%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : DAT327^1 : 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 : n017.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 07:48:47 AM UTC 2026
% Result : Theorem 0.21s 0.35s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT327^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n017.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 18:23:11 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.24 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
% 0.21/0.35 % (707298)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.35 % (707303)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1563523503:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.35 % (707307)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2060776810:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.35 % (707304)lrs+10_16_si=on:nwc=1.5:random_seed=1230817098:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.35 % (707305)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=633878420:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.35 % (707306)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=1036737167: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)
% 0.21/0.35 % (707309)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.35 % (707309)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
% 0.21/0.35 % (707305)Instruction limit reached!
% 0.21/0.35 % (707305)------------------------------
% 0.21/0.35 % (707305)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.35 % (707305)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.35 % (707305)CaDiCaL version: 2.1.3
% 0.21/0.35 % (707305)Termination reason: Instruction limit
% 0.21/0.35 % (707305)Termination phase: Saturation
% 0.21/0.35 % (707305)Time elapsed: 0.003 s
% 0.21/0.35 % (707305)Peak memory usage: 12 MB
% 0.21/0.35 % (707305)Instructions burned: 4 (million)
% 0.21/0.35 % (707309)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=1835287480:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.35 % (707308)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2613353287:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.35 % (707304)Instruction limit reached!
% 0.21/0.35 % (707304)------------------------------
% 0.21/0.35 % (707304)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.35 % (707304)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.35 % (707304)CaDiCaL version: 2.1.3
% 0.21/0.35 % (707304)Termination reason: Instruction limit
% 0.21/0.35 % (707304)Termination phase: Saturation
% 0.21/0.35 % (707304)Time elapsed: 0.012 s
% 0.21/0.35 % (707304)Peak memory usage: 12 MB
% 0.21/0.35 % (707304)Instructions burned: 19 (million)
% 0.21/0.35 % (707307)Instruction limit reached!
% 0.21/0.35 % (707307)------------------------------
% 0.21/0.35 % (707307)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.35 % (707307)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.35 % (707307)CaDiCaL version: 2.1.3
% 0.21/0.35 % (707307)Termination reason: Instruction limit
% 0.21/0.35 % (707307)Termination phase: Saturation
% 0.21/0.35 % (707307)Time elapsed: 0.014 s
% 0.21/0.35 % (707307)Peak memory usage: 12 MB
% 0.21/0.35 % (707307)Instructions burned: 24 (million)
% 0.21/0.35 % (707303)Instruction limit reached!
% 0.21/0.35 % (707303)------------------------------
% 0.21/0.35 % (707303)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.35 % (707303)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.35 % (707303)CaDiCaL version: 2.1.3
% 0.21/0.35 % (707303)Termination reason: Instruction limit
% 0.21/0.35 % (707303)Termination phase: Saturation
% 0.21/0.35 % (707303)Time elapsed: 0.024 s
% 0.21/0.35 % (707303)Peak memory usage: 12 MB
% 0.21/0.35 % (707303)Instructions burned: 89 (million)
% 0.21/0.35 % (707315)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2286248464:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.21/0.35 % (707315)Instruction limit reached!
% 0.21/0.35 % (707315)------------------------------
% 0.21/0.35 % (707315)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.35 % (707315)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.35 % (707315)CaDiCaL version: 2.1.3
% 0.21/0.35 % (707315)Termination reason: Instruction limit
% 0.21/0.35 % (707315)Termination phase: Saturation
% 0.21/0.35 % (707315)Time elapsed: 0.002 s
% 0.21/0.35 % (707315)Peak memory usage: 12 MB
% 0.21/0.35 % (707315)Instructions burned: 2 (million)
% 0.21/0.35 % (707320)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=508950263:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.21/0.35 % (707319)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.21/0.35 % (707318)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3182710959:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.21/0.35 % (707320)Instruction limit reached!
