%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ANA087^1 : 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 : n006.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 07:45:53 AM UTC 2026
% Result : Theorem 0.22s 0.33s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ANA087^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n006.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 17:40:25 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.24 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.33 % (1072307)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.33 % (1072312)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=188041871:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.33 % (1072318)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.33 % (1072318)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.22/0.33 % (1072313)lrs+10_16_si=on:nwc=1.5:random_seed=62980685:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.33 % (1072314)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3627658167:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.33 % (1072317)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2336486914:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.33 % (1072316)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3175217068:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.33 % (1072315)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=3755885908:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.22/0.33 % (1072318)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=3146633219:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.33 % (1072314)Instruction limit reached!
% 0.22/0.33 % (1072314)------------------------------
% 0.22/0.33 % (1072314)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.33 % (1072314)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.33 % (1072314)CaDiCaL version: 2.1.3
% 0.22/0.33 % (1072314)Termination reason: Instruction limit
% 0.22/0.33 % (1072314)Termination phase: Saturation
% 0.22/0.33 % (1072314)Time elapsed: 0.002 s
% 0.22/0.33 % (1072314)Peak memory usage: 11 MB
% 0.22/0.33 % (1072314)Instructions burned: 3 (million)
% 0.22/0.33 % (1072313)Instruction limit reached!
% 0.22/0.33 % (1072313)------------------------------
% 0.22/0.33 % (1072313)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.33 % (1072313)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.33 % (1072313)CaDiCaL version: 2.1.3
% 0.22/0.33 % (1072313)Termination reason: Instruction limit
% 0.22/0.33 % (1072313)Termination phase: Saturation
% 0.22/0.33 % (1072313)Time elapsed: 0.011 s
% 0.22/0.33 % (1072313)Peak memory usage: 12 MB
% 0.22/0.33 % (1072313)Instructions burned: 18 (million)
% 0.22/0.33 % (1072316)Instruction limit reached!
% 0.22/0.33 % (1072316)------------------------------
% 0.22/0.33 % (1072316)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.33 % (1072316)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.33 % (1072316)CaDiCaL version: 2.1.3
% 0.22/0.33 % (1072316)Termination reason: Instruction limit
% 0.22/0.33 % (1072316)Termination phase: Saturation
% 0.22/0.33 % (1072316)Time elapsed: 0.015 s
% 0.22/0.33 % (1072316)Peak memory usage: 12 MB
% 0.22/0.33 % (1072316)Instructions burned: 25 (million)
% 0.22/0.33 % (1072312)Instruction limit reached!
% 0.22/0.33 % (1072312)------------------------------
% 0.22/0.33 % (1072312)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.33 % (1072312)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.33 % (1072312)CaDiCaL version: 2.1.3
% 0.22/0.33 % (1072312)Termination reason: Instruction limit
% 0.22/0.33 % (1072312)Termination phase: Saturation
% 0.22/0.33 % (1072312)Time elapsed: 0.029 s
% 0.22/0.33 % (1072312)Peak memory usage: 12 MB
% 0.22/0.33 % (1072312)Instructions burned: 87 (million)
% 0.22/0.33 % (1072326)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=78053049:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.22/0.33 % (1072326)Instruction limit reached!
% 0.22/0.33 % (1072326)------------------------------
% 0.22/0.33 % (1072326)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.33 % (1072326)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.33 % (1072326)CaDiCaL version: 2.1.3
% 0.22/0.33 % (1072326)Termination reason: Instruction limit
% 0.22/0.33 % (1072326)Termination phase: Saturation
% 0.22/0.33 % (1072326)Time elapsed: 0.002 s
% 0.22/0.33 % (1072326)Peak memory usage: 11 MB
% 0.22/0.33 % (1072326)Instructions burned: 3 (million)
% 0.22/0.33 % (1072327)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2176617239:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.22/0.33 % (1072328)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.22/0.33 % (1072329)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1122402355:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.22/0.33 % (1072327)Instruction limit reached!
% 0.22/0.33 % (1072327)------------------------------
% 0.22/0.33 % (1072327)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.33 % (1072327)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.33 % (1072327)CaDiCaL version: 2.1.3
% 0.22/0.33 % (1072327)Termination reason: Instruction limit
% 0.22/0.33 % (1072327)Termination phase: Saturation
% 0.22/0.33 % (1072327)Time elapsed: 0.003 s
% 0.22/0.33 % (1072327)Peak memory usage: 11 MB
% 0.22/0.33 % (1072327)Instructions burned: 5 (million)
% 0.22/0.33 % (1072328)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2882813027:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.22/0.33 % (1072329)Instruction limit reached!
% 0.22/0.33 % (1072329)------------------------------
% 0.22/0.33 % (1072329)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.33 % (1072329)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.33 % (1072329)CaDiCaL version: 2.1.3
% 0.22/0.33 % (1072329)Termination reason: Instruction limit
% 0.22/0.33 % (1072329)Termination phase: Saturation
% 0.22/0.33 % (1072329)Time elapsed: 0.005 s
% 0.22/0.33 % (1072329)Peak memory usage: 12 MB
% 0.22/0.33 % (1072329)Instructions burned: 14 (million)
% 0.22/0.33 % (1072328)Instruction limit reached!
% 0.22/0.33 % (1072328)------------------------------
% 0.22/0.33 % (1072328)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.33 % (1072328)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.33 % (1072328)CaDiCaL version: 2.1.3
% 0.22/0.33 % (1072328)Termination reason: Instruction limit
% 0.22/0.33 % (1072328)Termination phase: Saturation
% 0.22/0.33 % (1072328)Time elapsed: 0.004 s
% 0.22/0.33 % (1072328)Peak memory usage: 12 MB
% 0.22/0.33 % (1072328)Instructions burned: 7 (million)
% 0.22/0.33 % (1072331)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.22/0.33 % (1072331)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.22/0.33 % (1072331)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2538491736:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.22/0.33 % (1072317)Instruction limit reached!
% 0.22/0.33 % (1072317)------------------------------
% 0.22/0.33 % (1072317)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.33 % (1072317)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.33 % (1072317)CaDiCaL version: 2.1.3
% 0.22/0.33 % (1072317)Termination reason: Instruction limit
% 0.22/0.33 % (1072317)Termination phase: Saturation
% 0.22/0.33 % (1072317)Time elapsed: 0.043 s
% 0.22/0.33 % (1072317)Peak memory usage: 12 MB
% 0.22/0.33 % (1072317)Instructions burned: 75 (million)
% 0.22/0.33 % (1072336)lrs+10_1_si=on:cs=on:random_seed=3255302031:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.22/0.33 % (1072315) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1072307-1072315"...
