%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL726^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 08:14:34 AM UTC 2026
% Result : Theorem 0.37s 0.46s
% Output : Refutation 0.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL726^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.25 % Computer : n014.cluster.edu
% 0.13/0.25 % Model : x86_64 x86_64
% 0.13/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.25 % Memory : 8046.5625MB
% 0.13/0.25 % OS : Linux 6.8.0-71-generic
% 0.13/0.25 % CPULimit : 300
% 0.13/0.25 % WCLimit : 300
% 0.13/0.25 % DateTime : Tue Sep 29 09:57:30 UTC 2026
% 0.13/0.26 % CPUTime :
% 0.13/0.26 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.27/0.31 Running higher-order theorem proving
% 0.27/0.33 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
% 0.37/0.46 % (2469485)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.37/0.46 % (2469490)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3802299633:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.37/0.46 % (2469496)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.37/0.46 % (2469496)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
% 0.37/0.46 % (2469491)lrs+10_16_si=on:nwc=1.5:random_seed=2704356172:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.37/0.46 % (2469492)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2775946188:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.37/0.46 % (2469494)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1038251766:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.37/0.46 % (2469496)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=1418503723:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.37/0.46 % (2469493)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=2383041447: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)
% 0.37/0.46 % (2469495)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3958281214:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.37/0.46 % (2469492)Instruction limit reached!
% 0.37/0.46 % (2469492)------------------------------
% 0.37/0.46 % (2469492)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.46 % (2469492)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.46 % (2469492)CaDiCaL version: 2.1.3
% 0.37/0.46 % (2469492)Termination reason: Instruction limit
% 0.37/0.46 % (2469492)Termination phase: Saturation
% 0.37/0.46 % (2469492)Time elapsed: 0.004 s
% 0.37/0.46 % (2469492)Peak memory usage: 12 MB
% 0.37/0.46 % (2469492)Instructions burned: 3 (million)
% 0.37/0.46 % (2469491)Instruction limit reached!
% 0.37/0.46 % (2469491)------------------------------
% 0.37/0.46 % (2469491)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.46 % (2469491)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.46 % (2469491)CaDiCaL version: 2.1.3
% 0.37/0.46 % (2469491)Termination reason: Instruction limit
% 0.37/0.46 % (2469491)Termination phase: Saturation
% 0.37/0.46 % (2469491)Time elapsed: 0.019 s
% 0.37/0.46 % (2469491)Peak memory usage: 12 MB
% 0.37/0.46 % (2469491)Instructions burned: 18 (million)
% 0.37/0.46 % (2469494)Instruction limit reached!
% 0.37/0.46 % (2469494)------------------------------
% 0.37/0.46 % (2469494)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.46 % (2469494)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.46 % (2469494)CaDiCaL version: 2.1.3
% 0.37/0.46 % (2469494)Termination reason: Instruction limit
% 0.37/0.46 % (2469494)Termination phase: Saturation
% 0.37/0.46 % (2469494)Time elapsed: 0.024 s
% 0.37/0.46 % (2469494)Peak memory usage: 11 MB
% 0.37/0.46 % (2469494)Instructions burned: 24 (million)
% 0.37/0.46 % (2469490)Instruction limit reached!
% 0.37/0.46 % (2469490)------------------------------
% 0.37/0.46 % (2469490)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.46 % (2469490)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.46 % (2469490)CaDiCaL version: 2.1.3
% 0.37/0.46 % (2469490)Termination reason: Instruction limit
% 0.37/0.46 % (2469490)Termination phase: Saturation
% 0.37/0.46 % (2469490)Time elapsed: 0.042 s
% 0.37/0.46 % (2469490)Peak memory usage: 12 MB
% 0.37/0.46 % (2469490)Instructions burned: 90 (million)
% 0.37/0.46 % (2469504)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1103714034:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.37/0.46 % (2469504)Instruction limit reached!
% 0.37/0.46 % (2469504)------------------------------
% 0.37/0.46 % (2469504)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.46 % (2469504)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.46 % (2469504)CaDiCaL version: 2.1.3
% 0.37/0.46 % (2469504)Termination reason: Instruction limit
% 0.37/0.46 % (2469504)Termination phase: Saturation
% 0.37/0.46 % (2469504)Time elapsed: 0.003 s
% 0.37/0.46 % (2469504)Peak memory usage: 12 MB
% 0.37/0.46 % (2469504)Instructions burned: 2 (million)
% 0.37/0.46 % (2469507)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1312301983:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.37/0.46 % (2469506)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.37/0.46 % (2469507)Instruction limit reached!
% 0.37/0.46 % (2469507)------------------------------
% 0.37/0.46 % (2469507)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.46 % (2469507)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.46 % (2469507)CaDiCaL version: 2.1.3
% 0.37/0.46 % (2469507)Termination reason: Instruction limit
% 0.37/0.46 % (2469507)Termination phase: Saturation
% 0.37/0.46 % (2469507)Time elapsed: 0.007 s
% 0.37/0.46 % (2469507)Peak memory usage: 12 MB
% 0.37/0.46 % (2469507)Instructions burned: 14 (million)
% 0.37/0.46 % (2469505)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=374700789:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.37/0.46 % (2469506)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=564538508:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.37/0.46 % (2469505) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2469485-2469505"...