% 0.21/0.35 % (707320)------------------------------
% 0.21/0.35 % (707320)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.35 % (707320)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.35 % (707320)CaDiCaL version: 2.1.3
% 0.21/0.35 % (707320)Termination reason: Instruction limit
% 0.21/0.35 % (707320)Termination phase: Saturation
% 0.21/0.35 % (707320)Time elapsed: 0.005 s
% 0.21/0.35 % (707320)Peak memory usage: 12 MB
% 0.21/0.35 % (707320)Instructions burned: 14 (million)
% 0.21/0.35 % (707319)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2630928385:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.21/0.35 % (707318)Instruction limit reached!
% 0.21/0.35 % (707318)------------------------------
% 0.21/0.35 % (707318)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.35 % (707318)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.35 % (707318)CaDiCaL version: 2.1.3
% 0.21/0.35 % (707318)Termination reason: Instruction limit
% 0.21/0.35 % (707318)Termination phase: Saturation
% 0.21/0.35 % (707318)Time elapsed: 0.004 s
% 0.21/0.35 % (707318)Peak memory usage: 12 MB
% 0.21/0.35 % (707318)Instructions burned: 5 (million)
% 0.21/0.35 % (707319)Instruction limit reached!
% 0.21/0.35 % (707319)------------------------------
% 0.21/0.35 % (707319)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.35 % (707319)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.35 % (707319)CaDiCaL version: 2.1.3
% 0.21/0.35 % (707319)Termination reason: Instruction limit
% 0.21/0.35 % (707319)Termination phase: Saturation
% 0.21/0.35 % (707319)Time elapsed: 0.005 s
% 0.21/0.35 % (707319)Peak memory usage: 12 MB
% 0.21/0.35 % (707319)Instructions burned: 8 (million)
% 0.21/0.35 % (707323)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
% 0.21/0.35 % (707323)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.21/0.35 % (707325)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=828953429:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.21/0.35 % (707323)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=4000506799:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.21/0.35 % (707308)Instruction limit reached!
% 0.21/0.35 % (707308)------------------------------
% 0.21/0.35 % (707308)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.35 % (707308)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.35 % (707308)CaDiCaL version: 2.1.3
% 0.21/0.35 % (707308)Termination reason: Instruction limit
% 0.21/0.35 % (707308)Termination phase: Saturation
% 0.21/0.35 % (707308)Time elapsed: 0.040 s
% 0.21/0.35 % (707308)Peak memory usage: 13 MB
% 0.21/0.35 % (707308)Instructions burned: 76 (million)
% 0.21/0.35 % (707327)lrs+10_1_si=on:cs=on:random_seed=959577605:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.21/0.35 % (707328)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.21/0.35 % (707328)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=460652531:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.21/0.35 % (707327)Instruction limit reached!
% 0.21/0.35 % (707327)------------------------------
% 0.21/0.35 % (707327)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.35 % (707327)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.35 % (707327)CaDiCaL version: 2.1.3
% 0.21/0.35 % (707327)Termination reason: Instruction limit
% 0.21/0.35 % (707327)Termination phase: Saturation
% 0.21/0.35 % (707327)Time elapsed: 0.005 s
% 0.21/0.35 % (707327)Peak memory usage: 12 MB
% 0.21/0.35 % (707327)Instructions burned: 9 (million)
% 0.21/0.35 % (707306) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-707298-707306"...
% 0.21/0.35 % (707328)Instruction limit reached!
% 0.21/0.35 % (707328)------------------------------
% 0.21/0.35 % (707328)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.35 % (707328)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.35 % (707328)CaDiCaL version: 2.1.3
% 0.21/0.35 % (707328)Termination reason: Instruction limit
% 0.21/0.35 % (707328)Termination phase: Saturation
% 0.21/0.35 % (707328)Time elapsed: 0.003 s
% 0.21/0.35 % (707328)Peak memory usage: 12 MB
% 0.21/0.35 % (707328)Instructions burned: 5 (million)
% 0.21/0.35 % (707323)Instruction limit reached!
