%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP165^2 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 08:08:38 AM UTC 2026
% Result : Theorem 0.63s 0.37s
% Output : Refutation 0.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP165^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.17 % Computer : n020.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Sep 29 20:05:20 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 Running higher-order theorem proving
% 0.09/0.24 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.63/0.37 % (1525122)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.63/0.37 % (1525127)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2321609115:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.63/0.37 % (1525133)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.63/0.37 % (1525133)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
% 0.63/0.37 % (1525128)lrs+10_16_si=on:nwc=1.5:random_seed=387914411:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.63/0.37 % (1525129)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3606155088:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.63/0.37 % (1525132)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=613556525:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.63/0.37 % (1525131)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=239861237:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.63/0.37 % (1525130)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=1411232916: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)
% 0.63/0.37 % (1525133)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=1827086964:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.63/0.37 % (1525129)Instruction limit reached!
% 0.63/0.37 % (1525129)------------------------------
% 0.63/0.37 % (1525129)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.37 % (1525129)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.37 % (1525129)CaDiCaL version: 2.1.3
% 0.63/0.37 % (1525129)Termination reason: Instruction limit
% 0.63/0.37 % (1525129)Termination phase: shuffling
% 0.63/0.37 % (1525129)Time elapsed: 0.003 s
% 0.63/0.37 % (1525129)Peak memory usage: 10 MB
% 0.63/0.37 % (1525129)Instructions burned: 6 (million)
% 0.63/0.37 % (1525128)Instruction limit reached!
% 0.63/0.37 % (1525128)------------------------------
% 0.63/0.37 % (1525128)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.37 % (1525128)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.37 % (1525128)CaDiCaL version: 2.1.3
% 0.63/0.37 % (1525128)Termination reason: Instruction limit
% 0.63/0.37 % (1525128)Termination phase: Property scanning
% 0.63/0.37 % (1525128)Time elapsed: 0.009 s
% 0.63/0.37 % (1525128)Peak memory usage: 10 MB
% 0.63/0.37 % (1525128)Instructions burned: 19 (million)
% 0.63/0.37 % (1525131)Instruction limit reached!
% 0.63/0.37 % (1525131)------------------------------
% 0.63/0.37 % (1525131)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.37 % (1525131)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.37 % (1525131)CaDiCaL version: 2.1.3
% 0.63/0.37 % (1525131)Termination reason: Instruction limit
% 0.63/0.37 % (1525131)Termination phase: Preprocessing 1
% 0.63/0.37 % (1525131)Time elapsed: 0.012 s
% 0.63/0.37 % (1525131)Peak memory usage: 10 MB
% 0.63/0.37 % (1525131)Instructions burned: 26 (million)
% 0.63/0.37 % (1525127)Instruction limit reached!
% 0.63/0.37 % (1525127)------------------------------
% 0.63/0.37 % (1525127)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.37 % (1525127)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.37 % (1525127)CaDiCaL version: 2.1.3
% 0.63/0.37 % (1525127)Termination reason: Instruction limit
% 0.63/0.37 % (1525127)Termination phase: Saturation
% 0.63/0.37 % (1525127)Time elapsed: 0.022 s
% 0.63/0.37 % (1525127)Peak memory usage: 13 MB
% 0.63/0.37 % (1525127)Instructions burned: 88 (million)
% 0.63/0.37 % (1525144)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=3755321488:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.63/0.37 % (1525141)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2599317758:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.63/0.37 % (1525143)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.63/0.37 % (1525144)Instruction limit reached!
% 0.63/0.37 % (1525144)------------------------------
% 0.63/0.37 % (1525144)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.37 % (1525144)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.37 % (1525144)CaDiCaL version: 2.1.3
% 0.63/0.37 % (1525144)Termination reason: Instruction limit
% 0.63/0.37 % (1525144)Termination phase: Property scanning
% 0.63/0.37 % (1525144)Time elapsed: 0.004 s
% 0.63/0.37 % (1525144)Peak memory usage: 10 MB
% 0.63/0.37 % (1525144)Instructions burned: 16 (million)
% 0.63/0.37 % (1525141)Instruction limit reached!
% 0.63/0.37 % (1525141)------------------------------
% 0.63/0.37 % (1525141)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.37 % (1525141)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.37 % (1525141)CaDiCaL version: 2.1.3
% 0.63/0.37 % (1525141)Termination reason: Instruction limit
% 0.63/0.37 % (1525141)Termination phase: shuffling
% 0.63/0.37 % (1525141)Time elapsed: 0.003 s
% 0.63/0.37 % (1525141)Peak memory usage: 10 MB
% 0.63/0.37 % (1525141)Instructions burned: 5 (million)
% 0.63/0.37 % (1525143)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3435330967:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.63/0.37 % (1525142)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1948458917:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.63/0.37 % (1525143)Instruction limit reached!
% 0.63/0.37 % (1525143)------------------------------
% 0.63/0.37 % (1525143)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.37 % (1525143)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.37 % (1525143)CaDiCaL version: 2.1.3
% 0.63/0.37 % (1525143)Termination reason: Instruction limit
% 0.63/0.37 % (1525143)Termination phase: shuffling
% 0.63/0.37 % (1525143)Time elapsed: 0.003 s
% 0.63/0.37 % (1525143)Peak memory usage: 10 MB
% 0.63/0.37 % (1525143)Instructions burned: 7 (million)
% 0.63/0.37 % (1525132)Instruction limit reached!