% 0.22/0.33 % (1072315)...printing done.
% 0.22/0.33 % (1072334)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=2471714970:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.22/0.33 % (1072336)Instruction limit reached!
% 0.22/0.33 % (1072336)------------------------------
% 0.22/0.33 % (1072336)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.33 % (1072336)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.33 % (1072336)CaDiCaL version: 2.1.3
% 0.22/0.33 % (1072336)Termination reason: Instruction limit
% 0.22/0.33 % (1072336)Termination phase: Saturation
% 0.22/0.33 % (1072336)Time elapsed: 0.005 s
% 0.22/0.33 % (1072336)Peak memory usage: 12 MB
% 0.22/0.33 % (1072336)Instructions burned: 16 (million)
% 0.22/0.33 % (1072337)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.22/0.33 % (1072315)Refutation found. Thanks to Tanya!
% 0.22/0.33 % SZS status Theorem for theBenchmark
% 0.22/0.33 % SZS output start Proof for theBenchmark
% 0.22/0.33 thf(type_def_5, type, 'type/realax/real': $tType).
% 0.22/0.33 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.22/0.33 thf(func_def_0, type, 'const/trivia/I': !>[X0: $tType]:((X0 > X0))).
% 0.22/0.33 thf(func_def_1, type, 'const/sets/SUBSET': !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > $o))).
% 0.22/0.33 thf(func_def_2, type, 'const/sets/inf': (('type/realax/real' > $o) > 'type/realax/real')).
% 0.22/0.33 thf(func_def_3, type, 'const/sets/IN': !>[X0: $tType]:((X0 > (X0 > $o) > $o))).
% 0.22/0.33 thf(func_def_4, type, 'const/sets/EMPTY': !>[X0: $tType]:((X0 > $o))).
% 0.22/0.33 thf(func_def_5, type, 'const/realax/real_le': ('type/realax/real' > 'type/realax/real' > $o)).
% 0.22/0.33 thf(func_def_9, type, sK0: ('type/realax/real' > ('type/realax/real' > $o) > 'type/realax/real')).
% 0.22/0.33 thf(func_def_10, type, sK1: ('type/realax/real' > $o)).
% 0.22/0.33 thf(func_def_11, type, sK2: ('type/realax/real' > $o)).
% 0.22/0.33 thf(func_def_12, type, sK3: 'type/realax/real').
% 0.22/0.33 thf(func_def_13, type, sK4: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.22/0.33 thf(func_def_14, type, sK5: ('type/realax/real' > ('type/realax/real' > $o) > 'type/realax/real')).
% 0.22/0.33 thf(func_def_15, type, sK6: ('type/realax/real' > ('type/realax/real' > $o) > 'type/realax/real')).
% 0.22/0.33 thf(func_def_16, type, sK7: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.22/0.33 thf(func_def_17, type, vNOT: ($o > $o)).
% 0.22/0.33 thf(func_def_19, type, sK9: 'type/realax/real').
% 0.22/0.33 thf(func_def_20, type, sK10: 'type/realax/real').
% 0.22/0.33 thf(func_def_21, type, sK11: 'type/realax/real').
% 0.22/0.33 thf(func_def_22, type, sK12: 'type/realax/real').
% 0.22/0.33 thf(func_def_23, type, sK13: 'type/realax/real').
% 0.22/0.33 thf(f1,axiom,(
% 0.22/0.33 ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (((X0 != 'const/sets/EMPTY' @ 'type/realax/real') & ! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) => ('const/realax/real_le' @ X1 @ X2))) => ('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0)))),
% 0.22/0.33 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/REAL_LE_INF_')).
% 0.22/0.33 thf(f3,axiom,(
% 0.22/0.33 ! [X0 : $tType,X2 : X0,X1 : (X0 > $o)] : ((('const/sets/IN' @ X0 @ X2 @ X1)) = ((X1 @ X2)))),
% 0.22/0.33 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/IN_')).
% 0.22/0.33 thf(f4,axiom,(
% 0.22/0.33 ! [X0 : $tType,X1 : X0] : ~('const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0)),
% 0.22/0.33 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/NOT_IN_EMPTY_')).
% 0.22/0.33 thf(f5,axiom,(
% 0.22/0.33 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : (! [X3 : X0] : ((('const/sets/IN' @ X0 @ X3 @ X1)) = (('const/sets/IN' @ X0 @ X3 @ X2))) = (X1 = X2))),
% 0.22/0.33 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/EXTENSION_')).
% 0.22/0.33 thf(f6,axiom,(
% 0.22/0.33 ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > $o)] : (! [X3 : X0] : (('const/sets/IN' @ X0 @ X3 @ X1) => ('const/sets/IN' @ X0 @ X3 @ X2)) = (('const/sets/SUBSET' @ X0 @ X1 @ X2)))),
% 0.22/0.33 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/SUBSET_')).
% 0.22/0.33 thf(f7,axiom,(
% 0.22/0.33 ! [X0 : ('type/realax/real' > $o)] : (((X0 != 'const/sets/EMPTY' @ 'type/realax/real') & ? [X1 : 'type/realax/real'] : ! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) => ('const/realax/real_le' @ X1 @ X2))) => (! [X1 : 'type/realax/real'] : (! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) => ('const/realax/real_le' @ X1 @ X2)) => ('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0))) & ! [X1 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X1 @ X0) => ('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X1))))),
% 0.22/0.33 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/INF_')).
% 0.22/0.33 thf(f8,conjecture,(
% 0.22/0.33 ! [X0 : ('type/realax/real' > $o),X1 : ('type/realax/real' > $o)] : ((('const/sets/SUBSET' @ 'type/realax/real' @ X1 @ X0) & ? [X2 : 'type/realax/real'] : ! [X3 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) => ('const/realax/real_le' @ X2 @ X3)) & (X1 != 'const/sets/EMPTY' @ 'type/realax/real')) => ('const/realax/real_le' @ ('const/sets/inf' @ X0) @ ('const/sets/inf' @ X1)))),
% 0.22/0.33 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/REAL_LE_INF_SUBSET_')).
% 0.22/0.33 thf(f9,negated_conjecture,(
% 0.22/0.33 ~ ! [X0 : ('type/realax/real' > $o),X1 : ('type/realax/real' > $o)] : ((('const/sets/SUBSET' @ 'type/realax/real' @ X1 @ X0) & ? [X2 : 'type/realax/real'] : ! [X3 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) => ('const/realax/real_le' @ X2 @ X3)) & (X1 != 'const/sets/EMPTY' @ 'type/realax/real')) => ('const/realax/real_le' @ ('const/sets/inf' @ X0) @ ('const/sets/inf' @ X1)))),
% 0.22/0.33 inference(negated_conjecture,[status(cth)],[f8])).
