sK34: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.65/0.45 thf(func_def_90, type, sK35: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.65/0.45 thf(func_def_91, type, sK36: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.65/0.45 thf(func_def_92, type, sK37: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.65/0.45 thf(func_def_93, type, sK38: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.65/0.45 thf(func_def_94, type, sK39: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.65/0.45 thf(func_def_95, type, sK40: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.65/0.45 thf(func_def_96, type, sK41: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.65/0.45 thf(func_def_97, type, sK42: !>[X0: $tType]:((X0 > X0))).
% 0.65/0.45 thf(func_def_98, type, sK43: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.65/0.45 thf(func_def_99, type, sK44: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.65/0.45 thf(func_def_100, type, sK45: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0))).
% 0.65/0.45 thf(func_def_101, type, sK46: !>[X0: $tType]:((X0 > X0 > X0 > X0))).
% 0.65/0.45 thf(func_def_102, type, sK47: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.65/0.45 thf(func_def_103, type, sK48: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.65/0.45 thf(func_def_104, type, sK49: !>[X0: $tType, X1: $tType]:((X0 > X1))).
% 0.65/0.45 thf(func_def_105, type, sK50: !>[X0: $tType]:((X0 > X0))).
% 0.65/0.45 thf(func_def_106, type, sK51: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.65/0.45 thf(func_def_107, type, sK52: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.65/0.45 thf(func_def_108, type, sK53: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.65/0.45 thf(func_def_109, type, sK54: !>[X0: $tType]:((X0 > X0))).
% 0.65/0.45 thf(func_def_110, type, sK55: !>[X0: $tType]:((X0 > X0))).
% 0.65/0.45 thf(func_def_111, type, sK56: !>[X0: $tType]:((X0 > X0 > X0 > X0))).
% 0.65/0.45 thf(func_def_112, type, sK57: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.65/0.45 thf(func_def_113, type, sK58: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.65/0.45 thf(func_def_114, type, sK59: !>[X0: $tType]:((X0 > X0))).
% 0.65/0.45 thf(func_def_115, type, sK60: !>[X0: $tType]:((X0 > X0))).
% 0.65/0.45 thf(func_def_116, type, sK61: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0))).
% 0.65/0.45 thf(func_def_117, type, sK62: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.65/0.45 thf(func_def_118, type, sK63: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.65/0.45 thf(func_def_119, type, sK64: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.65/0.45 thf(func_def_120, type, sK65: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.65/0.45 thf(func_def_121, type, sK66: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.65/0.45 thf(func_def_122, type, sK67: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.65/0.45 thf(func_def_123, type, sK68: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.65/0.45 thf(func_def_124, type, sK69: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.65/0.45 thf(func_def_125, type, sK70: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.65/0.45 thf(func_def_126, type, sK71: !>[X0: $tType, X1: $tType]:((X0 > X1))).
% 0.65/0.45 thf(func_def_127, type, sK72: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.65/0.45 thf(func_def_128, type, sK73: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.65/0.45 thf(func_def_129, type, sK74: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.65/0.45 thf(func_def_130, type, sK75: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.65/0.45 thf(func_def_131, type, sK76: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.65/0.45 thf(f276,axiom,(
% 0.65/0.45 (gram_L608943123e_subs @ a @ l1 @ l2) & (gram_L608943123e_subs @ a @ l2 @ l1)),
% 0.65/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 0.65/0.45 thf(f277,conjecture,(
% 0.65/0.45 (gram_L608943123e_subs @ a @ l1 @ l2)),
% 0.65/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1)).
% 0.65/0.45 thf(f278,negated_conjecture,(
% 0.65/0.45 ~(gram_L608943123e_subs @ a @ l1 @ l2)),
% 0.65/0.45 inference(negated_conjecture,[status(cth)],[f277])).
% 0.65/0.45 thf(f442,plain,(
% 0.65/0.45 ~(gram_L608943123e_subs @ a @ l1 @ l2)),
% 0.65/0.45 inference(rectify,[],[f278])).
% 0.65/0.45 thf(f443,plain,(
% 0.65/0.45 ~ (((gram_L608943123e_subs @ a @ l1 @ l2)) = $true)),
% 0.65/0.45 inference(fool_elimination,[],[f442])).
% 0.65/0.45 thf(f482,plain,(
% 0.65/0.45 (gram_L608943123e_subs @ a @ l1 @ l2) & (gram_L608943123e_subs @ a @ l2 @ l1)),
% 0.65/0.45 inference(rectify,[],[f276])).
% 0.65/0.45 thf(f483,plain,(
% 0.65/0.45 (((gram_L608943123e_subs @ a @ l1 @ l2)) = $true) & (((gram_L608943123e_subs @ a @ l2 @ l1)) = $true)),
% 0.65/0.45 inference(fool_elimination,[],[f482])).
% 0.65/0.45 thf(f826,plain,(
% 0.65/0.45 (((gram_L608943123e_subs @ a @ l1 @ l2)) != $true)),
% 0.65/0.45 inference(flattening,[],[f443])).
% 0.65/0.45 thf(f1813,plain,(
% 0.65/0.45 (((gram_L608943123e_subs @ a @ l1 @ l2)) = $true)),
% 0.65/0.45 inference(cnf_transformation,[],[f483])).
% 0.65/0.45 thf(f1821,plain,(
% 0.65/0.45 (((gram_L608943123e_subs @ a @ l1 @ l2)) != $true)),
% 0.65/0.45 inference(cnf_transformation,[],[f826])).
% 0.65/0.45 thf(f2218,definition,(
% 0.65/0.45 spl77_6 <=> (((gram_L608943123e_subs @ a @ l1 @ l2)) = $true)),
% 0.65/0.45 introduced(definition,[new_symbols(definition,[spl77_6])],[avatar_definition])).
% 0.65/0.45 thf(f2221,plain,(
% 0.65/0.45 spl77_6),
% 0.65/0.45 inference(avatar_split_clause,[],[f1813,f2218])).
% 0.65/0.45 thf(f2232,plain,(
% 0.65/0.45 ~spl77_6),
% 0.65/0.45 inference(avatar_split_clause,[],[f1821,f2218])).
% 0.65/0.45 cnf(s7, plain, spl77_6, inference(sat_conversion,[],[f2221])).
% 0.65/0.45 cnf(s11, plain, ~spl77_6, inference(sat_conversion,[],[f2232])).
% 0.65/0.45 cnf(s16, plain, $false, inference(rat,[],[s7,s11])).
% 0.65/0.45 thf(f2248,plain,(
% 0.65/0.45 $false),
% 0.65/0.45 inference(avatar_sat_refutation,[],[s16])).
% 0.65/0.45 % SZS output end Proof for theBenchmark
% 0.65/0.45 % (1384173)------------------------------
% 0.65/0.45 % (1384173)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.45 % (1384173)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.45 % (1384173)CaDiCaL version: 2.1.3
% 0.65/0.45 % (1384173)Termination reason: Refutation
% 0.65/0.45 % (1384173)Time elapsed: 0.097 s
% 0.65/0.45 % (1384173)Peak memory usage: 14 MB
% 0.65/0.45 % (1384173)Instructions burned: 162 (million)
% 0.65/0.45 % (1384165)Success in time 0.15 s
% 0.65/0.45 % Vampire exiting
%------------------------------------------------------------------------------