% 0.63/0.37 % (1525132)------------------------------
% 0.63/0.37 % (1525132)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.37 % (1525132)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.37 % (1525132)CaDiCaL version: 2.1.3
% 0.63/0.37 % (1525132)Termination reason: Instruction limit
% 0.63/0.37 % (1525132)Termination phase: Property scanning
% 0.63/0.37 % (1525132)Time elapsed: 0.037 s
% 0.63/0.37 % (1525132)Peak memory usage: 12 MB
% 0.63/0.37 % (1525132)Instructions burned: 76 (million)
% 0.63/0.37 % (1525147)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
% 0.63/0.37 % (1525147)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.63/0.37 % (1525142)Instruction limit reached!
% 0.63/0.37 % (1525142)------------------------------
% 0.63/0.37 % (1525142)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.37 % (1525142)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.37 % (1525142)CaDiCaL version: 2.1.3
% 0.63/0.37 % (1525142)Termination reason: Instruction limit
% 0.63/0.37 % (1525142)Termination phase: shuffling
% 0.63/0.37 % (1525142)Time elapsed: 0.006 s
% 0.63/0.37 % (1525142)Peak memory usage: 10 MB
% 0.63/0.37 % (1525142)Instructions burned: 5 (million)
% 0.63/0.37 % (1525147)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1209583751:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.63/0.37 % (1525147)Instruction limit reached!
% 0.63/0.37 % (1525147)------------------------------
% 0.63/0.37 % (1525147)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.37 % (1525147)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.37 % (1525147)CaDiCaL version: 2.1.3
% 0.63/0.37 % (1525147)Termination reason: Instruction limit
% 0.63/0.37 % (1525147)Termination phase: Property scanning
% 0.63/0.37 % (1525147)Time elapsed: 0.007 s
% 0.63/0.37 % (1525147)Peak memory usage: 10 MB
% 0.63/0.37 % (1525147)Instructions burned: 31 (million)
% 0.63/0.37 % (1525148)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=3604215838:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.63/0.37 % (1525154)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=1402986818:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.63/0.37 % (1525151)lrs+10_1_si=on:cs=on:random_seed=3901197614:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.63/0.37 % (1525153)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.63/0.37 % (1525151)Instruction limit reached!
% 0.63/0.37 % (1525151)------------------------------
% 0.63/0.37 % (1525151)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.37 % (1525151)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.37 % (1525151)CaDiCaL version: 2.1.3
% 0.63/0.37 % (1525151)Termination reason: Instruction limit
% 0.63/0.37 % (1525151)Termination phase: shuffling
% 0.63/0.37 % (1525151)Time elapsed: 0.005 s
% 0.63/0.37 % (1525151)Peak memory usage: 10 MB
% 0.63/0.37 % (1525151)Instructions burned: 9 (million)
% 0.63/0.37 % (1525130) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1525122-1525130"...
% 0.63/0.37 % (1525154)Instruction limit reached!
% 0.63/0.37 % (1525154)------------------------------
% 0.63/0.37 % (1525154)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.37 % (1525154)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.37 % (1525154)CaDiCaL version: 2.1.3
% 0.63/0.37 % (1525154)Termination reason: Instruction limit
% 0.63/0.37 % (1525154)Termination phase: Property scanning
% 0.63/0.37 % (1525154)Time elapsed: 0.010 s
% 0.63/0.37 % (1525154)Peak memory usage: 11 MB
% 0.63/0.37 % (1525154)Instructions burned: 38 (million)
% 0.63/0.37 % (1525153)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=2459246107:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.63/0.37 % (1525130)...printing done.
% 0.63/0.37 % (1525130)Refutation found. Thanks to Tanya!
% 0.63/0.37 % SZS status Theorem for theBenchmark
% 0.63/0.37 % SZS output start Proof for theBenchmark
% 0.63/0.37 thf(type_def_5, type, refine1665802226e_nres: $tType > $tType).
% 0.63/0.37 thf(type_def_6, type, product_unit: $tType).
% 0.63/0.37 thf(type_def_7, type, set: $tType > $tType).
% 0.63/0.37 thf(type_def_8, type, a: $tType).
% 0.63/0.37 thf(type_def_9, type, sTfun: ($tType * $tType) > $tType).
% 0.63/0.37 thf(func_def_0, type, type: !>[X0: $tType]:($o)).
% 0.63/0.37 thf(func_def_1, type, bot: !>[X0: $tType]:($o)).
% 0.63/0.37 thf(func_def_2, type, ord: !>[X0: $tType]:($o)).
% 0.63/0.37 thf(func_def_3, type, top: !>[X0: $tType]:($o)).
% 0.63/0.37 thf(func_def_4, type, order: !>[X0: $tType]:($o)).
% 0.63/0.37 thf(func_def_5, type, group_add: !>[X0: $tType]:($o)).
% 0.63/0.37 thf(func_def_6, type, linorder: !>[X0: $tType]:($o)).
% 0.63/0.37 thf(func_def_7, type, preorder: !>[X0: $tType]:($o)).
% 0.63/0.37 thf(func_def_8, type, order_bot: !>[X0: $tType]:($o)).
% 0.63/0.37 thf(func_def_9, type, order_top: !>[X0: $tType]:($o)).
% 0.63/0.37 thf(func_def_10, type, boolean_algebra: !>[X0: $tType]:($o)).
% 0.63/0.37 thf(func_def_11, type, ordered_ab_group_add: !>[X0: $tType]:($o)).
% 0.63/0.37 thf(func_def_12, type, comple187826305attice: !>[X0: $tType]:($o)).
% 0.63/0.37 thf(func_def_13, type, uminus_uminus: !>[X0: $tType]:((X0 > X0))).
% 0.63/0.37 thf(func_def_14, type, if: !>[X0: $tType]:(($o > X0 > X0 > X0))).