% 0.22/0.33 thf(f10,plain,(
% 0.22/0.33 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : (! [X3 : X0] : (('const/sets/IN' @ X0 @ X3 @ X2) => ('const/sets/IN' @ X0 @ X3 @ X1)) = (('const/sets/SUBSET' @ X0 @ X2 @ X1)))),
% 0.22/0.33 inference(rectify,[],[f6])).
% 0.22/0.33 thf(f11,plain,(
% 0.22/0.33 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : (! [X3 : X0] : (((('const/sets/IN' @ X0 @ X3 @ X2)) = $true) => ((('const/sets/IN' @ X0 @ X3 @ X1)) = $true)) <=> ($true = (('const/sets/SUBSET' @ X0 @ X2 @ X1))))),
% 0.22/0.33 inference(fool_elimination,[],[f10])).
% 0.22/0.33 thf(f12,plain,(
% 0.22/0.33 ! [X0 : ('type/realax/real' > $o)] : (((X0 != 'const/sets/EMPTY' @ 'type/realax/real') & ? [X1 : 'type/realax/real'] : ! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) => ('const/realax/real_le' @ X1 @ X2))) => (! [X3 : 'type/realax/real'] : (! [X4 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X4 @ X0) => ('const/realax/real_le' @ X3 @ X4)) => ('const/realax/real_le' @ X3 @ ('const/sets/inf' @ X0))) & ! [X5 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X5 @ X0) => ('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X5))))),
% 0.22/0.33 inference(rectify,[],[f7])).
% 0.22/0.33 thf(f13,plain,(
% 0.22/0.33 ! [X0 : ('type/realax/real' > $o)] : ((('const/sets/EMPTY' @ 'type/realax/real' != X0) & ? [X1 : 'type/realax/real'] : ! [X2 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0)) = $true) => ((('const/realax/real_le' @ X1 @ X2)) = $true))) => (! [X5 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X5 @ X0)) = $true) => ((('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X5)) = $true)) & ! [X3 : 'type/realax/real'] : (! [X4 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ X4 @ X0))) => ((('const/realax/real_le' @ X3 @ X4)) = $true)) => ((('const/realax/real_le' @ X3 @ ('const/sets/inf' @ X0))) = $true))))),
% 0.22/0.33 inference(fool_elimination,[],[f12])).
% 0.22/0.33 thf(f14,plain,(
% 0.22/0.33 ~ ! [X0 : ('type/realax/real' > $o),X1 : ('type/realax/real' > $o)] : ((('const/sets/SUBSET' @ 'type/realax/real' @ X1 @ X0) & ? [X2 : 'type/realax/real'] : ! [X3 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X3 @ X0) => ('const/realax/real_le' @ X2 @ X3)) & (X1 != 'const/sets/EMPTY' @ 'type/realax/real')) => ('const/realax/real_le' @ ('const/sets/inf' @ X0) @ ('const/sets/inf' @ X1)))),
% 0.22/0.33 inference(rectify,[],[f9])).
% 0.22/0.33 thf(f15,plain,(
% 0.22/0.33 ~ ! [X1 : ('type/realax/real' > $o),X0 : ('type/realax/real' > $o)] : ((('const/sets/EMPTY' @ 'type/realax/real' != X1) & ? [X2 : 'type/realax/real'] : ! [X3 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0)) = $true) => ((('const/realax/real_le' @ X2 @ X3)) = $true)) & ((('const/sets/SUBSET' @ 'type/realax/real' @ X1 @ X0)) = $true)) => ((('const/realax/real_le' @ ('const/sets/inf' @ X0) @ ('const/sets/inf' @ X1))) = $true))),
% 0.22/0.33 inference(fool_elimination,[],[f14])).
% 0.22/0.33 thf(f16,plain,(
% 0.22/0.33 ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > $o)] : (! [X3 : X0] : ((('const/sets/IN' @ X0 @ X3 @ X1)) = (('const/sets/IN' @ X0 @ X3 @ X2))) <=> (X1 = X2))),
% 0.22/0.33 inference(fool_elimination,[],[f5])).
% 0.22/0.33 thf(f17,plain,(
% 0.22/0.33 ! [X0 : $tType,X1 : X0] : ~('const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0)),
% 0.22/0.33 inference(rectify,[],[f4])).
% 0.22/0.33 thf(f18,plain,(
% 0.22/0.33 ! [X0 : $tType,X1 : X0] : ~ ((('const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0)) = $true)),
% 0.22/0.33 inference(fool_elimination,[],[f17])).
% 0.22/0.33 thf(f19,plain,(
% 0.22/0.33 ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (((X0 != 'const/sets/EMPTY' @ 'type/realax/real') & ! [X2 : 'type/realax/real'] : (('const/sets/IN' @ 'type/realax/real' @ X2 @ X0) => ('const/realax/real_le' @ X1 @ X2))) => ('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0)))),
% 0.22/0.33 inference(rectify,[],[f1])).
% 0.22/0.33 thf(f20,plain,(
% 0.22/0.33 ! [X1 : 'type/realax/real',X0 : ('type/realax/real' > $o)] : ((! [X2 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0)) = $true) => ((('const/realax/real_le' @ X1 @ X2)) = $true)) & ('const/sets/EMPTY' @ 'type/realax/real' != X0)) => ((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0))) = $true))),
% 0.22/0.33 inference(fool_elimination,[],[f19])).
% 0.22/0.33 thf(f21,plain,(
% 0.22/0.33 ! [X0 : $tType,X1 : X0] : ((('const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0)) != $true)),
% 0.22/0.33 inference(flattening,[],[f18])).
% 0.22/0.33 thf(f22,plain,(
% 0.22/0.33 ? [X1 : ('type/realax/real' > $o),X0 : ('type/realax/real' > $o)] : (((('const/realax/real_le' @ ('const/sets/inf' @ X0) @ ('const/sets/inf' @ X1))) != $true) & (('const/sets/EMPTY' @ 'type/realax/real' != X1) & ? [X2 : 'type/realax/real'] : ! [X3 : 'type/realax/real'] : (((('const/realax/real_le' @ X2 @ X3)) = $true) | ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0)) != $true)) & ((('const/sets/SUBSET' @ 'type/realax/real' @ X1 @ X0)) = $true)))),
% 0.22/0.33 inference(ennf_transformation,[],[f15])).