% 0.37/0.46 % (2469505)...printing done.
% 0.37/0.46 % (2469505)Refutation found. Thanks to Tanya!
% 0.37/0.46 % SZS status Theorem for theBenchmark
% 0.37/0.46 % SZS output start Proof for theBenchmark
% 0.37/0.46 thf(type_def_5, type, a: $tType).
% 0.37/0.46 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.37/0.46 thf(func_def_3, type, diff: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > X1) > X0))).
% 0.37/0.46 thf(func_def_4, type, vEPSILON: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.37/0.46 thf(func_def_5, type, sK0: (((a > $o) > a) > a > $o)).
% 0.37/0.46 thf(func_def_6, type, sK1: (((a > $o) > a) > a)).
% 0.37/0.46 thf(func_def_7, type, sK2: (((a > $o) > $o) > (a > $o) > a)).
% 0.37/0.46 thf(func_def_8, type, sK3: (((a > $o) > $o) > a > $o)).
% 0.37/0.46 thf(func_def_9, type, vNOT: ($o > $o)).
% 0.37/0.46 thf(func_def_10, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.37/0.46 thf(func_def_11, type, db0: !>[X0: $tType]:(X0)).
% 0.37/0.46 thf(func_def_12, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.37/0.46 thf(f1,conjecture,(
% 0.37/0.46 ! [X0 : ((a > $o) > $o)] : (! [X1 : (a > $o)] : ((X0 @ X1) => ? [X2 : a] : (X1 @ X2)) => ? [X3 : ((a > $o) > a)] : ! [X1 : (a > $o)] : ((X0 @ X1) => (X1 @ (X3 @ X1)))) => ! [X4 : (((a > $o) > a) > a > $o)] : (! [X5 : ((a > $o) > a)] : ? [X6 : a] : (X4 @ X5 @ X6) => ? [X3 : ((a > $o) > a)] : (X4 @ X3 @ (X3 @ (X4 @ X3))))),
% 0.37/0.46 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM534)).
% 0.37/0.46 thf(f2,negated_conjecture,(
% 0.37/0.46 ~(! [X0 : ((a > $o) > $o)] : (! [X1 : (a > $o)] : ((X0 @ X1) => ? [X2 : a] : (X1 @ X2)) => ? [X3 : ((a > $o) > a)] : ! [X1 : (a > $o)] : ((X0 @ X1) => (X1 @ (X3 @ X1)))) => ! [X4 : (((a > $o) > a) > a > $o)] : (! [X5 : ((a > $o) > a)] : ? [X6 : a] : (X4 @ X5 @ X6) => ? [X3 : ((a > $o) > a)] : (X4 @ X3 @ (X3 @ (X4 @ X3)))))),
% 0.37/0.46 inference(negated_conjecture,[status(cth)],[f1])).
% 0.37/0.46 thf(f3,plain,(
% 0.37/0.46 ~(! [X0 : ((a > $o) > $o)] : (! [X1 : (a > $o)] : ((X0 @ X1) => ? [X2 : a] : (X1 @ X2)) => ? [X3 : ((a > $o) > a)] : ! [X4 : (a > $o)] : ((X0 @ X4) => (X4 @ (X3 @ X4)))) => ! [X5 : (((a > $o) > a) > a > $o)] : (! [X6 : ((a > $o) > a)] : ? [X7 : a] : (X5 @ X6 @ X7) => ? [X8 : ((a > $o) > a)] : (X5 @ X8 @ (X8 @ (X5 @ X8)))))),
% 0.37/0.46 inference(rectify,[],[f2])).
% 0.37/0.46 thf(f4,plain,(
% 0.37/0.46 ~(! [X0 : ((a > $o) > $o)] : (! [X1 : (a > $o)] : ((((X0 @ X1)) = $true) => ? [X2 : a] : (((X1 @ X2)) = $true)) => ? [X3 : ((a > $o) > a)] : ! [X4 : (a > $o)] : (($true = ((X0 @ X4))) => ($true = ((X4 @ (X3 @ X4)))))) => ! [X5 : (((a > $o) > a) > a > $o)] : (! [X6 : ((a > $o) > a)] : ? [X7 : a] : ($true = ((X5 @ X6 @ X7))) => ? [X8 : ((a > $o) > a)] : ($true = ((X5 @ X8 @ (X8 @ (X5 @ X8)))))))),
% 0.37/0.46 inference(fool_elimination,[],[f3])).
% 0.37/0.46 thf(f6,plain,(
% 0.37/0.46 ( ! [X0 : $tType,X2 : X0,X1 : (X0 > $o)] : (($true = ((X1 @ (vEPSILON @ X0 @ X1)))) | ($false = ((X1 @ X2)))) )),
% 0.37/0.46 introduced(theory,[Hilbert's_choice_axiom_instance])).