% 0.21/0.35 % (707323)------------------------------
% 0.21/0.35 % (707323)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.35 % (707323)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.35 % (707323)CaDiCaL version: 2.1.3
% 0.21/0.35 % (707323)Termination reason: Instruction limit
% 0.21/0.35 % (707323)Termination phase: Saturation
% 0.21/0.35 % (707323)Time elapsed: 0.017 s
% 0.21/0.35 % (707323)Peak memory usage: 12 MB
% 0.21/0.35 % (707323)Instructions burned: 29 (million)
% 0.21/0.35 % (707306)...printing done.
% 0.21/0.35 % (707306)Refutation found. Thanks to Tanya!
% 0.21/0.35 % SZS status Theorem for theBenchmark
% 0.21/0.35 % SZS output start Proof for theBenchmark
% 0.21/0.35 thf(type_def_5, type, 'type/ind_types/list': $tType > $tType).
% 0.21/0.35 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.35 thf(type_def_7, type, sK0: $tType).
% 0.21/0.35 thf(func_def_0, type, 'const/sets/set_of_list': !>[X0: $tType]:(('type/ind_types/list' @ X0 > X0 > $o))).
% 0.21/0.35 thf(func_def_1, type, 'const/sets/INSERT': !>[X0: $tType]:((X0 > (X0 > $o) > X0 > $o))).
% 0.21/0.35 thf(func_def_2, type, 'const/sets/EMPTY': !>[X0: $tType]:((X0 > $o))).
% 0.21/0.35 thf(func_def_3, type, 'const/ind_types/NIL': !>[X0: $tType]:('type/ind_types/list' @ X0)).
% 0.21/0.35 thf(func_def_4, type, 'const/ind_types/CONS': !>[X0: $tType]:((X0 > 'type/ind_types/list' @ X0 > 'type/ind_types/list' @ X0))).
% 0.21/0.35 thf(func_def_8, type, sK1: 'type/ind_types/list' @ sK0).
% 0.21/0.35 thf(func_def_9, type, sK2: !>[X0: $tType]:((('type/ind_types/list' @ X0 > $o) > X0))).
% 0.21/0.35 thf(func_def_10, type, sK3: !>[X0: $tType]:((('type/ind_types/list' @ X0 > $o) > 'type/ind_types/list' @ X0))).
% 0.21/0.35 thf(func_def_11, type, vNOT: ($o > $o)).
% 0.21/0.35 thf(func_def_13, type, sK5: !>[X0: $tType]:((X0 > (X0 > $o) > X0))).
% 0.21/0.35 thf(func_def_14, type, sK6: !>[X0: $tType]:((X0 > 'type/ind_types/list' @ X0 > X0))).
% 0.21/0.35 thf(func_def_15, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.21/0.35 thf(func_def_16, type, db0: !>[X0: $tType]:(X0)).
% 0.21/0.35 thf(func_def_17, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.21/0.35 thf(func_def_18, type, sK7: !>[X0: $tType]:(('type/ind_types/list' @ X0 > X0))).
% 0.21/0.35 thf(func_def_19, type, sK8: ('type/ind_types/list' @ sK0 > sK0)).
% 0.21/0.35 thf(f1,axiom,(
% 0.21/0.35 ! [X0 : $tType,X1 : ('type/ind_types/list' @ X0 > $o)] : (((X1 @ 'const/ind_types/NIL' @ X0) & ! [X2 : X0,X3 : 'type/ind_types/list' @ X0] : ((X1 @ X3) => (X1 @ ('const/ind_types/CONS' @ X0 @ X2 @ X3)))) => ! [X2 : 'type/ind_types/list' @ X0] : (X1 @ X2))),
% 0.21/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/ind_types/list_INDUCT_')).