% 0.63/0.37 thf(func_def_15, type, bot_bot: !>[X0: $tType]:(X0)).
% 0.63/0.37 thf(func_def_16, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.63/0.37 thf(func_def_17, type, order_Greatest: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.63/0.37 thf(func_def_18, type, top_top: !>[X0: $tType]:(X0)).
% 0.63/0.37 thf(func_def_19, type, partial_flat_ord: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.63/0.37 thf(func_def_20, type, refine1946708059ASSUME: ($o > refine1665802226e_nres @ product_unit)).
% 0.63/0.37 thf(func_def_21, type, refine1687780735RETURN: !>[X0: $tType]:((X0 > refine1665802226e_nres @ X0))).
% 0.63/0.37 thf(func_def_22, type, refine463715084e_bind: !>[X0: $tType, X1: $tType]:((refine1665802226e_nres @ X0 > (X0 > refine1665802226e_nres @ X1) > refine1665802226e_nres @ X1))).
% 0.63/0.37 thf(func_def_23, type, refine1315500908_inres: !>[X0: $tType]:((refine1665802226e_nres @ X0 > X0 > $o))).
% 0.63/0.37 thf(func_def_24, type, refine406925620_inres: !>[X0: $tType]:((refine1665802226e_nres @ X0 > X0 > $o))).
% 0.63/0.37 thf(func_def_25, type, refine1102455758nofail: !>[X0: $tType]:((refine1665802226e_nres @ X0 > $o))).
% 0.63/0.37 thf(func_def_26, type, refine1767639642_FAILi: !>[X0: $tType]:(refine1665802226e_nres @ X0)).
% 0.63/0.37 thf(func_def_27, type, refine605929679le_RES: !>[X0: $tType]:((set @ X0 > refine1665802226e_nres @ X0))).
% 0.63/0.37 thf(func_def_28, type, refine60818195e_nres: !>[X0: $tType, X1: $tType]:((X0 > (set @ X1 > X0) > refine1665802226e_nres @ X1 > X0))).
% 0.63/0.37 thf(func_def_29, type, refine1442219249c_nres: !>[X0: $tType, X1: $tType]:((X0 > (set @ X1 > X0) > refine1665802226e_nres @ X1 > X0))).
% 0.63/0.37 thf(func_def_30, type, refine1672542526he_RES: !>[X0: $tType]:((refine1665802226e_nres @ X0 > set @ X0))).
% 0.63/0.37 thf(func_def_31, type, refine_strict: !>[X0: $tType, X1: $tType]:(((X0 > X1) > $o))).
% 0.63/0.37 thf(func_def_32, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.63/0.37 thf(func_def_33, type, insert: !>[X0: $tType]:((X0 > set @ X0 > set @ X0))).
% 0.63/0.37 thf(func_def_34, type, is_empty: !>[X0: $tType]:((set @ X0 > $o))).
% 0.63/0.37 thf(func_def_35, type, is_singleton: !>[X0: $tType]:((set @ X0 > $o))).
% 0.63/0.37 thf(func_def_36, type, the_elem: !>[X0: $tType]:((set @ X0 > X0))).
% 0.63/0.37 thf(func_def_37, type, set_atLeast: !>[X0: $tType]:(((X0 > X0 > $o) > X0 > set @ X0))).
% 0.63/0.37 thf(func_def_38, type, set_atLeastAtMost: !>[X0: $tType]:(((X0 > X0 > $o) > X0 > X0 > set @ X0))).
% 0.63/0.37 thf(func_def_39, type, set_atMost: !>[X0: $tType]:(((X0 > X0 > $o) > X0 > set @ X0))).
% 0.63/0.37 thf(func_def_40, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.63/0.37 thf(func_def_41, type, s1: refine1665802226e_nres @ a).
% 0.63/0.37 thf(func_def_42, type, s2: refine1665802226e_nres @ a).
% 0.63/0.37 thf(func_def_43, type, phi: (a > $o)).
% 0.63/0.37 thf(func_def_44, type, b: $o).
% 0.63/0.37 thf(func_def_48, type, vAND: ($o > $o > $o)).
% 0.63/0.37 thf(func_def_49, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.63/0.37 thf(func_def_50, type, db2: !>[X0: $tType]:(X0)).
% 0.63/0.37 thf(func_def_51, type, db0: !>[X0: $tType]:(X0)).
% 0.63/0.37 thf(func_def_52, type, db1: !>[X0: $tType]:(X0)).
% 0.63/0.37 thf(func_def_53, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.63/0.37 thf(func_def_54, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.63/0.37 thf(func_def_55, type, vIMP: ($o > $o > $o)).
% 0.63/0.37 thf(func_def_56, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.63/0.37 thf(func_def_57, type, vNOT: ($o > $o)).
% 0.63/0.37 thf(func_def_58, type, sP0: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.63/0.37 thf(func_def_59, type, sP1: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.63/0.37 thf(func_def_60, type, sP2: !>[X0: $tType]:((refine1665802226e_nres @ X0 > $o > refine1665802226e_nres @ X0 > $o))).
% 0.63/0.37 thf(func_def_61, type, sK3: !>[X0: $tType]:(((X0 > $o) > set @ X0 > X0))).
% 0.63/0.37 thf(func_def_62, type, sK4: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.63/0.37 thf(func_def_63, type, sK5: !>[X0: $tType]:((set @ X0 > X0))).
% 0.63/0.37 thf(func_def_64, type, sK6: !>[X0: $tType]:((set @ X0 > X0))).