% 0.37/0.46 thf(f7,plain,(
% 0.37/0.46 ? [X5 : (((a > $o) > a) > a > $o)] : (! [X8 : ((a > $o) > a)] : ($true != ((X5 @ X8 @ (X8 @ (X5 @ X8))))) & ! [X6 : ((a > $o) > a)] : ? [X7 : a] : ($true = ((X5 @ X6 @ X7)))) & ! [X0 : ((a > $o) > $o)] : (? [X3 : ((a > $o) > a)] : ! [X4 : (a > $o)] : (($true = ((X4 @ (X3 @ X4)))) | ($true != ((X0 @ X4)))) | ? [X1 : (a > $o)] : ((((X0 @ X1)) = $true) & ! [X2 : a] : (((X1 @ X2)) != $true)))),
% 0.37/0.46 inference(ennf_transformation,[],[f4])).
% 0.37/0.46 thf(f8,plain,(
% 0.37/0.46 ? [X0 : (((a > $o) > a) > a > $o)] : (! [X1 : ((a > $o) > a)] : ($true != ((X0 @ X1 @ (X1 @ (X0 @ X1))))) & ! [X2 : ((a > $o) > a)] : ? [X3 : a] : ($true = ((X0 @ X2 @ X3)))) & ! [X4 : ((a > $o) > $o)] : (? [X5 : ((a > $o) > a)] : ! [X6 : (a > $o)] : (($true = ((X6 @ (X5 @ X6)))) | ($true != ((X4 @ X6)))) | ? [X7 : (a > $o)] : (($true = ((X4 @ X7))) & ! [X8 : a] : ($true != ((X7 @ X8)))))),
% 0.37/0.46 inference(rectify,[],[f7])).
% 0.37/0.46 thf(f9,plain,(
% 0.37/0.46 (! [X1 : ((a > $o) > a)] : ($true != ((sK0 @ X1 @ (X1 @ (sK0 @ X1))))) & ! [X2 : ((a > $o) > a)] : ($true = ((sK0 @ X2 @ (sK1 @ X2))))) & ! [X4 : ((a > $o) > $o)] : (! [X6 : (a > $o)] : (($true = ((X6 @ (sK2 @ X4 @ X6)))) | ($true != ((X4 @ X6)))) | (($true = ((X4 @ (sK3 @ X4)))) & ! [X8 : a] : ($true != ((sK3 @ X4 @ X8)))))),
% 0.37/0.46 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,vAPP,vAPP,vAPP]),skolemize(X0,sK0),skolemize(X7,sK3 @ X4),skolemize(X7,sK3 @ X4),skolemize(X7,sK3 @ X4)],[f8])).
% 0.37/0.46 thf(f12,plain,(
% 0.37/0.46 ( ! [X2 : ((a > $o) > a)] : (($true = ((sK0 @ X2 @ (sK1 @ X2))))) )),
% 0.37/0.46 inference(cnf_transformation,[],[f9])).
% 0.37/0.46 thf(f13,plain,(
% 0.37/0.46 ( ! [X1 : ((a > $o) > a)] : (($true != ((sK0 @ X1 @ (X1 @ (sK0 @ X1)))))) )),
% 0.37/0.46 inference(cnf_transformation,[],[f9])).
% 0.37/0.46 thf(f31,plain,(
% 0.37/0.46 ( ! [X0 : a] : (($true != $true) | (((sK0 @ vEPSILON @ a @ X0)) = $false)) )),
% 0.37/0.46 inference(superposition,[],[f13,f6])).
% 0.37/0.46 thf(f32,plain,(
% 0.37/0.46 ( ! [X0 : a] : ((((sK0 @ vEPSILON @ a @ X0)) = $false)) )),
% 0.37/0.46 inference(trivial_inequality_removal,[],[f31])).
% 0.37/0.46 thf(f33,plain,(
% 0.37/0.46 ($true = $false)),
% 0.37/0.46 inference(superposition,[],[f32,f12])).
% 0.37/0.46 thf(f38,plain,(
% 0.37/0.46 $false),
% 0.37/0.46 inference(trivial_inequality_removal,[],[f33])).
% 0.37/0.46 % SZS output end Proof for theBenchmark
% 0.37/0.46 % (2469505)------------------------------
% 0.37/0.46 % (2469505)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.46 % (2469505)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.46 % (2469505)CaDiCaL version: 2.1.3
% 0.37/0.46 % (2469505)Termination reason: Refutation
% 0.37/0.46 % (2469505)Time elapsed: 0.005 s
% 0.37/0.46 % (2469505)Peak memory usage: 12 MB
% 0.37/0.46 % (2469505)Instructions burned: 3 (million)
% 0.37/0.46 % (2469485)Success in time 0.113 s
% 0.37/0.46 % Vampire exiting
%------------------------------------------------------------------------------