% 0.21/0.35 thf(f3,axiom,(
% 0.21/0.35 ! [X0 : $tType,X1 : X0,X2 : (X0 > $o)] : ((('const/sets/INSERT' @ X0 @ X1 @ X2)) != 'const/sets/EMPTY' @ X0)),
% 0.21/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/NOT_INSERT_EMPTY_')).
% 0.21/0.35 thf(f4,axiom,(
% 0.21/0.35 ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : X0] : ((('const/sets/set_of_list' @ X0 @ ('const/ind_types/CONS' @ X0 @ X1 @ X2))) = (('const/sets/INSERT' @ X0 @ X1 @ ('const/sets/set_of_list' @ X0 @ X2))))),
% 0.21/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/set_of_list_1')).
% 0.21/0.35 thf(f5,axiom,(
% 0.21/0.35 ! [X0 : $tType] : ((('const/sets/set_of_list' @ X0 @ 'const/ind_types/NIL' @ X0)) = 'const/sets/EMPTY' @ X0)),
% 0.21/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/set_of_list_0')).
% 0.21/0.35 thf(f6,conjecture,(
% 0.21/0.35 ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : ((X1 = 'const/ind_types/NIL' @ X0) = ((('const/sets/set_of_list' @ X0 @ X1)) = 'const/sets/EMPTY' @ X0))),
% 0.21/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/SET_OF_LIST_EQ_EMPTY_')).
% 0.21/0.35 thf(f7,negated_conjecture,(
% 0.21/0.35 ~ ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : ((X1 = 'const/ind_types/NIL' @ X0) = ((('const/sets/set_of_list' @ X0 @ X1)) = 'const/sets/EMPTY' @ X0))),
% 0.21/0.35 inference(negated_conjecture,[status(cth)],[f6])).
% 0.21/0.35 thf(f8,plain,(
% 0.21/0.35 ! [X0 : $tType,X1 : ('type/ind_types/list' @ X0 > $o)] : (((X1 @ 'const/ind_types/NIL' @ X0) & ! [X2 : X0,X3 : 'type/ind_types/list' @ X0] : ((X1 @ X3) => (X1 @ ('const/ind_types/CONS' @ X0 @ X2 @ X3)))) => ! [X4 : 'type/ind_types/list' @ X0] : (X1 @ X4))),
% 0.21/0.35 inference(rectify,[],[f1])).
% 0.21/0.35 thf(f9,plain,(
% 0.21/0.35 ! [X0 : $tType,X1 : ('type/ind_types/list' @ X0 > $o)] : (((((X1 @ 'const/ind_types/NIL' @ X0)) = $true) & ! [X3 : 'type/ind_types/list' @ X0,X2 : X0] : ((((X1 @ X3)) = $true) => (((X1 @ ('const/ind_types/CONS' @ X0 @ X2 @ X3))) = $true))) => ! [X4 : 'type/ind_types/list' @ X0] : (((X1 @ X4)) = $true))),
% 0.21/0.35 inference(fool_elimination,[],[f8])).
% 0.21/0.35 thf(f10,plain,(
% 0.21/0.35 ~ ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : (('const/sets/EMPTY' @ X0 = (('const/sets/set_of_list' @ X0 @ X1))) <=> ('const/ind_types/NIL' @ X0 = X1))),
% 0.21/0.35 inference(fool_elimination,[],[f7])).
% 0.21/0.35 thf(f11,plain,(
% 0.21/0.35 ! [X0 : $tType,X2 : X0,X1 : 'type/ind_types/list' @ X0] : ((('const/sets/INSERT' @ X0 @ X2 @ ('const/sets/set_of_list' @ X0 @ X1))) = (('const/sets/set_of_list' @ X0 @ ('const/ind_types/CONS' @ X0 @ X2 @ X1))))),
% 0.21/0.35 inference(rectify,[],[f4])).
% 0.21/0.35 thf(f12,plain,(
% 0.21/0.35 ? [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : (('const/sets/EMPTY' @ X0 = (('const/sets/set_of_list' @ X0 @ X1))) <~> ('const/ind_types/NIL' @ X0 = X1))),
% 0.21/0.35 inference(ennf_transformation,[],[f10])).