% 0.22/0.33 thf(f23,plain,(
% 0.22/0.33 ? [X0 : ('type/realax/real' > $o),X1 : ('type/realax/real' > $o)] : (((('const/sets/SUBSET' @ 'type/realax/real' @ X1 @ X0)) = $true) & ((('const/realax/real_le' @ ('const/sets/inf' @ X0) @ ('const/sets/inf' @ X1))) != $true) & ? [X2 : 'type/realax/real'] : ! [X3 : 'type/realax/real'] : (((('const/realax/real_le' @ X2 @ X3)) = $true) | ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0)) != $true)) & ('const/sets/EMPTY' @ 'type/realax/real' != X1))),
% 0.22/0.33 inference(flattening,[],[f22])).
% 0.22/0.33 thf(f24,plain,(
% 0.22/0.33 ! [X0 : ('type/realax/real' > $o)] : ((! [X5 : 'type/realax/real'] : (((('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X5)) = $true) | ((('const/sets/IN' @ 'type/realax/real' @ X5 @ X0)) != $true)) & ! [X3 : 'type/realax/real'] : (? [X4 : 'type/realax/real'] : (((('const/realax/real_le' @ X3 @ X4)) != $true) & ($true = (('const/sets/IN' @ 'type/realax/real' @ X4 @ X0)))) | ((('const/realax/real_le' @ X3 @ ('const/sets/inf' @ X0))) = $true))) | (('const/sets/EMPTY' @ 'type/realax/real' = X0) | ! [X1 : 'type/realax/real'] : ? [X2 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0)) = $true) & ((('const/realax/real_le' @ X1 @ X2)) != $true))))),
% 0.22/0.33 inference(ennf_transformation,[],[f13])).
% 0.22/0.33 thf(f25,plain,(
% 0.22/0.33 ! [X0 : ('type/realax/real' > $o)] : (('const/sets/EMPTY' @ 'type/realax/real' = X0) | (! [X5 : 'type/realax/real'] : (((('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X5)) = $true) | ((('const/sets/IN' @ 'type/realax/real' @ X5 @ X0)) != $true)) & ! [X3 : 'type/realax/real'] : (? [X4 : 'type/realax/real'] : (((('const/realax/real_le' @ X3 @ X4)) != $true) & ($true = (('const/sets/IN' @ 'type/realax/real' @ X4 @ X0)))) | ((('const/realax/real_le' @ X3 @ ('const/sets/inf' @ X0))) = $true))) | ! [X1 : 'type/realax/real'] : ? [X2 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0)) = $true) & ((('const/realax/real_le' @ X1 @ X2)) != $true)))),
% 0.22/0.33 inference(flattening,[],[f24])).
% 0.22/0.33 thf(f26,plain,(
% 0.22/0.33 ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > $o)] : (($true = (('const/sets/SUBSET' @ X0 @ X2 @ X1))) <=> ! [X3 : X0] : (((('const/sets/IN' @ X0 @ X3 @ X1)) = $true) | ((('const/sets/IN' @ X0 @ X3 @ X2)) != $true)))),
% 0.22/0.33 inference(ennf_transformation,[],[f11])).
% 0.22/0.33 thf(f27,plain,(
% 0.22/0.33 ! [X1 : 'type/realax/real',X0 : ('type/realax/real' > $o)] : (((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0))) = $true) | (? [X2 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ X2)) != $true) & ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0)) = $true)) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)))),
% 0.22/0.33 inference(ennf_transformation,[],[f20])).
% 0.22/0.33 thf(f28,plain,(
% 0.22/0.33 ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0))) = $true) | ? [X2 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ X2)) != $true) & ((('const/sets/IN' @ 'type/realax/real' @ X2 @ X0)) = $true)) | ('const/sets/EMPTY' @ 'type/realax/real' = X0))),
% 0.22/0.33 inference(flattening,[],[f27])).
% 0.22/0.33 thf(f29,plain,(
% 0.22/0.33 ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0))) = $true) | (((('const/realax/real_le' @ X1 @ (sK0 @ X1 @ X0))) != $true) & ((('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X1 @ X0) @ X0)) = $true)) | ('const/sets/EMPTY' @ 'type/realax/real' = X0))),
% 0.22/0.33 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X2,sK0 @ X1 @ X0)],[f28])).
% 0.22/0.33 thf(f30,plain,(
% 0.22/0.33 ($true = (('const/sets/SUBSET' @ 'type/realax/real' @ sK2 @ sK1))) & ((('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ ('const/sets/inf' @ sK2))) != $true) & ! [X3 : 'type/realax/real'] : (((('const/realax/real_le' @ sK3 @ X3)) = $true) | ((('const/sets/IN' @ 'type/realax/real' @ X3 @ sK1)) != $true)) & ('const/sets/EMPTY' @ 'type/realax/real' != sK2)),
% 0.22/0.33 inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3)],[f23])).
% 0.22/0.33 thf(f31,plain,(
% 0.22/0.33 ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > $o)] : ((! [X3 : X0] : ((('const/sets/IN' @ X0 @ X3 @ X1)) = (('const/sets/IN' @ X0 @ X3 @ X2))) | (X1 != X2)) & ((X1 = X2) | ? [X3 : X0] : ((('const/sets/IN' @ X0 @ X3 @ X1)) != (('const/sets/IN' @ X0 @ X3 @ X2)))))),
% 0.22/0.33 inference(nnf_transformation,[],[f16])).
% 0.22/0.33 thf(f32,plain,(
% 0.22/0.33 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : ((! [X3 : X0] : ((('const/sets/IN' @ X0 @ X3 @ X1)) = (('const/sets/IN' @ X0 @ X3 @ X2))) | (X1 != X2)) & ((X1 = X2) | ? [X4 : X0] : ((('const/sets/IN' @ X0 @ X4 @ X1)) != (('const/sets/IN' @ X0 @ X4 @ X2)))))),
% 0.22/0.33 inference(rectify,[],[f31])).
% 0.22/0.33 thf(f33,plain,(
% 0.22/0.33 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : ((! [X3 : X0] : ((('const/sets/IN' @ X0 @ X3 @ X1)) = (('const/sets/IN' @ X0 @ X3 @ X2))) | (X1 != X2)) & ((X1 = X2) | ((('const/sets/IN' @ X0 @ (sK4 @ X0 @ X2 @ X1) @ X2)) != (('const/sets/IN' @ X0 @ (sK4 @ X0 @ X2 @ X1) @ X1)))))),
% 0.22/0.33 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X2,sK0 @ X1 @ X0)],[f32])).
% 0.22/0.33 thf(f34,plain,(
% 0.22/0.33 ! [X0 : $tType,X1 : X0,X2 : (X0 > $o)] : ((('const/sets/IN' @ X0 @ X1 @ X2)) = ((X2 @ X1)))),
% 0.22/0.33 inference(rectify,[],[f3])).