% 0.63/0.37 thf(func_def_65, type, sK7: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.63/0.37 thf(func_def_66, type, sK8: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.63/0.37 thf(func_def_67, type, sK9: !>[X0: $tType, X1: $tType]:(((X1 > refine1665802226e_nres @ X0) > refine1665802226e_nres @ X0 > refine1665802226e_nres @ X1 > X1))).
% 0.63/0.37 thf(func_def_68, type, sK10: !>[X0: $tType]:(((X0 > $o) > set @ X0 > X0))).
% 0.63/0.37 thf(func_def_69, type, sK11: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 0.63/0.37 thf(func_def_70, type, sK12: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.63/0.37 thf(func_def_71, type, sK13: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.63/0.37 thf(func_def_72, type, sK14: !>[X0: $tType]:(((refine1665802226e_nres @ X0 > $o) > set @ X0))).
% 0.63/0.37 thf(func_def_73, type, sK15: !>[X0: $tType]:((refine1665802226e_nres @ X0 > set @ X0))).
% 0.63/0.37 thf(func_def_74, type, sK16: !>[X0: $tType]:((refine1665802226e_nres @ X0 > refine1665802226e_nres @ X0 > set @ X0))).
% 0.63/0.37 thf(func_def_75, type, sK17: !>[X0: $tType]:((refine1665802226e_nres @ X0 > refine1665802226e_nres @ X0 > set @ X0))).
% 0.63/0.37 thf(func_def_76, type, sK18: !>[X0: $tType]:((X0 > set @ X0 > set @ X0))).
% 0.63/0.37 thf(func_def_77, type, sK19: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.63/0.37 thf(func_def_78, type, sK20: !>[X0: $tType]:((refine1665802226e_nres @ X0 > refine1665802226e_nres @ X0 > X0))).
% 0.63/0.37 thf(func_def_79, type, sK21: !>[X0: $tType]:((refine1665802226e_nres @ X0 > refine1665802226e_nres @ X0 > set @ X0))).
% 0.63/0.37 thf(func_def_80, type, sK22: !>[X0: $tType]:((refine1665802226e_nres @ X0 > refine1665802226e_nres @ X0 > set @ X0))).
% 0.63/0.37 thf(func_def_81, type, sK23: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.63/0.37 thf(func_def_82, type, sK24: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.63/0.37 thf(func_def_83, type, sK25: !>[X0: $tType, X1: $tType]:((refine1665802226e_nres @ X1 > (X1 > refine1665802226e_nres @ X0) > X1))).
% 0.63/0.37 thf(func_def_84, type, sK26: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > X1) > X0))).
% 0.63/0.37 thf(func_def_85, type, sK27: !>[X0: $tType]:((refine1665802226e_nres @ X0 > refine1665802226e_nres @ X0 > X0))).
% 0.63/0.37 thf(func_def_86, type, sK28: !>[X0: $tType, X1: $tType]:((refine1665802226e_nres @ X1 > refine1665802226e_nres @ X0 > (X1 > refine1665802226e_nres @ X0) > X1))).
% 0.63/0.37 thf(func_def_87, type, sK29: !>[X0: $tType]:((set @ X0 > X0))).
% 0.63/0.37 thf(func_def_88, type, sK30: !>[X0: $tType]:((set @ X0 > X0))).
% 0.63/0.37 thf(func_def_89, type, sK31: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.63/0.37 thf(func_def_90, type, sK32: !>[X0: $tType]:((X0 > set @ X0 > set @ X0 > X0 > set @ X0))).
% 0.63/0.37 thf(func_def_91, type, sK33: !>[X0: $tType]:((refine1665802226e_nres @ X0 > X0))).
% 0.63/0.37 thf(func_def_92, type, sK34: !>[X0: $tType]:((refine1665802226e_nres @ X0 > refine1665802226e_nres @ X0 > X0))).
% 0.63/0.37 thf(func_def_93, type, sK35: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > X1) > X0))).
% 0.63/0.37 thf(func_def_94, type, sK36: !>[X0: $tType]:((set @ X0 > X0))).
% 0.63/0.37 thf(func_def_95, type, sK37: !>[X0: $tType]:(((refine1665802226e_nres @ X0 > refine1665802226e_nres @ X0 > $o) > refine1665802226e_nres @ X0))).
% 0.63/0.37 thf(func_def_96, type, sK38: !>[X0: $tType]:(((refine1665802226e_nres @ X0 > refine1665802226e_nres @ X0 > $o) > set @ X0))).
% 0.63/0.37 thf(func_def_97, type, sK39: !>[X0: $tType]:(((refine1665802226e_nres @ X0 > refine1665802226e_nres @ X0 > $o) > set @ X0))).
% 0.63/0.37 thf(func_def_98, type, sK40: !>[X0: $tType]:(((refine1665802226e_nres @ X0 > refine1665802226e_nres @ X0 > $o) > set @ X0))).
% 0.63/0.37 thf(func_def_99, type, sK41: !>[X0: $tType]:((set @ X0 > X0))).
% 0.63/0.37 thf(func_def_100, type, sK42: !>[X0: $tType, X1: $tType]:(((X1 > refine1665802226e_nres @ X0) > (X1 > refine1665802226e_nres @ X0) > X1))).
% 0.63/0.37 thf(func_def_101, type, sK43: !>[X0: $tType]:(((refine1665802226e_nres @ X0 > refine1665802226e_nres @ X0 > $o) > set @ X0))).
% 0.63/0.37 thf(func_def_102, type, sK44: !>[X0: $tType]:(((refine1665802226e_nres @ X0 > refine1665802226e_nres @ X0 > $o) > set @ X0))).
% 0.63/0.37 thf(func_def_103, type, sK45: !>[X0: $tType]:(((refine1665802226e_nres @ X0 > refine1665802226e_nres @ X0 > $o) > set @ X0))).