% 0.21/0.35 thf(f13,plain,(
% 0.21/0.35 ! [X0 : $tType,X1 : ('type/ind_types/list' @ X0 > $o)] : (! [X4 : 'type/ind_types/list' @ X0] : (((X1 @ X4)) = $true) | ((((X1 @ 'const/ind_types/NIL' @ X0)) != $true) | ? [X2 : X0,X3 : 'type/ind_types/list' @ X0] : ((((X1 @ X3)) = $true) & (((X1 @ ('const/ind_types/CONS' @ X0 @ X2 @ X3))) != $true))))),
% 0.21/0.35 inference(ennf_transformation,[],[f9])).
% 0.21/0.35 thf(f14,plain,(
% 0.21/0.35 ! [X0 : $tType,X1 : ('type/ind_types/list' @ X0 > $o)] : ((((X1 @ 'const/ind_types/NIL' @ X0)) != $true) | ? [X2 : X0,X3 : 'type/ind_types/list' @ X0] : ((((X1 @ X3)) = $true) & (((X1 @ ('const/ind_types/CONS' @ X0 @ X2 @ X3))) != $true)) | ! [X4 : 'type/ind_types/list' @ X0] : (((X1 @ X4)) = $true))),
% 0.21/0.35 inference(flattening,[],[f13])).
% 0.21/0.35 thf(f15,plain,(
% 0.21/0.35 ? [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : ((('const/ind_types/NIL' @ X0 != X1) | ('const/sets/EMPTY' @ X0 != (('const/sets/set_of_list' @ X0 @ X1)))) & (('const/ind_types/NIL' @ X0 = X1) | ('const/sets/EMPTY' @ X0 = (('const/sets/set_of_list' @ X0 @ X1)))))),
% 0.21/0.35 inference(nnf_transformation,[],[f12])).
% 0.21/0.35 thf(f16,plain,(
% 0.21/0.35 ((sK1 != 'const/ind_types/NIL' @ sK0) | ((('const/sets/set_of_list' @ sK0 @ sK1)) != 'const/sets/EMPTY' @ sK0)) & ((sK1 = 'const/ind_types/NIL' @ sK0) | ((('const/sets/set_of_list' @ sK0 @ sK1)) = 'const/sets/EMPTY' @ sK0))),
% 0.21/0.35 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f15])).
% 0.21/0.35 thf(f17,plain,(
% 0.21/0.35 ! [X0 : $tType,X1 : ('type/ind_types/list' @ X0 > $o)] : ((((X1 @ 'const/ind_types/NIL' @ X0)) != $true) | ((((X1 @ (sK3 @ X0 @ X1))) = $true) & (((X1 @ ('const/ind_types/CONS' @ X0 @ (sK2 @ X0 @ X1) @ (sK3 @ X0 @ X1)))) != $true)) | ! [X4 : 'type/ind_types/list' @ X0] : (((X1 @ X4)) = $true))),
% 0.21/0.35 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP]),skolemize(X3,sK3 @ X0 @ X1),skolemize(X3,sK3 @ X0 @ X1)],[f14])).
% 0.21/0.35 thf(f18,plain,(
% 0.21/0.35 ! [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0] : ((('const/sets/set_of_list' @ X0 @ ('const/ind_types/CONS' @ X0 @ X1 @ X2))) = (('const/sets/INSERT' @ X0 @ X1 @ ('const/sets/set_of_list' @ X0 @ X2))))),
% 0.21/0.35 inference(rectify,[],[f11])).
% 0.21/0.35 thf(f20,plain,(
% 0.21/0.35 ( ! [X0 : $tType] : (('const/sets/EMPTY' @ X0 = (('const/sets/set_of_list' @ X0 @ 'const/ind_types/NIL' @ X0)))) )),
% 0.21/0.35 inference(cnf_transformation,[],[f5])).
