%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL734^5 : 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 : n019.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 08:14:35 AM UTC 2026
% Result : Theorem 0.20s 0.31s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL734^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n019.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 10:07:33 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.23 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
% 0.20/0.31 % (564332)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.31 % (564338)lrs+10_16_si=on:nwc=1.5:random_seed=1657463176:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.31 % (564338)Instruction limit reached!
% 0.20/0.31 % (564338)------------------------------
% 0.20/0.31 % (564338)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.31 % (564338)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.31 % (564338)CaDiCaL version: 2.1.3
% 0.20/0.31 % (564338)Termination reason: Instruction limit
% 0.20/0.31 % (564338)Termination phase: Saturation
% 0.20/0.31 % (564338)Time elapsed: 0.006 s
% 0.20/0.31 % (564338)Peak memory usage: 12 MB
% 0.20/0.31 % (564338)Instructions burned: 20 (million)
% 0.20/0.31 % (564337)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=4229094904:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.31 % (564339)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=619535756:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.31 % (564339)Refutation not found, incomplete strategy
% 0.20/0.31 % (564339)------------------------------
% 0.20/0.31 % (564339)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.31 % (564339)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.31 % (564339)CaDiCaL version: 2.1.3
% 0.20/0.31 % (564339)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.31 % (564339)Time elapsed: 0.002 s
% 0.20/0.31 % (564339)Peak memory usage: 12 MB
% 0.20/0.31 % (564339)Instructions burned: 3 (million)
% 0.20/0.31 % (564339)------------------------------
% 0.20/0.31 % (564339)------------------------------
% 0.20/0.31 % (564347)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3538293910:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.20/0.31 % (564347)Instruction limit reached!
% 0.20/0.31 % (564347)------------------------------
% 0.20/0.31 % (564347)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.31 % (564347)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.31 % (564347)CaDiCaL version: 2.1.3
% 0.20/0.31 % (564347)Termination reason: Instruction limit
% 0.20/0.31 % (564347)Termination phase: Saturation
% 0.20/0.31 % (564347)Time elapsed: 0.002 s
% 0.20/0.31 % (564347)Peak memory usage: 12 MB
% 0.20/0.31 % (564347)Instructions burned: 6 (million)
% 0.20/0.31 % (564340)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=874903299: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)
% 0.20/0.31 % (564351)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.20/0.31 % (564348)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2498744060:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.20/0.31 % (564351)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=551243631:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.20/0.31 % (564348) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-564332-564348"...
% 0.20/0.31 % (564351)Instruction limit reached!
% 0.20/0.31 % (564351)------------------------------
% 0.20/0.31 % (564351)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.31 % (564351)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.31 % (564351)CaDiCaL version: 2.1.3
% 0.20/0.31 % (564351)Termination reason: Instruction limit
% 0.20/0.31 % (564351)Termination phase: Saturation
% 0.20/0.31 % (564351)Time elapsed: 0.003 s
% 0.20/0.31 % (564351)Peak memory usage: 12 MB
% 0.20/0.31 % (564351)Instructions burned: 10 (million)
% 0.20/0.31 % (564340)Refutation not found, incomplete strategy
% 0.20/0.31 % (564340)------------------------------
% 0.20/0.31 % (564340)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.31 % (564340)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.31 % (564340)CaDiCaL version: 2.1.3
% 0.20/0.31 % (564340)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.31 % (564340)Time elapsed: 0.014 s
% 0.20/0.31 % (564340)Peak memory usage: 12 MB
% 0.20/0.31 % (564340)Instructions burned: 13 (million)
% 0.20/0.31 % (564348)...printing done.
% 0.20/0.31 % (564340)------------------------------
% 0.20/0.31 % (564340)------------------------------
% 0.20/0.31 % (564348)Refutation found. Thanks to Tanya!
% 0.20/0.31 % SZS status Theorem for theBenchmark
% 0.20/0.31 % SZS output start Proof for theBenchmark
% 0.20/0.31 thf(type_def_5, type, b: $tType).
% 0.20/0.31 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.31 thf(func_def_3, type, diff: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > X1) > X0))).
% 0.20/0.31 thf(func_def_4, type, vEPSILON: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.20/0.31 thf(func_def_5, type, sK0: (((b > $o) > b) > b > $o)).
% 0.20/0.31 thf(func_def_6, type, sK1: (((b > $o) > b) > b)).
% 0.20/0.31 thf(func_def_7, type, sK2: (((b > $o) > b > $o) > ((b > $o) > b > $o) > b > $o)).