% 0.22/0.33 thf(f35,plain,(
% 0.22/0.33 ! [X0 : ('type/realax/real' > $o)] : (('const/sets/EMPTY' @ 'type/realax/real' = X0) | (! [X1 : 'type/realax/real'] : (((('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X1)) = $true) | ((('const/sets/IN' @ 'type/realax/real' @ X1 @ X0)) != $true)) & ! [X2 : 'type/realax/real'] : (? [X3 : 'type/realax/real'] : (((('const/realax/real_le' @ X2 @ X3)) != $true) & ((('const/sets/IN' @ 'type/realax/real' @ X3 @ X0)) = $true)) | ((('const/realax/real_le' @ X2 @ ('const/sets/inf' @ X0))) = $true))) | ! [X4 : 'type/realax/real'] : ? [X5 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X5 @ X0)) = $true) & ((('const/realax/real_le' @ X4 @ X5)) != $true)))),
% 0.22/0.33 inference(rectify,[],[f25])).
% 0.22/0.33 thf(f36,plain,(
% 0.22/0.33 ! [X0 : ('type/realax/real' > $o)] : (('const/sets/EMPTY' @ 'type/realax/real' = X0) | (! [X1 : 'type/realax/real'] : (((('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X1)) = $true) | ((('const/sets/IN' @ 'type/realax/real' @ X1 @ X0)) != $true)) & ! [X2 : 'type/realax/real'] : ((($true != (('const/realax/real_le' @ X2 @ (sK5 @ X2 @ X0)))) & ((('const/sets/IN' @ 'type/realax/real' @ (sK5 @ X2 @ X0) @ X0)) = $true)) | ((('const/realax/real_le' @ X2 @ ('const/sets/inf' @ X0))) = $true))) | ! [X4 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK6 @ X4 @ X0) @ X0))) & ((('const/realax/real_le' @ X4 @ (sK6 @ X4 @ X0))) != $true)))),
% 0.22/0.33 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP]),skolemize(X2,sK0 @ X1 @ X0),skolemize(X2,sK0 @ X1 @ X0)],[f35])).
% 0.22/0.33 thf(f37,plain,(
% 0.22/0.33 ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > $o)] : ((($true = (('const/sets/SUBSET' @ X0 @ X2 @ X1))) | ? [X3 : X0] : (((('const/sets/IN' @ X0 @ X3 @ X1)) != $true) & ((('const/sets/IN' @ X0 @ X3 @ X2)) = $true))) & (! [X3 : X0] : (((('const/sets/IN' @ X0 @ X3 @ X1)) = $true) | ((('const/sets/IN' @ X0 @ X3 @ X2)) != $true)) | ($true != (('const/sets/SUBSET' @ X0 @ X2 @ X1)))))),
% 0.22/0.33 inference(nnf_transformation,[],[f26])).
% 0.22/0.33 thf(f38,plain,(
% 0.22/0.33 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : ((((('const/sets/SUBSET' @ X0 @ X1 @ X2)) = $true) | ? [X3 : X0] : (((('const/sets/IN' @ X0 @ X3 @ X2)) != $true) & ((('const/sets/IN' @ X0 @ X3 @ X1)) = $true))) & (! [X4 : X0] : (($true = (('const/sets/IN' @ X0 @ X4 @ X2))) | ((('const/sets/IN' @ X0 @ X4 @ X1)) != $true)) | ((('const/sets/SUBSET' @ X0 @ X1 @ X2)) != $true)))),
% 0.22/0.33 inference(rectify,[],[f37])).
% 0.22/0.33 thf(f39,plain,(
% 0.22/0.33 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : ((((('const/sets/SUBSET' @ X0 @ X1 @ X2)) = $true) | (($true != (('const/sets/IN' @ X0 @ (sK7 @ X0 @ X2 @ X1) @ X2))) & ((('const/sets/IN' @ X0 @ (sK7 @ X0 @ X2 @ X1) @ X1)) = $true))) & (! [X4 : X0] : (($true = (('const/sets/IN' @ X0 @ X4 @ X2))) | ((('const/sets/IN' @ X0 @ X4 @ X1)) != $true)) | ((('const/sets/SUBSET' @ X0 @ X1 @ X2)) != $true)))),
% 0.22/0.33 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X2,sK0 @ X1 @ X0)],[f38])).
% 0.22/0.33 thf(f40,plain,(
% 0.22/0.33 ( ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ (sK0 @ X1 @ X0) @ X0)) = $true) | ((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0))) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 0.22/0.33 inference(cnf_transformation,[],[f29])).
% 0.22/0.33 thf(f41,plain,(
% 0.22/0.33 ( ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real'] : (((('const/realax/real_le' @ X1 @ (sK0 @ X1 @ X0))) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ((('const/realax/real_le' @ X1 @ ('const/sets/inf' @ X0))) = $true)) )),
% 0.22/0.33 inference(cnf_transformation,[],[f29])).
% 0.22/0.33 thf(f42,plain,(
% 0.22/0.33 ('const/sets/EMPTY' @ 'type/realax/real' != sK2)),
% 0.22/0.33 inference(cnf_transformation,[],[f30])).
% 0.22/0.33 thf(f43,plain,(
% 0.22/0.33 ( ! [X3 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X3 @ sK1)) != $true) | ((('const/realax/real_le' @ sK3 @ X3)) = $true)) )),
% 0.22/0.33 inference(cnf_transformation,[],[f30])).
% 0.22/0.33 thf(f44,plain,(
% 0.22/0.33 ((('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ ('const/sets/inf' @ sK2))) != $true)),
% 0.22/0.33 inference(cnf_transformation,[],[f30])).
% 0.22/0.33 thf(f45,plain,(
% 0.22/0.33 ($true = (('const/sets/SUBSET' @ 'type/realax/real' @ sK2 @ sK1)))),
% 0.22/0.33 inference(cnf_transformation,[],[f30])).
% 0.22/0.33 thf(f46,plain,(
% 0.22/0.33 ( ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > $o)] : (((('const/sets/IN' @ X0 @ (sK4 @ X0 @ X2 @ X1) @ X2)) != (('const/sets/IN' @ X0 @ (sK4 @ X0 @ X2 @ X1) @ X1))) | (X1 = X2)) )),
% 0.22/0.33 inference(cnf_transformation,[],[f33])).
% 0.22/0.33 thf(f49,plain,(
% 0.22/0.33 ( ! [X0 : $tType,X2 : (X0 > $o),X1 : X0] : (((('const/sets/IN' @ X0 @ X1 @ X2)) = ((X2 @ X1)))) )),
% 0.22/0.33 inference(cnf_transformation,[],[f34])).