% 0.21/0.35 thf(f21,plain,(
% 0.21/0.35 ((('const/sets/set_of_list' @ sK0 @ sK1)) = 'const/sets/EMPTY' @ sK0) | (sK1 = 'const/ind_types/NIL' @ sK0)),
% 0.21/0.35 inference(cnf_transformation,[],[f16])).
% 0.21/0.35 thf(f22,plain,(
% 0.21/0.35 ((('const/sets/set_of_list' @ sK0 @ sK1)) != 'const/sets/EMPTY' @ sK0) | (sK1 != 'const/ind_types/NIL' @ sK0)),
% 0.21/0.35 inference(cnf_transformation,[],[f16])).
% 0.21/0.35 thf(f23,plain,(
% 0.21/0.35 ( ! [X0 : $tType,X1 : ('type/ind_types/list' @ X0 > $o),X4 : 'type/ind_types/list' @ X0] : ((((X1 @ ('const/ind_types/CONS' @ X0 @ (sK2 @ X0 @ X1) @ (sK3 @ X0 @ X1)))) != $true) | (((X1 @ X4)) = $true) | (((X1 @ 'const/ind_types/NIL' @ X0)) != $true)) )),
% 0.21/0.35 inference(cnf_transformation,[],[f17])).
% 0.21/0.35 thf(f25,plain,(
% 0.21/0.35 ( ! [X0 : $tType,X2 : (X0 > $o),X1 : X0] : (((('const/sets/INSERT' @ X0 @ X1 @ X2)) != 'const/sets/EMPTY' @ X0)) )),
% 0.21/0.35 inference(cnf_transformation,[],[f3])).
% 0.21/0.35 thf(f26,plain,(
% 0.21/0.35 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : X0] : (((('const/sets/set_of_list' @ X0 @ ('const/ind_types/CONS' @ X0 @ X1 @ X2))) = (('const/sets/INSERT' @ X0 @ X1 @ ('const/sets/set_of_list' @ X0 @ X2))))) )),
% 0.21/0.35 inference(cnf_transformation,[],[f18])).
% 0.21/0.35 thf(f29,definition,(
% 0.21/0.35 spl4_1 <=> (sK1 = 'const/ind_types/NIL' @ sK0)),
% 0.21/0.35 introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition])).
% 0.21/0.35 thf(f33,definition,(
% 0.21/0.35 spl4_2 <=> ((('const/sets/set_of_list' @ sK0 @ sK1)) = 'const/sets/EMPTY' @ sK0)),
% 0.21/0.35 introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition])).
% 0.21/0.35 thf(f34,plain,(
% 0.21/0.35 ((('const/sets/set_of_list' @ sK0 @ sK1)) = 'const/sets/EMPTY' @ sK0) | ~spl4_2),
% 0.21/0.35 inference(avatar_component_clause,[],[f33])).
% 0.21/0.35 thf(f35,plain,(
% 0.21/0.35 ((('const/sets/set_of_list' @ sK0 @ sK1)) != 'const/sets/EMPTY' @ sK0) | spl4_2),
% 0.21/0.35 inference(avatar_component_clause,[],[f33])).
% 0.21/0.35 thf(f36,plain,(
% 0.21/0.35 ~spl4_1 | ~spl4_2),
% 0.21/0.35 inference(avatar_split_clause,[],[f22,f33,f29])).
% 0.21/0.35 thf(f37,plain,(
% 0.21/0.35 spl4_1 | spl4_2),
% 0.21/0.35 inference(avatar_split_clause,[],[f21,f33,f29])).
% 0.21/0.35 thf(f43,plain,(
% 0.21/0.35 ((('const/sets/set_of_list' @ sK0 @ 'const/ind_types/NIL' @ sK0)) = (('const/sets/set_of_list' @ sK0 @ sK1))) | ~spl4_2),
% 0.21/0.35 inference(superposition,[],[f34,f20])).