% 0.63/0.37 thf(func_def_104, type, sK46: !>[X0: $tType]:(((refine1665802226e_nres @ X0 > refine1665802226e_nres @ X0 > $o) > refine1665802226e_nres @ X0))).
% 0.63/0.37 thf(func_def_105, type, sK47: !>[X0: $tType]:((refine1665802226e_nres @ X0 > $o > refine1665802226e_nres @ X0 > set @ X0))).
% 0.63/0.37 thf(func_def_106, type, sK48: !>[X0: $tType]:((refine1665802226e_nres @ X0 > $o > refine1665802226e_nres @ X0 > set @ X0))).
% 0.63/0.37 thf(func_def_107, type, sK49: !>[X0: $tType]:((refine1665802226e_nres @ X0 > set @ X0))).
% 0.63/0.37 thf(func_def_108, type, sK50: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.63/0.37 thf(func_def_109, type, sK51: !>[X0: $tType]:((refine1665802226e_nres @ X0 > refine1665802226e_nres @ X0 > X0))).
% 0.63/0.37 thf(func_def_110, type, sK52: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.63/0.37 thf(func_def_111, type, sK53: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.63/0.37 thf(func_def_112, type, sK54: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.63/0.37 thf(func_def_113, type, sK55: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.63/0.37 thf(func_def_114, type, sK56: !>[X0: $tType]:((set @ X0 > X0))).
% 0.63/0.37 thf(func_def_115, type, sK57: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.63/0.37 thf(func_def_116, type, sK58: !>[X0: $tType, X1: $tType]:((refine1665802226e_nres @ X1 > (X1 > refine1665802226e_nres @ X0) > (X1 > refine1665802226e_nres @ X0) > X1))).
% 0.63/0.37 thf(func_def_117, type, sK59: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.63/0.37 thf(func_def_118, type, sK60: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.63/0.37 thf(func_def_119, type, sK61: !>[X0: $tType]:((X0 > (X0 > $o) > X0))).
% 0.63/0.37 thf(func_def_120, type, sK62: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.63/0.37 thf(func_def_121, type, sK63: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.63/0.37 thf(func_def_122, type, sK64: !>[X0: $tType]:(((X0 > $o) > X0 > X0))).
% 0.63/0.37 thf(func_def_123, type, sK65: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.63/0.37 thf(func_def_124, type, sK66: !>[X0: $tType]:((set @ X0 > X0))).
% 0.63/0.37 thf(func_def_125, type, sK67: !>[X0: $tType, X1: $tType]:((refine1665802226e_nres @ X1 > (X1 > refine1665802226e_nres @ X0) > (X1 > refine1665802226e_nres @ X0) > X1))).
% 0.63/0.37 thf(func_def_126, type, sK68: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.63/0.37 thf(func_def_127, type, sK69: !>[X0: $tType]:((refine1665802226e_nres @ X0 > refine1665802226e_nres @ X0 > X0))).
% 0.63/0.37 thf(func_def_128, type, sK70: !>[X0: $tType]:((X0 > set @ X0 > set @ X0))).
% 0.63/0.37 thf(func_def_129, type, sK71: !>[X0: $tType, X1: $tType, X2: $tType]:(((X1 > X0) > (X2 > X0) > (X1 > X2) > X1))).
% 0.63/0.37 thf(func_def_130, type, sK72: !>[X0: $tType]:((refine1665802226e_nres @ X0 > set @ X0))).
% 0.63/0.37 thf(func_def_131, type, sK73: !>[X0: $tType]:((set @ X0 > X0))).
% 0.63/0.37 thf(func_def_132, type, sK74: !>[X0: $tType]:((refine1665802226e_nres @ X0 > set @ X0))).
% 0.63/0.37 thf(func_def_133, type, sK75: !>[X0: $tType]:(((refine1665802226e_nres @ X0 > refine1665802226e_nres @ X0 > $o) > refine1665802226e_nres @ X0))).
% 0.63/0.37 thf(func_def_134, type, sK76: !>[X0: $tType]:(((refine1665802226e_nres @ X0 > refine1665802226e_nres @ X0 > $o) > set @ X0))).
% 0.63/0.37 thf(func_def_135, type, sK77: !>[X0: $tType]:(((refine1665802226e_nres @ X0 > refine1665802226e_nres @ X0 > $o) > set @ X0))).
% 0.63/0.37 thf(func_def_136, type, sK78: !>[X0: $tType]:(((refine1665802226e_nres @ X0 > refine1665802226e_nres @ X0 > $o) > set @ X0))).
% 0.63/0.37 thf(func_def_138, type, inv_refine605929679le_RES_80: !>[X0: $tType]:((refine1665802226e_nres @ X0 > set @ X0))).
% 0.63/0.37 thf(f302,axiom,(
% 0.63/0.37 ! [X0 : $tType,X2 : X0,X1 : X0] : (X2 = ((if @ X0 @ $false @ X1 @ X2)))),
% 0.63/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_T)).
% 0.63/0.37 thf(f303,axiom,(
% 0.63/0.37 ! [X0 : $tType,X1 : X0,X2 : X0] : (X1 = ((if @ X0 @ $true @ X1 @ X2)))),
% 0.63/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_T)).
% 0.63/0.37 thf(f304,axiom,(
% 0.63/0.37 b => (ord_less_eq @ refine1665802226e_nres @ a @ s1 @ (refine605929679le_RES @ a @ (collect @ a @ phi)))),
% 0.63/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 0.63/0.37 thf(f305,axiom,(
% 0.63/0.37 ~b => (ord_less_eq @ refine1665802226e_nres @ a @ s2 @ (refine605929679le_RES @ a @ (collect @ a @ phi)))),
% 0.63/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1)).