% 0.20/0.31 thf(func_def_8, type, sK3: (((b > $o) > b > $o) > ((b > $o) > b > $o) > (b > $o) > b)).
% 0.20/0.31 thf(func_def_9, type, vNOT: ($o > $o)).
% 0.20/0.31 thf(func_def_10, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.20/0.31 thf(func_def_11, type, db0: !>[X0: $tType]:(X0)).
% 0.20/0.31 thf(func_def_12, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.20/0.31 thf(f1,conjecture,(
% 0.20/0.31 ! [X1 : ((b > $o) > b > $o),X0 : ((b > $o) > b > $o)] : (! [X2 : (b > $o)] : ? [X3 : b] : ((X1 @ X2 @ X3) | (X0 @ X2 @ X3)) => ? [X4 : ((b > $o) > b)] : ! [X2 : (b > $o)] : ((X0 @ X2 @ (X4 @ X2)) | (X1 @ X2 @ (X4 @ X2)))) => ? [X5 : ((b > $o) > b)] : ! [X6 : (b > $o)] : (? [X7 : b] : (X6 @ X7) => (X6 @ (X5 @ X6)))),
% 0.20/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cX5310B)).
% 0.20/0.31 thf(f2,negated_conjecture,(
% 0.20/0.31 ~(! [X1 : ((b > $o) > b > $o),X0 : ((b > $o) > b > $o)] : (! [X2 : (b > $o)] : ? [X3 : b] : ((X1 @ X2 @ X3) | (X0 @ X2 @ X3)) => ? [X4 : ((b > $o) > b)] : ! [X2 : (b > $o)] : ((X0 @ X2 @ (X4 @ X2)) | (X1 @ X2 @ (X4 @ X2)))) => ? [X5 : ((b > $o) > b)] : ! [X6 : (b > $o)] : (? [X7 : b] : (X6 @ X7) => (X6 @ (X5 @ X6))))),
% 0.20/0.31 inference(negated_conjecture,[status(cth)],[f1])).
% 0.20/0.31 thf(f3,plain,(
% 0.20/0.31 ~(! [X0 : ((b > $o) > b > $o),X1 : ((b > $o) > b > $o)] : (! [X2 : (b > $o)] : ? [X3 : b] : ((X0 @ X2 @ X3) | (X1 @ X2 @ X3)) => ? [X4 : ((b > $o) > b)] : ! [X5 : (b > $o)] : ((X1 @ X5 @ (X4 @ X5)) | (X0 @ X5 @ (X4 @ X5)))) => ? [X6 : ((b > $o) > b)] : ! [X7 : (b > $o)] : (? [X8 : b] : (X7 @ X8) => (X7 @ (X6 @ X7))))),
% 0.20/0.31 inference(rectify,[],[f2])).
% 0.20/0.31 thf(f4,plain,(
% 0.20/0.31 ~(! [X1 : ((b > $o) > b > $o),X0 : ((b > $o) > b > $o)] : (! [X2 : (b > $o)] : ? [X3 : b] : ((((X0 @ X2 @ X3)) = $true) | (((X1 @ X2 @ X3)) = $true)) => ? [X4 : ((b > $o) > b)] : ! [X5 : (b > $o)] : ((((X0 @ X5 @ (X4 @ X5))) = $true) | (((X1 @ X5 @ (X4 @ X5))) = $true))) => ? [X6 : ((b > $o) > b)] : ! [X7 : (b > $o)] : (? [X8 : b] : ($true = ((X7 @ X8))) => (((X7 @ (X6 @ X7))) = $true)))),
% 0.20/0.31 inference(fool_elimination,[],[f3])).
% 0.20/0.31 thf(f6,plain,(
% 0.20/0.31 ( ! [X0 : $tType,X2 : X0,X1 : (X0 > $o)] : ((((X1 @ (vEPSILON @ X0 @ X1))) = $true) | ($false = ((X1 @ X2)))) )),
% 0.20/0.31 introduced(theory,[Hilbert's_choice_axiom_instance])).
% 0.20/0.31 thf(f7,plain,(
% 0.20/0.31 ! [X6 : ((b > $o) > b)] : ? [X7 : (b > $o)] : (? [X8 : b] : ($true = ((X7 @ X8))) & (((X7 @ (X6 @ X7))) != $true)) & ! [X1 : ((b > $o) > b > $o),X0 : ((b > $o) > b > $o)] : (? [X2 : (b > $o)] : ! [X3 : b] : ((((X0 @ X2 @ X3)) != $true) & (((X1 @ X2 @ X3)) != $true)) | ? [X4 : ((b > $o) > b)] : ! [X5 : (b > $o)] : ((((X0 @ X5 @ (X4 @ X5))) = $true) | (((X1 @ X5 @ (X4 @ X5))) = $true)))),
% 0.20/0.31 inference(ennf_transformation,[],[f4])).