% 0.21/0.35 thf(f47,definition,(
% 0.21/0.35 spl4_3 <=> ((('const/sets/set_of_list' @ sK0 @ 'const/ind_types/NIL' @ sK0)) = (('const/sets/set_of_list' @ sK0 @ sK1)))),
% 0.21/0.35 introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition])).
% 0.21/0.35 thf(f49,plain,(
% 0.21/0.35 ((('const/sets/set_of_list' @ sK0 @ 'const/ind_types/NIL' @ sK0)) = (('const/sets/set_of_list' @ sK0 @ sK1))) | ~spl4_3),
% 0.21/0.35 inference(avatar_component_clause,[],[f47])).
% 0.21/0.35 thf(f50,plain,(
% 0.21/0.35 spl4_3 | ~spl4_2),
% 0.21/0.35 inference(avatar_split_clause,[],[f43,f33,f47])).
% 0.21/0.35 thf(f61,plain,(
% 0.21/0.35 ( ! [X0 : $tType,X2 : (X0 > $o),X1 : X0] : (((('const/sets/INSERT' @ X0 @ X1 @ X2)) != (('const/sets/set_of_list' @ X0 @ 'const/ind_types/NIL' @ X0)))) )),
% 0.21/0.35 inference(forward_demodulation,[],[f25,f20])).
% 0.21/0.35 thf(f68,plain,(
% 0.21/0.35 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : X0] : (((('const/sets/set_of_list' @ X0 @ ('const/ind_types/CONS' @ X0 @ X1 @ X2))) != (('const/sets/set_of_list' @ X0 @ 'const/ind_types/NIL' @ X0)))) )),
% 0.21/0.35 inference(superposition,[],[f61,f26])).
% 0.21/0.35 thf(f355,plain,(
% 0.21/0.35 ( ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : (((((^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1))) @ 'const/ind_types/NIL' @ X0)) != $true) | ((('const/ind_types/CONS' @ X0 @ (sK2 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1)))) @ (sK3 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1)))))) = X1)) )),
% 0.21/0.35 inference(leibniz_equality_elimination,[],[f23])).
% 0.21/0.35 thf(f368,plain,(
% 0.21/0.35 ( ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : (((('const/ind_types/CONS' @ X0 @ (sK2 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1)))) @ (sK3 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1)))))) = X1) | (((~ ('const/ind_types/NIL' @ X0 = X1))) != $true)) )),
% 0.21/0.35 inference(beta-eta_normalization,[],[f355])).
% 0.21/0.35 thf(f369,plain,(
% 0.21/0.35 ( ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : (((('const/ind_types/NIL' @ X0 = X1)) = $true) | ((('const/ind_types/CONS' @ X0 @ (sK2 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1)))) @ (sK3 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1)))))) = X1)) )),
% 0.21/0.35 inference(not_proxy_clausification,[],[f368])).
% 0.21/0.35 thf(f370,plain,(
% 0.21/0.35 ( ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : (((('const/ind_types/CONS' @ X0 @ (sK2 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1)))) @ (sK3 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1)))))) = X1) | ('const/ind_types/NIL' @ X0 = X1)) )),
% 0.21/0.35 inference(equality_proxy_clausification,[],[f369])).
% 0.21/0.35 thf(f698,plain,(
% 0.21/0.35 ( ! [X1 : $tType,X0 : 'type/ind_types/list' @ X1] : (((('const/sets/set_of_list' @ X1 @ 'const/ind_types/NIL' @ X1)) != (('const/sets/set_of_list' @ X1 @ X0))) | ('const/ind_types/NIL' @ X1 = X0)) )),
% 0.21/0.35 inference(superposition,[],[f68,f370])).
% 0.21/0.35 thf(f712,plain,(
% 0.21/0.35 ( ! [X0 : 'type/ind_types/list' @ sK0] : (((('const/sets/set_of_list' @ sK0 @ X0)) != (('const/sets/set_of_list' @ sK0 @ sK1))) | ('const/ind_types/NIL' @ sK0 = X0)) ) | ~spl4_3),
% 0.21/0.35 inference(superposition,[],[f698,f49])).