% 0.22/0.33 thf(f50,plain,(
% 0.22/0.33 ( ! [X0 : $tType,X1 : X0] : (((('const/sets/IN' @ X0 @ X1 @ 'const/sets/EMPTY' @ X0)) != $true)) )),
% 0.22/0.33 inference(cnf_transformation,[],[f21])).
% 0.22/0.33 thf(f55,plain,(
% 0.22/0.33 ( ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real',X4 : 'type/realax/real'] : (((('const/realax/real_le' @ X4 @ (sK6 @ X4 @ X0))) != $true) | ((('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X1)) = $true) | ((('const/sets/IN' @ 'type/realax/real' @ X1 @ X0)) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) )),
% 0.22/0.33 inference(cnf_transformation,[],[f36])).
% 0.22/0.33 thf(f56,plain,(
% 0.22/0.33 ( ! [X0 : ('type/realax/real' > $o),X1 : 'type/realax/real',X4 : 'type/realax/real'] : (($true = (('const/sets/IN' @ 'type/realax/real' @ (sK6 @ X4 @ X0) @ X0))) | ((('const/sets/IN' @ 'type/realax/real' @ X1 @ X0)) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ((('const/realax/real_le' @ ('const/sets/inf' @ X0) @ X1)) = $true)) )),
% 0.22/0.33 inference(cnf_transformation,[],[f36])).
% 0.22/0.33 thf(f57,plain,(
% 0.22/0.33 ( ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > $o),X4 : X0] : (((('const/sets/SUBSET' @ X0 @ X1 @ X2)) != $true) | ((('const/sets/IN' @ X0 @ X4 @ X1)) != $true) | ($true = (('const/sets/IN' @ X0 @ X4 @ X2)))) )),
% 0.22/0.33 inference(cnf_transformation,[],[f39])).
% 0.22/0.33 thf(f62,plain,(
% 0.22/0.33 ( ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > $o)] : (($true = (('const/sets/IN' @ X0 @ (sK4 @ X0 @ X2 @ X1) @ X1))) | ((('const/sets/IN' @ X0 @ (sK4 @ X0 @ X2 @ X1) @ X2)) = $true) | (X1 = X2)) )),
% 0.22/0.33 inference(xor_proxy_clausification,[],[f46])).
% 0.22/0.33 thf(f66,plain,(
% 0.22/0.33 ( ! [X0 : $tType,X2 : (X0 > $o),X1 : X0] : (((('const/sets/IN' @ X0 @ X1 @ X2)) = $true) | ($false = ((X2 @ X1)))) )),
% 0.22/0.33 inference(iff_proxy_clausification,[],[f49])).
% 0.22/0.33 thf(f67,plain,(
% 0.22/0.33 ( ! [X0 : $tType,X2 : (X0 > $o),X1 : X0] : (((('const/sets/IN' @ X0 @ X1 @ X2)) = $false) | ($true = ((X2 @ X1)))) )),
% 0.22/0.33 inference(iff_proxy_clausification,[],[f49])).
% 0.22/0.33 thf(f69,definition,(
% 0.22/0.33 spl8_1 <=> ($true = (('const/sets/SUBSET' @ 'type/realax/real' @ sK2 @ sK1)))),
% 0.22/0.33 introduced(definition,[new_symbols(definition,[spl8_1])],[avatar_definition])).
% 0.22/0.33 thf(f71,plain,(
% 0.22/0.33 ($true = (('const/sets/SUBSET' @ 'type/realax/real' @ sK2 @ sK1))) | ~spl8_1),
% 0.22/0.33 inference(avatar_component_clause,[],[f69])).
% 0.22/0.33 thf(f72,plain,(
% 0.22/0.33 spl8_1),
% 0.22/0.33 inference(avatar_split_clause,[],[f45,f69])).
% 0.22/0.33 thf(f74,definition,(
% 0.22/0.33 spl8_2 <=> ((('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ ('const/sets/inf' @ sK2))) = $true)),
% 0.22/0.33 introduced(definition,[new_symbols(definition,[spl8_2])],[avatar_definition])).
% 0.22/0.33 thf(f76,plain,(
% 0.22/0.33 ((('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ ('const/sets/inf' @ sK2))) != $true) | spl8_2),
% 0.22/0.33 inference(avatar_component_clause,[],[f74])).
% 0.22/0.33 thf(f77,plain,(
% 0.22/0.33 ~spl8_2),
% 0.22/0.33 inference(avatar_split_clause,[],[f44,f74])).
% 0.22/0.33 thf(f79,definition,(
% 0.22/0.33 spl8_3 <=> ('const/sets/EMPTY' @ 'type/realax/real' = sK2)),
% 0.22/0.33 introduced(definition,[new_symbols(definition,[spl8_3])],[avatar_definition])).
% 0.22/0.33 thf(f81,plain,(
% 0.22/0.33 ('const/sets/EMPTY' @ 'type/realax/real' != sK2) | spl8_3),
% 0.22/0.33 inference(avatar_component_clause,[],[f79])).
% 0.22/0.33 thf(f82,plain,(
% 0.22/0.33 ~spl8_3),
% 0.22/0.33 inference(avatar_split_clause,[],[f42,f79])).
% 0.22/0.33 thf(f110,plain,(
% 0.22/0.33 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK2))) | ((('const/sets/IN' @ 'type/realax/real' @ X0 @ sK1)) = $true)) ) | ~spl8_1),
% 0.22/0.33 inference(superposition,[],[f57,f71])).
% 0.22/0.33 thf(f111,plain,(
% 0.22/0.33 ( ! [X0 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X0 @ sK1)) = $true) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK2)))) ) | ~spl8_1),
% 0.22/0.33 inference(trivial_inequality_removal,[],[f110])).
% 0.22/0.33 thf(f118,definition,(
% 0.22/0.33 spl8_9 <=> ('const/sets/EMPTY' @ 'type/realax/real' = sK1)),
% 0.22/0.33 introduced(definition,[new_symbols(definition,[spl8_9])],[avatar_definition])).
% 0.22/0.33 thf(f120,plain,(
% 0.22/0.33 ('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ~spl8_9),
% 0.22/0.33 inference(avatar_component_clause,[],[f118])).
% 0.22/0.33 thf(f122,plain,(
% 0.22/0.33 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ sK3 @ (sK6 @ X0 @ sK1)))) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ X1))) | ($true != $true) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X1 @ sK1))) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1)) )),
% 0.22/0.33 inference(superposition,[],[f43,f56])).