% 0.20/0.31 thf(f8,plain,(
% 0.20/0.31 ! [X0 : ((b > $o) > b)] : ? [X1 : (b > $o)] : (? [X2 : b] : (((X1 @ X2)) = $true) & (((X1 @ (X0 @ X1))) != $true)) & ! [X3 : ((b > $o) > b > $o),X4 : ((b > $o) > b > $o)] : (? [X5 : (b > $o)] : ! [X6 : b] : ((((X4 @ X5 @ X6)) != $true) & (((X3 @ X5 @ X6)) != $true)) | ? [X7 : ((b > $o) > b)] : ! [X8 : (b > $o)] : ((((X4 @ X8 @ (X7 @ X8))) = $true) | (((X3 @ X8 @ (X7 @ X8))) = $true)))),
% 0.20/0.31 inference(rectify,[],[f7])).
% 0.20/0.31 thf(f9,plain,(
% 0.20/0.31 ! [X0 : ((b > $o) > b)] : ((((sK0 @ X0 @ (sK1 @ X0))) = $true) & ($true != ((sK0 @ X0 @ (X0 @ (sK0 @ X0)))))) & ! [X3 : ((b > $o) > b > $o),X4 : ((b > $o) > b > $o)] : (! [X6 : b] : ((((X4 @ (sK2 @ X4 @ X3) @ X6)) != $true) & ($true != ((X3 @ (sK2 @ X4 @ X3) @ X6)))) | ! [X8 : (b > $o)] : ((((X4 @ X8 @ (sK3 @ X4 @ X3 @ X8))) = $true) | ($true = ((X3 @ X8 @ (sK3 @ X4 @ X3 @ X8))))))),
% 0.20/0.31 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,vAPP,vAPP]),skolemize(X7,sK3 @ X4 @ X3),skolemize(X7,sK3 @ X4 @ X3),skolemize(X7,sK3 @ X4 @ X3),skolemize(X7,sK3 @ X4 @ X3)],[f8])).
% 0.20/0.31 thf(f12,plain,(
% 0.20/0.31 ( ! [X0 : ((b > $o) > b)] : (($true != ((sK0 @ X0 @ (X0 @ (sK0 @ X0)))))) )),
% 0.20/0.31 inference(cnf_transformation,[],[f9])).
% 0.20/0.31 thf(f13,plain,(
% 0.20/0.31 ( ! [X0 : ((b > $o) > b)] : ((((sK0 @ X0 @ (sK1 @ X0))) = $true)) )),
% 0.20/0.31 inference(cnf_transformation,[],[f9])).
% 0.20/0.31 thf(f31,plain,(
% 0.20/0.31 ( ! [X0 : b] : (($true != $true) | ($false = ((sK0 @ vEPSILON @ b @ X0)))) )),
% 0.20/0.31 inference(superposition,[],[f12,f6])).
% 0.20/0.31 thf(f32,plain,(
% 0.20/0.31 ( ! [X0 : b] : (($false = ((sK0 @ vEPSILON @ b @ X0)))) )),
% 0.20/0.31 inference(trivial_inequality_removal,[],[f31])).
% 0.20/0.31 thf(f33,plain,(
% 0.20/0.31 ($false = $true)),
% 0.20/0.31 inference(superposition,[],[f32,f13])).
% 0.20/0.31 thf(f39,plain,(
% 0.20/0.31 $false),
% 0.20/0.31 inference(trivial_inequality_removal,[],[f33])).
% 0.20/0.31 % SZS output end Proof for theBenchmark
% 0.20/0.31 % (564348)------------------------------
% 0.20/0.31 % (564348)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.31 % (564348)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.31 % (564348)CaDiCaL version: 2.1.3
% 0.20/0.31 % (564348)Termination reason: Refutation
% 0.20/0.31 % (564348)Time elapsed: 0.003 s
% 0.20/0.31 % (564348)Peak memory usage: 12 MB
% 0.20/0.31 % (564348)Instructions burned: 4 (million)
% 0.20/0.31 % (564332)Success in time 0.074 s
% 0.20/0.31 % Vampire exiting
%------------------------------------------------------------------------------