% 0.63/0.37 thf(f306,conjecture,(
% 0.63/0.37 (ord_less_eq @ refine1665802226e_nres @ a @ (if @ refine1665802226e_nres @ a @ b @ s1 @ s2) @ (refine605929679le_RES @ a @ (collect @ a @ phi)))),
% 0.63/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2)).
% 0.63/0.37 thf(f307,negated_conjecture,(
% 0.63/0.37 ~(ord_less_eq @ refine1665802226e_nres @ a @ (if @ refine1665802226e_nres @ a @ b @ s1 @ s2) @ (refine605929679le_RES @ a @ (collect @ a @ phi)))),
% 0.63/0.37 inference(negated_conjecture,[status(cth)],[f306])).
% 0.63/0.37 thf(f316,plain,(
% 0.63/0.37 ~b => (ord_less_eq @ refine1665802226e_nres @ a @ s2 @ (refine605929679le_RES @ a @ (collect @ a @ phi)))),
% 0.63/0.37 inference(rectify,[],[f305])).
% 0.63/0.37 thf(f317,plain,(
% 0.63/0.37 ~ (b = $true) => (((ord_less_eq @ refine1665802226e_nres @ a @ s2 @ (refine605929679le_RES @ a @ (collect @ a @ phi)))) = $true)),
% 0.63/0.37 inference(fool_elimination,[],[f316])).
% 0.63/0.37 thf(f442,plain,(
% 0.63/0.37 b => (ord_less_eq @ refine1665802226e_nres @ a @ s1 @ (refine605929679le_RES @ a @ (collect @ a @ phi)))),
% 0.63/0.37 inference(rectify,[],[f304])).
% 0.63/0.37 thf(f443,plain,(
% 0.63/0.37 (b = $true) => (((ord_less_eq @ refine1665802226e_nres @ a @ s1 @ (refine605929679le_RES @ a @ (collect @ a @ phi)))) = $true)),
% 0.63/0.37 inference(fool_elimination,[],[f442])).
% 0.63/0.37 thf(f598,plain,(
% 0.63/0.37 ! [X0 : $tType,X1 : X0,X2 : X0] : (X1 = ((if @ X0 @ $true @ X1 @ X2)))),
% 0.63/0.37 inference(rectify,[],[f303])).
% 0.63/0.37 thf(f599,plain,(
% 0.63/0.37 ! [X0 : $tType,X2 : X0,X1 : X0] : (((if @ X0 @ $true @ X1 @ X2)) = X1)),
% 0.63/0.37 inference(fool_elimination,[],[f598])).
% 0.63/0.37 thf(f754,plain,(
% 0.63/0.37 ! [X0 : $tType,X1 : X0,X2 : X0] : (X1 = ((if @ X0 @ $false @ X2 @ X1)))),
% 0.63/0.37 inference(rectify,[],[f302])).
% 0.63/0.37 thf(f755,plain,(
% 0.63/0.37 ! [X0 : $tType,X1 : X0,X2 : X0] : (((if @ X0 @ $false @ X2 @ X1)) = X1)),
% 0.63/0.37 inference(fool_elimination,[],[f754])).
% 0.63/0.37 thf(f790,plain,(
% 0.63/0.37 ~(ord_less_eq @ refine1665802226e_nres @ a @ (if @ refine1665802226e_nres @ a @ b @ s1 @ s2) @ (refine605929679le_RES @ a @ (collect @ a @ phi)))),
% 0.63/0.37 inference(rectify,[],[f307])).
% 0.63/0.37 thf(f791,plain,(
% 0.63/0.37 ~ (((ord_less_eq @ refine1665802226e_nres @ a @ (if @ refine1665802226e_nres @ a @ b @ s1 @ s2) @ (refine605929679le_RES @ a @ (collect @ a @ phi)))) = $true)),
% 0.63/0.37 inference(fool_elimination,[],[f790])).
% 0.63/0.37 thf(f799,plain,(
% 0.63/0.37 (b != $true) => (((ord_less_eq @ refine1665802226e_nres @ a @ s2 @ (refine605929679le_RES @ a @ (collect @ a @ phi)))) = $true)),
% 0.63/0.37 inference(flattening,[],[f317])).
% 0.63/0.37 thf(f849,plain,(
% 0.63/0.37 (((ord_less_eq @ refine1665802226e_nres @ a @ (if @ refine1665802226e_nres @ a @ b @ s1 @ s2) @ (refine605929679le_RES @ a @ (collect @ a @ phi)))) != $true)),
% 0.63/0.37 inference(flattening,[],[f791])).
% 0.63/0.37 thf(f943,plain,(
% 0.63/0.37 (((ord_less_eq @ refine1665802226e_nres @ a @ s1 @ (refine605929679le_RES @ a @ (collect @ a @ phi)))) = $true) | (b != $true)),
% 0.63/0.37 inference(ennf_transformation,[],[f443])).
% 0.63/0.37 thf(f1051,plain,(
% 0.63/0.37 (((ord_less_eq @ refine1665802226e_nres @ a @ s2 @ (refine605929679le_RES @ a @ (collect @ a @ phi)))) = $true) | (b = $true)),
% 0.63/0.37 inference(ennf_transformation,[],[f799])).
% 0.63/0.37 thf(f1169,plain,(
% 0.63/0.37 ! [X0 : $tType,X1 : X0,X2 : X0] : (((if @ X0 @ $true @ X2 @ X1)) = X2)),
% 0.63/0.37 inference(rectify,[],[f599])).