% 0.21/0.35 thf(f727,plain,(
% 0.21/0.35 (sK1 = 'const/ind_types/NIL' @ sK0) | ~spl4_3),
% 0.21/0.35 inference(equality_resolution,[],[f712])).
% 0.21/0.35 thf(f737,plain,(
% 0.21/0.35 spl4_1 | ~spl4_3),
% 0.21/0.35 inference(avatar_split_clause,[],[f727,f47,f29])).
% 0.21/0.35 thf(f738,plain,(
% 0.21/0.35 ((('const/sets/set_of_list' @ sK0 @ 'const/ind_types/NIL' @ sK0)) != (('const/sets/set_of_list' @ sK0 @ sK1))) | spl4_2),
% 0.21/0.35 inference(forward_demodulation,[],[f35,f20])).
% 0.21/0.35 thf(f739,plain,(
% 0.21/0.35 $false | (spl4_2 | ~spl4_3)),
% 0.21/0.35 inference(forward_subsumption_resolution,[],[f738,f49])).
% 0.21/0.35 thf(f740,plain,(
% 0.21/0.35 spl4_2 | ~spl4_3),
% 0.21/0.35 inference(avatar_contradiction_clause,[],[f739])).
% 0.21/0.35 thf(f741,definition,(
% 0.21/0.35 (sK1 != 'const/ind_types/NIL' @ sK0) | ((('const/sets/set_of_list' @ sK0 @ 'const/ind_types/NIL' @ sK0)) = (('const/sets/set_of_list' @ sK0 @ sK1)))),
% 0.21/0.35 introduced(theory,[theory_tautology_sat_conflict])).
% 0.21/0.35 cnf(s1, plain, ~spl4_1 | ~spl4_2, inference(sat_conversion,[],[f36])).
% 0.21/0.35 cnf(s2, plain, spl4_1 | spl4_2, inference(sat_conversion,[],[f37])).
% 0.21/0.35 cnf(s3, plain, ~spl4_2 | spl4_3, inference(sat_conversion,[],[f50])).
% 0.21/0.35 cnf(s19, plain, spl4_1 | ~spl4_3, inference(sat_conversion,[],[f737])).
% 0.21/0.35 cnf(s20, plain, spl4_2 | ~spl4_3, inference(sat_conversion,[],[f740])).
% 0.21/0.35 cnf(s21, plain, ~spl4_1 | spl4_3, inference(sat_conversion,[],[f741])).
% 0.21/0.35 cnf(s22, plain, spl4_1, inference(rat,[],[s3,s2,s19])).
% 0.21/0.35 cnf(s23, plain, spl4_3, inference(rat,[],[s21,s22])).
% 0.21/0.35 cnf(s24, plain, ~spl4_2, inference(rat,[],[s1,s22])).
% 0.21/0.35 cnf(s25, plain, $false, inference(rat,[],[s20,s23,s24])).
% 0.21/0.35 thf(f742,plain,(
% 0.21/0.35 $false),
% 0.21/0.35 inference(avatar_sat_refutation,[],[s25])).
% 0.21/0.35 % SZS output end Proof for theBenchmark
% 0.21/0.35 % (707306)------------------------------
% 0.21/0.35 % (707306)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.35 % (707306)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.35 % (707306)CaDiCaL version: 2.1.3
% 0.21/0.35 % (707306)Termination reason: Refutation
% 0.21/0.35 % (707306)Time elapsed: 0.062 s
% 0.21/0.35 % (707306)Peak memory usage: 13 MB
% 0.21/0.35 % (707306)Instructions burned: 106 (million)
% 0.21/0.35 % (707298)Success in time 0.095 s
% 0.21/0.35 % Vampire exiting
%------------------------------------------------------------------------------