% 0.22/0.33 thf(f123,plain,(
% 0.22/0.33 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ X1))) | ($true = (('const/realax/real_le' @ sK3 @ (sK6 @ X0 @ sK1)))) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X1 @ sK1)))) )),
% 0.22/0.33 inference(trivial_inequality_removal,[],[f122])).
% 0.22/0.34 thf(f125,definition,(
% 0.22/0.34 spl8_10 <=> ! [X0 : 'type/realax/real'] : ($true = (('const/realax/real_le' @ sK3 @ (sK6 @ X0 @ sK1))))),
% 0.22/0.34 introduced(definition,[new_symbols(definition,[spl8_10])],[avatar_definition])).
% 0.22/0.34 thf(f126,plain,(
% 0.22/0.34 ( ! [X0 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ sK3 @ (sK6 @ X0 @ sK1))))) ) | ~spl8_10),
% 0.22/0.34 inference(avatar_component_clause,[],[f125])).
% 0.22/0.34 thf(f128,definition,(
% 0.22/0.34 spl8_11 <=> ! [X1 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ X1))) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X1 @ sK1))))),
% 0.22/0.34 introduced(definition,[new_symbols(definition,[spl8_11])],[avatar_definition])).
% 0.22/0.34 thf(f129,plain,(
% 0.22/0.34 ( ! [X1 : 'type/realax/real'] : (($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ X1))) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X1 @ sK1)))) ) | ~spl8_11),
% 0.22/0.34 inference(avatar_component_clause,[],[f128])).
% 0.22/0.34 thf(f130,plain,(
% 0.22/0.34 spl8_9 | spl8_10 | spl8_11),
% 0.22/0.34 inference(avatar_split_clause,[],[f123,f128,f125,f118])).
% 0.22/0.34 thf(f175,plain,(
% 0.22/0.34 ( ! [X0 : $tType,X1 : (X0 > $o)] : (($true = (('const/sets/IN' @ X0 @ (sK4 @ X0 @ X1 @ 'const/sets/EMPTY' @ X0) @ X1))) | ('const/sets/EMPTY' @ X0 = X1) | ($true != $true)) )),
% 0.22/0.34 inference(superposition,[],[f50,f62])).
% 0.22/0.34 thf(f178,plain,(
% 0.22/0.34 ( ! [X0 : $tType,X1 : (X0 > $o)] : (($true = (('const/sets/IN' @ X0 @ (sK4 @ X0 @ X1 @ 'const/sets/EMPTY' @ X0) @ X1))) | ('const/sets/EMPTY' @ X0 = X1)) )),
% 0.22/0.34 inference(trivial_inequality_removal,[],[f175])).
% 0.22/0.34 thf(f209,plain,(
% 0.22/0.34 ( ! [X0 : 'type/realax/real'] : (((('const/sets/IN' @ 'type/realax/real' @ X0 @ sK1)) != $true)) ) | ~spl8_9),
% 0.22/0.34 inference(superposition,[],[f50,f120])).
% 0.22/0.34 thf(f212,plain,(
% 0.22/0.34 ( ! [X0 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK1) | ((('const/sets/IN' @ 'type/realax/real' @ X0 @ sK1)) != $true) | ($true != $true) | ((('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ X0)) = $true)) ) | ~spl8_10),
% 0.22/0.34 inference(superposition,[],[f55,f126])).
% 0.22/0.34 thf(f213,plain,(
% 0.22/0.34 ( ! [X0 : 'type/realax/real'] : (((('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ X0)) = $true) | ((('const/sets/IN' @ 'type/realax/real' @ X0 @ sK1)) != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK1)) ) | ~spl8_10),
% 0.22/0.34 inference(trivial_inequality_removal,[],[f212])).
% 0.22/0.34 thf(f333,plain,(
% 0.22/0.34 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK2)))) ) | (~spl8_1 | ~spl8_9)),
% 0.22/0.34 inference(superposition,[],[f209,f111])).
% 0.22/0.34 thf(f346,plain,(
% 0.22/0.34 ( ! [X0 : 'type/realax/real'] : (($true != (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK2)))) ) | (~spl8_1 | ~spl8_9)),
% 0.22/0.34 inference(trivial_inequality_removal,[],[f333])).
% 0.22/0.34 thf(f380,plain,(
% 0.22/0.34 ($true != $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | (~spl8_1 | ~spl8_9)),
% 0.22/0.34 inference(superposition,[],[f346,f178])).
% 0.22/0.34 thf(f389,plain,(
% 0.22/0.34 ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | (~spl8_1 | ~spl8_9)),
% 0.22/0.34 inference(trivial_inequality_removal,[],[f380])).
% 0.22/0.34 thf(f397,plain,(
% 0.22/0.34 $false | (~spl8_1 | spl8_3 | ~spl8_9)),
% 0.22/0.34 inference(forward_subsumption_resolution,[],[f389,f81])).
% 0.22/0.34 thf(f398,plain,(
% 0.22/0.34 ~spl8_1 | spl8_3 | ~spl8_9),
% 0.22/0.34 inference(avatar_contradiction_clause,[],[f397])).
% 0.22/0.34 thf(f425,plain,(
% 0.22/0.34 spl8_11 | spl8_9 | ~spl8_10),
% 0.22/0.34 inference(avatar_split_clause,[],[f213,f125,f118,f128])).
% 0.22/0.34 thf(f433,plain,(
% 0.22/0.34 ( ! [X0 : ('type/realax/real' > $o)] : (($true != $true) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ ('const/sets/inf' @ X0)))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ((('const/sets/IN' @ 'type/realax/real' @ (sK0 @ ('const/sets/inf' @ sK1) @ X0) @ sK1)) != $true)) ) | ~spl8_11),
% 0.22/0.34 inference(superposition,[],[f41,f129])).
% 0.22/0.34 thf(f437,plain,(
% 0.22/0.34 ( ! [X0 : ('type/realax/real' > $o)] : (((('const/sets/IN' @ 'type/realax/real' @ (sK0 @ ('const/sets/inf' @ sK1) @ X0) @ sK1)) != $true) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ ('const/sets/inf' @ X0)))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) ) | ~spl8_11),
% 0.22/0.34 inference(trivial_inequality_removal,[],[f433])).
% 0.22/0.34 thf(f700,plain,(
% 0.22/0.34 ( ! [X0 : 'type/realax/real'] : (($true = $false) | ($true != (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK2))) | (((sK1 @ X0)) = $true)) ) | ~spl8_1),
% 0.22/0.34 inference(superposition,[],[f111,f67])).
