%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL736^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 08:14:36 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
% 0.00/0.03 % Problem : LCL736^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n002.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 10:11:22 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running higher-order theorem proving
% 0.09/0.25 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 % (1085735)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.33 % (1085741)lrs+10_16_si=on:nwc=1.5:random_seed=3935931341:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.33 % (1085744)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=650393087:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.33 % (1085742)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3752830395:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.33 % (1085746)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 % (1085746)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 % (1085742)Instruction limit reached!
% 0.22/0.33 % (1085742)------------------------------
% 0.22/0.33 % (1085742)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.33 % (1085742)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.33 % (1085742)CaDiCaL version: 2.1.3
% 0.22/0.33 % (1085742)Termination reason: Instruction limit
% 0.22/0.33 % (1085742)Termination phase: Saturation
% 0.22/0.33 % (1085742)Time elapsed: 0.003 s
% 0.22/0.33 % (1085742)Peak memory usage: 12 MB
% 0.22/0.33 % (1085742)Instructions burned: 4 (million)
% 0.22/0.33 % (1085745)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=357883700:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.33 % (1085743)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=4289753052: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 % (1085746)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=3561481854:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.33 % (1085740)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3580767124:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.33 % (1085741)Instruction limit reached!
% 0.22/0.33 % (1085741)------------------------------
% 0.22/0.33 % (1085741)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.33 % (1085741)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.33 % (1085741)CaDiCaL version: 2.1.3
% 0.22/0.33 % (1085741)Termination reason: Instruction limit
% 0.22/0.33 % (1085741)Termination phase: Saturation
% 0.22/0.33 % (1085741)Time elapsed: 0.010 s
% 0.22/0.33 % (1085741)Peak memory usage: 12 MB
% 0.22/0.33 % (1085741)Instructions burned: 18 (million)
% 0.22/0.33 % (1085744)Instruction limit reached!
% 0.22/0.33 % (1085744)------------------------------
% 0.22/0.33 % (1085744)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.33 % (1085744)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.33 % (1085744)CaDiCaL version: 2.1.3
% 0.22/0.33 % (1085744)Termination reason: Instruction limit
% 0.22/0.33 % (1085744)Termination phase: Saturation
% 0.22/0.33 % (1085744)Time elapsed: 0.014 s
% 0.22/0.33 % (1085744)Peak memory usage: 12 MB
% 0.22/0.33 % (1085744)Instructions burned: 25 (million)
% 0.22/0.33 % (1085743)Refutation not found, incomplete strategy
% 0.22/0.33 % (1085743)------------------------------
% 0.22/0.33 % (1085743)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.33 % (1085743)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.33 % (1085743)CaDiCaL version: 2.1.3
% 0.22/0.33 % (1085743)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.33 % (1085743)Time elapsed: 0.020 s
% 0.22/0.33 % (1085743)Peak memory usage: 12 MB
% 0.22/0.33 % (1085743)Instructions burned: 36 (million)
% 0.22/0.33 % (1085746)Refutation not found, incomplete strategy
% 0.22/0.33 % (1085746)------------------------------
% 0.22/0.33 % (1085746)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.33 % (1085746)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.33 % (1085746)CaDiCaL version: 2.1.3
% 0.22/0.33 % (1085746)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.33 % (1085746)Time elapsed: 0.018 s
% 0.22/0.33 % (1085746)Peak memory usage: 12 MB
% 0.22/0.33 % (1085746)Instructions burned: 33 (million)
% 0.22/0.33 % (1085743)------------------------------
% 0.22/0.33 % (1085743)------------------------------
% 0.22/0.33 % (1085746)------------------------------
% 0.22/0.33 % (1085746)------------------------------
% 0.22/0.33 % (1085752)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1066541977:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.22/0.33 % (1085752)Instruction limit reached!
% 0.22/0.33 % (1085752)------------------------------
% 0.22/0.33 % (1085752)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.33 % (1085752)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.33 % (1085752)CaDiCaL version: 2.1.3
% 0.22/0.33 % (1085752)Termination reason: Instruction limit
% 0.22/0.33 % (1085752)Termination phase: Saturation
% 0.22/0.33 % (1085752)Time elapsed: 0.003 s
% 0.22/0.33 % (1085752)Peak memory usage: 12 MB
% 0.22/0.33 % (1085752)Instructions burned: 4 (million)
% 0.22/0.33 % (1085756)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 % (1085755)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=700424555:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.22/0.33 % (1085755) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1085735-1085755"...
% 0.22/0.33 % (1085756)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1307300801: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 % (1085755)...printing done.
% 0.22/0.33 % (1085755)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, b: $tType).
% 0.22/0.33 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.22/0.33 thf(func_def_3, type, diff: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > X1) > X0))).
% 0.22/0.33 thf(func_def_4, type, vEPSILON: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.22/0.33 thf(func_def_5, type, sK0: (((b > $o) > b > b > $o) > ((b > $o) > b > b > $o) > (b > $o) > b)).