% 0.63/0.37 thf(f1350,plain,(
% 0.63/0.37 (((ord_less_eq @ refine1665802226e_nres @ a @ s1 @ (refine605929679le_RES @ a @ (collect @ a @ phi)))) = $true) | (b != $true)),
% 0.63/0.37 inference(cnf_transformation,[],[f943])).
% 0.63/0.37 thf(f1414,plain,(
% 0.63/0.37 (((ord_less_eq @ refine1665802226e_nres @ a @ s2 @ (refine605929679le_RES @ a @ (collect @ a @ phi)))) = $true) | (b = $true)),
% 0.63/0.37 inference(cnf_transformation,[],[f1051])).
% 0.63/0.37 thf(f1512,plain,(
% 0.63/0.37 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((((if @ X0 @ $false @ X2 @ X1)) = X1)) )),
% 0.63/0.37 inference(cnf_transformation,[],[f755])).
% 0.63/0.37 thf(f1531,plain,(
% 0.63/0.37 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((((if @ X0 @ $true @ X2 @ X1)) = X2)) )),
% 0.63/0.37 inference(cnf_transformation,[],[f1169])).
% 0.63/0.37 thf(f1726,plain,(
% 0.63/0.37 (((ord_less_eq @ refine1665802226e_nres @ a @ (if @ refine1665802226e_nres @ a @ b @ s1 @ s2) @ (refine605929679le_RES @ a @ (collect @ a @ phi)))) != $true)),
% 0.63/0.37 inference(cnf_transformation,[],[f849])).
% 0.63/0.37 thf(f1973,definition,(
% 0.63/0.37 spl79_13 <=> (((ord_less_eq @ refine1665802226e_nres @ a @ (if @ refine1665802226e_nres @ a @ b @ s1 @ s2) @ (refine605929679le_RES @ a @ (collect @ a @ phi)))) = $true)),
% 0.63/0.37 introduced(definition,[new_symbols(definition,[spl79_13])],[avatar_definition])).
% 0.63/0.37 thf(f1975,plain,(
% 0.63/0.37 (((ord_less_eq @ refine1665802226e_nres @ a @ (if @ refine1665802226e_nres @ a @ b @ s1 @ s2) @ (refine605929679le_RES @ a @ (collect @ a @ phi)))) != $true) | spl79_13),
% 0.63/0.37 inference(avatar_component_clause,[],[f1973])).
% 0.63/0.37 thf(f1976,plain,(
% 0.63/0.37 ~spl79_13),
% 0.63/0.37 inference(avatar_split_clause,[],[f1726,f1973])).
% 0.63/0.37 thf(f1983,definition,(
% 0.63/0.37 spl79_15 <=> (((ord_less_eq @ refine1665802226e_nres @ a @ s2 @ (refine605929679le_RES @ a @ (collect @ a @ phi)))) = $true)),
% 0.63/0.37 introduced(definition,[new_symbols(definition,[spl79_15])],[avatar_definition])).
% 0.63/0.37 thf(f1987,definition,(
% 0.63/0.37 spl79_16 <=> (b = $true)),
% 0.63/0.37 introduced(definition,[new_symbols(definition,[spl79_16])],[avatar_definition])).
% 0.63/0.37 thf(f1988,plain,(
% 0.63/0.37 (b != $true) | spl79_16),
% 0.63/0.37 inference(avatar_component_clause,[],[f1987])).
% 0.63/0.37 thf(f1989,plain,(
% 0.63/0.37 (b = $true) | ~spl79_16),
% 0.63/0.37 inference(avatar_component_clause,[],[f1987])).
% 0.63/0.37 thf(f1990,plain,(
% 0.63/0.37 spl79_15 | spl79_16),
% 0.63/0.37 inference(avatar_split_clause,[],[f1414,f1987,f1983])).
% 0.63/0.37 thf(f2022,definition,(
% 0.63/0.37 spl79_23 <=> (((ord_less_eq @ refine1665802226e_nres @ a @ s1 @ (refine605929679le_RES @ a @ (collect @ a @ phi)))) = $true)),
% 0.63/0.37 introduced(definition,[new_symbols(definition,[spl79_23])],[avatar_definition])).
% 0.63/0.37 thf(f2025,plain,(
% 0.63/0.37 spl79_23 | ~spl79_16),
% 0.63/0.37 inference(avatar_split_clause,[],[f1350,f1987,f2022])).
% 0.63/0.37 thf(f2039,definition,(
% 0.63/0.37 spl79_26 <=> ($true = ((ord_less_eq @ refine1665802226e_nres @ a @ (if @ refine1665802226e_nres @ a @ $true @ s1 @ s2) @ (refine605929679le_RES @ a @ (collect @ a @ phi)))))),
% 0.63/0.37 introduced(definition,[new_symbols(definition,[spl79_26])],[avatar_definition])).
% 0.63/0.37 thf(f2041,plain,(
% 0.63/0.37 ($true != ((ord_less_eq @ refine1665802226e_nres @ a @ (if @ refine1665802226e_nres @ a @ $true @ s1 @ s2) @ (refine605929679le_RES @ a @ (collect @ a @ phi))))) | spl79_26),
% 0.63/0.37 inference(avatar_component_clause,[],[f2039])).
% 0.63/0.37 thf(f2043,definition,(
% 0.63/0.37 spl79_27 <=> (b = $false)),
% 0.63/0.37 introduced(definition,[new_symbols(definition,[spl79_27])],[avatar_definition])).
% 0.63/0.37 thf(f2044,plain,(
% 0.63/0.37 (b != $false) | spl79_27),
% 0.63/0.37 inference(avatar_component_clause,[],[f2043])).