% 0.22/0.34 thf(f713,plain,(
% 0.22/0.34 ( ! [X0 : 'type/realax/real'] : (($true != (('const/sets/IN' @ 'type/realax/real' @ X0 @ sK2))) | (((sK1 @ X0)) = $true)) ) | ~spl8_1),
% 0.22/0.34 inference(trivial_inequality_removal,[],[f700])).
% 0.22/0.34 thf(f731,plain,(
% 0.22/0.34 ( ! [X0 : 'type/realax/real'] : (($true != $true) | ($true = ((sK1 @ (sK0 @ X0 @ sK2)))) | ((('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK2))) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2)) ) | ~spl8_1),
% 0.22/0.34 inference(superposition,[],[f713,f40])).
% 0.22/0.34 thf(f744,plain,(
% 0.22/0.34 ( ! [X0 : 'type/realax/real'] : (('const/sets/EMPTY' @ 'type/realax/real' = sK2) | ((('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK2))) = $true) | ($true = ((sK1 @ (sK0 @ X0 @ sK2))))) ) | ~spl8_1),
% 0.22/0.34 inference(trivial_inequality_removal,[],[f731])).
% 0.22/0.34 thf(f752,plain,(
% 0.22/0.34 ( ! [X0 : 'type/realax/real'] : (($true = ((sK1 @ (sK0 @ X0 @ sK2)))) | ((('const/realax/real_le' @ X0 @ ('const/sets/inf' @ sK2))) = $true)) ) | (~spl8_1 | spl8_3)),
% 0.22/0.34 inference(forward_subsumption_resolution,[],[f744,f81])).
% 0.22/0.34 thf(f796,plain,(
% 0.22/0.34 ( ! [X0 : ('type/realax/real' > $o)] : (($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ ('const/sets/inf' @ X0)))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0) | ($true != $true) | (((sK1 @ (sK0 @ ('const/sets/inf' @ sK1) @ X0))) = $false)) ) | ~spl8_11),
% 0.22/0.34 inference(superposition,[],[f437,f66])).
% 0.22/0.34 thf(f797,plain,(
% 0.22/0.34 ( ! [X0 : ('type/realax/real' > $o)] : ((((sK1 @ (sK0 @ ('const/sets/inf' @ sK1) @ X0))) = $false) | ($true = (('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ ('const/sets/inf' @ X0)))) | ('const/sets/EMPTY' @ 'type/realax/real' = X0)) ) | ~spl8_11),
% 0.22/0.34 inference(trivial_inequality_removal,[],[f796])).
% 0.22/0.34 thf(f1016,plain,(
% 0.22/0.34 ($true = $false) | ((('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ ('const/sets/inf' @ sK2))) = $true) | ((('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ ('const/sets/inf' @ sK2))) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | (~spl8_1 | spl8_3 | ~spl8_11)),
% 0.22/0.34 inference(superposition,[],[f752,f797])).
% 0.22/0.34 thf(f1019,plain,(
% 0.22/0.34 ($true = $false) | ((('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ ('const/sets/inf' @ sK2))) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | (~spl8_1 | spl8_3 | ~spl8_11)),
% 0.22/0.34 inference(duplicate_literal_removal,[],[f1016])).
% 0.22/0.34 thf(f1020,plain,(
% 0.22/0.34 ((('const/realax/real_le' @ ('const/sets/inf' @ sK1) @ ('const/sets/inf' @ sK2))) = $true) | ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | (~spl8_1 | spl8_3 | ~spl8_11)),
% 0.22/0.34 inference(trivial_inequality_removal,[],[f1019])).
% 0.22/0.34 thf(f1022,plain,(
% 0.22/0.34 ('const/sets/EMPTY' @ 'type/realax/real' = sK2) | (~spl8_1 | spl8_2 | spl8_3 | ~spl8_11)),
% 0.22/0.34 inference(forward_subsumption_resolution,[],[f1020,f76])).
% 0.22/0.34 thf(f1025,plain,(
% 0.22/0.34 $false | (~spl8_1 | spl8_2 | spl8_3 | ~spl8_11)),
% 0.22/0.34 inference(forward_subsumption_resolution,[],[f1022,f81])).
% 0.22/0.34 thf(f1026,plain,(
% 0.22/0.34 ~spl8_1 | spl8_2 | spl8_3 | ~spl8_11),
% 0.22/0.34 inference(avatar_contradiction_clause,[],[f1025])).
% 0.22/0.34 cnf(s1, plain, spl8_1, inference(sat_conversion,[],[f72])).
% 0.22/0.34 cnf(s2, plain, ~spl8_2, inference(sat_conversion,[],[f77])).
% 0.22/0.34 cnf(s3, plain, ~spl8_3, inference(sat_conversion,[],[f82])).
% 0.22/0.34 cnf(s7, plain, spl8_9 | spl8_10 | spl8_11, inference(sat_conversion,[],[f130])).
% 0.22/0.34 cnf(s26, plain, ~spl8_1 | spl8_3 | ~spl8_9, inference(sat_conversion,[],[f398])).
% 0.22/0.34 cnf(s35, plain, spl8_9 | ~spl8_10 | spl8_11, inference(sat_conversion,[],[f425])).
% 0.22/0.34 cnf(s152, plain, ~spl8_1 | spl8_2 | spl8_3 | ~spl8_11, inference(sat_conversion,[],[f1026])).
% 0.22/0.34 cnf(s159, plain, ~spl8_11, inference(rat,[],[s152,s2,s3,s1])).
% 0.22/0.34 cnf(s164, plain, ~spl8_9, inference(rat,[],[s26,s3,s1])).
% 0.22/0.34 cnf(s166, plain, ~spl8_10, inference(rat,[],[s35,s159,s164])).
% 0.22/0.34 cnf(s169, plain, $false, inference(rat,[],[s7,s159,s166,s164])).
% 0.22/0.34 thf(f1027,plain,(
% 0.22/0.34 $false),
% 0.22/0.34 inference(avatar_sat_refutation,[],[s169])).
% 0.22/0.34 % SZS output end Proof for theBenchmark
% 0.22/0.34 % (1072315)------------------------------
% 0.22/0.34 % (1072315)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.34 % (1072315)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.34 % (1072315)CaDiCaL version: 2.1.3
% 0.22/0.34 % (1072315)Termination reason: Refutation
% 0.22/0.34 % (1072315)Time elapsed: 0.051 s
% 0.22/0.34 % (1072315)Peak memory usage: 13 MB
% 0.22/0.34 % (1072315)Instructions burned: 79 (million)
% 0.22/0.34 % (1072307)Success in time 0.086 s
% 0.22/0.34 % Vampire exiting
%------------------------------------------------------------------------------