% 0.22/0.33 thf(func_def_6, type, sK1: ((b > $o) > ((b > $o) > b > b > $o) > ((b > $o) > b > b > $o) > b)).
% 0.22/0.33 thf(func_def_7, type, sK2: (((b > $o) > b > b > $o) > ((b > $o) > b > b > $o) > b > $o)).
% 0.22/0.33 thf(func_def_8, type, sK3: (((b > $o) > b) > b > $o)).
% 0.22/0.33 thf(func_def_9, type, sK4: (((b > $o) > b) > b)).
% 0.22/0.33 thf(func_def_10, type, vNOT: ($o > $o)).
% 0.22/0.33 thf(func_def_11, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.22/0.33 thf(func_def_12, type, db0: !>[X0: $tType]:(X0)).
% 0.22/0.33 thf(func_def_13, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.22/0.33 thf(f1,conjecture,(
% 0.22/0.33 ! [X0 : ((b > $o) > b > b > $o),X1 : ((b > $o) > b > b > $o)] : (! [X2 : (b > $o)] : ? [X4 : b,X3 : b] : ((X1 @ X2 @ X3 @ X4) | (X0 @ X2 @ X3 @ X4)) => ? [X5 : ((b > $o) > b)] : ! [X2 : (b > $o)] : ? [X4 : b] : ((X0 @ X2 @ (X5 @ X2) @ X4) | (X1 @ X2 @ (X5 @ X2) @ X4))) => ? [X6 : ((b > $o) > b)] : ! [X7 : (b > $o)] : (? [X8 : b] : (X7 @ X8) => (X7 @ (X6 @ X7)))),
% 0.22/0.33 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cX5310D)).
% 0.22/0.33 thf(f2,negated_conjecture,(
% 0.22/0.33 ~(! [X0 : ((b > $o) > b > b > $o),X1 : ((b > $o) > b > b > $o)] : (! [X2 : (b > $o)] : ? [X4 : b,X3 : b] : ((X1 @ X2 @ X3 @ X4) | (X0 @ X2 @ X3 @ X4)) => ? [X5 : ((b > $o) > b)] : ! [X2 : (b > $o)] : ? [X4 : b] : ((X0 @ X2 @ (X5 @ X2) @ X4) | (X1 @ X2 @ (X5 @ X2) @ X4))) => ? [X6 : ((b > $o) > b)] : ! [X7 : (b > $o)] : (? [X8 : b] : (X7 @ X8) => (X7 @ (X6 @ X7))))),
% 0.22/0.33 inference(negated_conjecture,[status(cth)],[f1])).
% 0.22/0.33 thf(f3,plain,(
% 0.22/0.33 ~(! [X0 : ((b > $o) > b > b > $o),X1 : ((b > $o) > b > b > $o)] : (! [X2 : (b > $o)] : ? [X3 : b,X4 : b] : ((X1 @ X2 @ X4 @ X3) | (X0 @ X2 @ X4 @ X3)) => ? [X5 : ((b > $o) > b)] : ! [X6 : (b > $o)] : ? [X7 : b] : ((X0 @ X6 @ (X5 @ X6) @ X7) | (X1 @ X6 @ (X5 @ X6) @ X7))) => ? [X8 : ((b > $o) > b)] : ! [X9 : (b > $o)] : (? [X10 : b] : (X9 @ X10) => (X9 @ (X8 @ X9))))),
% 0.22/0.33 inference(rectify,[],[f2])).
% 0.22/0.33 thf(f4,plain,(
% 0.22/0.33 ~(! [X1 : ((b > $o) > b > b > $o),X0 : ((b > $o) > b > b > $o)] : (! [X2 : (b > $o)] : ? [X3 : b,X4 : b] : (($true = ((X1 @ X2 @ X4 @ X3))) | ($true = ((X0 @ X2 @ X4 @ X3)))) => ? [X5 : ((b > $o) > b)] : ! [X6 : (b > $o)] : ? [X7 : b] : ((((X1 @ X6 @ (X5 @ X6) @ X7)) = $true) | (((X0 @ X6 @ (X5 @ X6) @ X7)) = $true))) => ? [X8 : ((b > $o) > b)] : ! [X9 : (b > $o)] : (? [X10 : b] : ($true = ((X9 @ X10))) => ($true = ((X9 @ (X8 @ X9))))))),
% 0.22/0.33 inference(fool_elimination,[],[f3])).
% 0.22/0.33 thf(f6,plain,(
% 0.22/0.33 ( ! [X0 : $tType,X2 : X0,X1 : (X0 > $o)] : ((((X1 @ (vEPSILON @ X0 @ X1))) = $true) | ($false = ((X1 @ X2)))) )),
% 0.22/0.33 introduced(theory,[Hilbert's_choice_axiom_instance])).