% 0.63/0.37 thf(f2045,plain,(
% 0.63/0.37 (b = $false) | ~spl79_27),
% 0.63/0.37 inference(avatar_component_clause,[],[f2043])).
% 0.63/0.37 thf(f2049,plain,(
% 0.63/0.37 ($true != ((ord_less_eq @ refine1665802226e_nres @ a @ (if @ refine1665802226e_nres @ a @ $true @ s1 @ s2) @ (refine605929679le_RES @ a @ (collect @ a @ phi))))) | (spl79_13 | ~spl79_16)),
% 0.63/0.37 inference(superposition,[],[f1975,f1989])).
% 0.63/0.37 thf(f2050,plain,(
% 0.63/0.37 ~spl79_26 | spl79_13 | ~spl79_16),
% 0.63/0.37 inference(avatar_split_clause,[],[f2049,f1987,f1973,f2039])).
% 0.63/0.37 thf(f2058,plain,(
% 0.63/0.37 (((ord_less_eq @ refine1665802226e_nres @ a @ s1 @ (refine605929679le_RES @ a @ (collect @ a @ phi)))) != $true) | spl79_26),
% 0.63/0.37 inference(superposition,[],[f2041,f1531])).
% 0.63/0.37 thf(f2059,plain,(
% 0.63/0.37 ~spl79_23 | spl79_26),
% 0.63/0.37 inference(avatar_split_clause,[],[f2058,f2039,f2022])).
% 0.63/0.37 thf(f2062,plain,(
% 0.63/0.37 (((ord_less_eq @ refine1665802226e_nres @ a @ (if @ refine1665802226e_nres @ a @ $false @ s1 @ s2) @ (refine605929679le_RES @ a @ (collect @ a @ phi)))) != $true) | (spl79_13 | ~spl79_27)),
% 0.63/0.37 inference(superposition,[],[f1975,f2045])).
% 0.63/0.37 thf(f2063,plain,(
% 0.63/0.37 (((ord_less_eq @ refine1665802226e_nres @ a @ s2 @ (refine605929679le_RES @ a @ (collect @ a @ phi)))) != $true) | (spl79_13 | ~spl79_27)),
% 0.63/0.37 inference(forward_demodulation,[],[f2062,f1512])).
% 0.63/0.37 thf(f2064,plain,(
% 0.63/0.37 ~spl79_15 | spl79_13 | ~spl79_27),
% 0.63/0.37 inference(avatar_split_clause,[],[f2063,f2043,f1973,f1983])).
% 0.63/0.37 thf(f2125,plain,(
% 0.63/0.37 ($true != $true) | (b = $false) | spl79_16),
% 0.63/0.37 inference(fool_paramodulation,[],[f1988])).
% 0.63/0.37 thf(f2126,plain,(
% 0.63/0.37 (b = $false) | spl79_16),
% 0.63/0.37 inference(trivial_inequality_removal,[],[f2125])).
% 0.63/0.37 thf(f2127,plain,(
% 0.63/0.37 $false | (spl79_16 | spl79_27)),
% 0.63/0.37 inference(forward_subsumption_resolution,[],[f2126,f2044])).
% 0.63/0.37 thf(f2128,plain,(
% 0.63/0.37 spl79_16 | spl79_27),
% 0.63/0.37 inference(avatar_contradiction_clause,[],[f2127])).
% 0.63/0.37 cnf(s13, plain, ~spl79_13, inference(sat_conversion,[],[f1976])).
% 0.63/0.37 cnf(s15, plain, spl79_15 | spl79_16, inference(sat_conversion,[],[f1990])).
% 0.63/0.37 cnf(s22, plain, ~spl79_16 | spl79_23, inference(sat_conversion,[],[f2025])).
% 0.63/0.37 cnf(s27, plain, spl79_13 | ~spl79_16 | ~spl79_26, inference(sat_conversion,[],[f2050])).
% 0.63/0.37 cnf(s28, plain, ~spl79_23 | spl79_26, inference(sat_conversion,[],[f2059])).
% 0.63/0.37 cnf(s30, plain, spl79_13 | ~spl79_15 | ~spl79_27, inference(sat_conversion,[],[f2064])).
% 0.63/0.38 cnf(s32, plain, spl79_16 | spl79_27, inference(sat_conversion,[],[f2128])).
% 0.63/0.38 cnf(s33, plain, ~spl79_16, inference(rat,[],[s28,s22,s27,s13])).
% 0.63/0.38 cnf(s34, plain, spl79_27, inference(rat,[],[s32,s33])).
% 0.63/0.38 cnf(s35, plain, spl79_15, inference(rat,[],[s15,s33])).
% 0.63/0.38 cnf(s36, plain, $false, inference(rat,[],[s30,s13,s34,s35])).
% 0.63/0.38 thf(f2129,plain,(
% 0.63/0.38 $false),
% 0.63/0.38 inference(avatar_sat_refutation,[],[s36])).
% 0.63/0.38 % SZS output end Proof for theBenchmark
% 0.63/0.38 % (1525130)------------------------------
% 0.63/0.38 % (1525130)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.38 % (1525130)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.38 % (1525130)CaDiCaL version: 2.1.3
% 0.63/0.38 % (1525130)Termination reason: Refutation
% 0.63/0.38 % (1525130)Time elapsed: 0.066 s
% 0.63/0.38 % (1525130)Peak memory usage: 14 MB
% 0.63/0.38 % (1525130)Instructions burned: 127 (million)
% 0.63/0.38 % (1525122)Success in time 0.118 s
% 0.63/0.38 % Vampire exiting
%------------------------------------------------------------------------------