% 0.22/0.33 thf(f7,plain,(
% 0.22/0.33 ! [X0 : ((b > $o) > b > b > $o),X1 : ((b > $o) > b > b > $o)] : (? [X5 : ((b > $o) > b)] : ! [X6 : (b > $o)] : ? [X7 : b] : ((((X1 @ X6 @ (X5 @ X6) @ X7)) = $true) | (((X0 @ X6 @ (X5 @ X6) @ X7)) = $true)) | ? [X2 : (b > $o)] : ! [X3 : b,X4 : b] : (($true != ((X1 @ X2 @ X4 @ X3))) & ($true != ((X0 @ X2 @ X4 @ X3))))) & ! [X8 : ((b > $o) > b)] : ? [X9 : (b > $o)] : (($true != ((X9 @ (X8 @ X9)))) & ? [X10 : b] : ($true = ((X9 @ X10))))),
% 0.22/0.33 inference(ennf_transformation,[],[f4])).
% 0.22/0.33 thf(f8,plain,(
% 0.22/0.33 ! [X0 : ((b > $o) > b > b > $o),X1 : ((b > $o) > b > b > $o)] : (? [X2 : ((b > $o) > b)] : ! [X3 : (b > $o)] : ? [X4 : b] : ((((X1 @ X3 @ (X2 @ X3) @ X4)) = $true) | (((X0 @ X3 @ (X2 @ X3) @ X4)) = $true)) | ? [X5 : (b > $o)] : ! [X6 : b,X7 : b] : (($true != ((X1 @ X5 @ X7 @ X6))) & ($true != ((X0 @ X5 @ X7 @ X6))))) & ! [X8 : ((b > $o) > b)] : ? [X9 : (b > $o)] : (($true != ((X9 @ (X8 @ X9)))) & ? [X10 : b] : ($true = ((X9 @ X10))))),
% 0.22/0.33 inference(rectify,[],[f7])).
% 0.22/0.33 thf(f9,plain,(
% 0.22/0.33 ! [X0 : ((b > $o) > b > b > $o),X1 : ((b > $o) > b > b > $o)] : (! [X3 : (b > $o)] : ((((X1 @ X3 @ (sK0 @ X1 @ X0 @ X3) @ (sK1 @ X3 @ X1 @ X0))) = $true) | ($true = ((X0 @ X3 @ (sK0 @ X1 @ X0 @ X3) @ (sK1 @ X3 @ X1 @ X0))))) | ! [X6 : b,X7 : b] : (($true != ((X1 @ (sK2 @ X1 @ X0) @ X7 @ X6))) & ($true != ((X0 @ (sK2 @ X1 @ X0) @ X7 @ X6))))) & ! [X8 : ((b > $o) > b)] : (($true != ((sK3 @ X8 @ (X8 @ (sK3 @ X8))))) & ($true = ((sK3 @ X8 @ (sK4 @ X8)))))),
% 0.22/0.33 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,vAPP,vAPP,vAPP]),skolemize(X10,sK4 @ X8),skolemize(X10,sK4 @ X8),skolemize(X10,sK4 @ X8),skolemize(X10,sK4 @ X8),skolemize(X10,sK4 @ X8)],[f8])).
% 0.22/0.33 thf(f10,plain,(
% 0.22/0.33 ( ! [X8 : ((b > $o) > b)] : (($true = ((sK3 @ X8 @ (sK4 @ X8))))) )),
% 0.22/0.33 inference(cnf_transformation,[],[f9])).
% 0.22/0.33 thf(f11,plain,(
% 0.22/0.33 ( ! [X8 : ((b > $o) > b)] : (($true != ((sK3 @ X8 @ (X8 @ (sK3 @ X8)))))) )),
% 0.22/0.33 inference(cnf_transformation,[],[f9])).
% 0.22/0.33 thf(f31,plain,(
% 0.22/0.33 ( ! [X0 : b] : (($false = ((sK3 @ vEPSILON @ b @ X0))) | ($true != $true)) )),
% 0.22/0.33 inference(superposition,[],[f11,f6])).
% 0.22/0.33 thf(f32,plain,(
% 0.22/0.33 ( ! [X0 : b] : (($false = ((sK3 @ vEPSILON @ b @ X0)))) )),
% 0.22/0.33 inference(trivial_inequality_removal,[],[f31])).
% 0.22/0.33 thf(f35,plain,(
% 0.22/0.33 ($true = $false)),
% 0.22/0.33 inference(superposition,[],[f10,f32])).
% 0.22/0.33 thf(f38,plain,(
% 0.22/0.33 $false),
% 0.22/0.33 inference(trivial_inequality_removal,[],[f35])).
% 0.22/0.33 % SZS output end Proof for theBenchmark
% 0.22/0.33 % (1085755)------------------------------
% 0.22/0.33 % (1085755)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.33 % (1085755)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.33 % (1085755)CaDiCaL version: 2.1.3
% 0.22/0.33 % (1085755)Termination reason: Refutation
% 0.22/0.33 % (1085755)Time elapsed: 0.003 s
% 0.22/0.33 % (1085755)Peak memory usage: 12 MB
% 0.22/0.33 % (1085755)Instructions burned: 4 (million)
% 0.22/0.33 % (1085735)Success in time 0.07 s
% 0.22/0.33 % Vampire exiting
%------------------------------------------------------------------------------