%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL730^5 : 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 : n005.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 0.21s 0.31s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL730^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n005.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 10:02:57 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 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
% 0.21/0.31 % (1463764)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.31 % (1463778)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2332981116:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.31 % (1463778)Refutation not found, incomplete strategy
% 0.21/0.31 % (1463778)------------------------------
% 0.21/0.31 % (1463778)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (1463778)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (1463778)CaDiCaL version: 2.1.3
% 0.21/0.31 % (1463778)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.31 % (1463778)Time elapsed: 0.002 s
% 0.21/0.31 % (1463778)Peak memory usage: 12 MB
% 0.21/0.31 % (1463778)Instructions burned: 4 (million)
% 0.21/0.31 % (1463778)------------------------------
% 0.21/0.31 % (1463778)------------------------------
% 0.21/0.31 % (1463784)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.31 % (1463784)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
% 0.21/0.31 % (1463779)lrs+10_16_si=on:nwc=1.5:random_seed=2262219794:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.31 % (1463780)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=4061022377:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.31 % (1463782)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1018189604:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.31 % (1463781)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=3366004330: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)
% 0.21/0.31 % (1463783)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2436093529:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.31 % (1463784)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=2073700207:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.31 % (1463780)Refutation not found, incomplete strategy
% 0.21/0.31 % (1463780)------------------------------
% 0.21/0.31 % (1463780)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (1463780)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (1463780)CaDiCaL version: 2.1.3
% 0.21/0.31 % (1463780)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.31 % (1463780)Time elapsed: 0.001 s
% 0.21/0.31 % (1463780)Peak memory usage: 12 MB
% 0.21/0.31 % (1463780)Instructions burned: 1 (million)
% 0.21/0.31 % (1463780)------------------------------
% 0.21/0.31 % (1463780)------------------------------
% 0.21/0.31 % (1463781)Refutation not found, incomplete strategy
% 0.21/0.31 % (1463781)------------------------------
% 0.21/0.31 % (1463781)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (1463781)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (1463781)CaDiCaL version: 2.1.3
% 0.21/0.31 % (1463781)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.31 % (1463781)Time elapsed: 0.003 s
% 0.21/0.31 % (1463781)Peak memory usage: 12 MB
% 0.21/0.31 % (1463781)Instructions burned: 3 (million)
% 0.21/0.31 % (1463782)Refutation not found, incomplete strategy
% 0.21/0.31 % (1463782)------------------------------
% 0.21/0.31 % (1463782)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (1463782)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (1463782)CaDiCaL version: 2.1.3
% 0.21/0.31 % (1463782)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.31 % (1463782)Time elapsed: 0.003 s
% 0.21/0.31 % (1463782)Peak memory usage: 12 MB
% 0.21/0.31 % (1463782)Instructions burned: 5 (million)
% 0.21/0.31 % (1463781)------------------------------
% 0.21/0.31 % (1463781)------------------------------
% 0.21/0.31 % (1463795)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3459268413:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.21/0.31 % (1463782)------------------------------
% 0.21/0.31 % (1463782)------------------------------
% 0.21/0.31 % (1463784)Refutation not found, incomplete strategy
% 0.21/0.31 % (1463784)------------------------------
% 0.21/0.31 % (1463784)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (1463784)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (1463784)CaDiCaL version: 2.1.3
% 0.21/0.31 % (1463784)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.31 % (1463784)Time elapsed: 0.005 s
% 0.21/0.31 % (1463784)Peak memory usage: 12 MB
% 0.21/0.31 % (1463784)Instructions burned: 7 (million)
% 0.21/0.31 % (1463795)Instruction limit reached!
% 0.21/0.31 % (1463795)------------------------------
% 0.21/0.31 % (1463795)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (1463795)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (1463795)CaDiCaL version: 2.1.3
% 0.21/0.31 % (1463795)Termination reason: Instruction limit
% 0.21/0.31 % (1463795)Termination phase: Saturation
% 0.21/0.31 % (1463795)Time elapsed: 0.001 s
% 0.21/0.31 % (1463795)Peak memory usage: 12 MB
% 0.21/0.31 % (1463795)Instructions burned: 3 (million)
% 0.21/0.31 % (1463784)------------------------------
% 0.21/0.31 % (1463784)------------------------------
% 0.21/0.31 % (1463779)Instruction limit reached!
% 0.21/0.31 % (1463779)------------------------------
% 0.21/0.31 % (1463779)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (1463779)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (1463779)CaDiCaL version: 2.1.3
% 0.21/0.31 % (1463779)Termination reason: Instruction limit
% 0.21/0.31 % (1463779)Termination phase: Saturation
% 0.21/0.31 % (1463779)Time elapsed: 0.011 s
% 0.21/0.31 % (1463779)Peak memory usage: 12 MB
% 0.21/0.31 % (1463779)Instructions burned: 19 (million)
% 0.21/0.31 % (1463810)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
% 0.21/0.31 % (1463810)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.21/0.31 % (1463810)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3893770484:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.21/0.31 % (1463808)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.21/0.31 % (1463806)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1911725883:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.21/0.31 % (1463808)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2042792366:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.21/0.31 % (1463809)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=4034896250:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.21/0.31 % (1463810)Instruction limit reached!
% 0.21/0.31 % (1463810)------------------------------
% 0.21/0.31 % (1463810)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (1463810)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (1463810)CaDiCaL version: 2.1.3
% 0.21/0.31 % (1463810)Termination reason: Instruction limit
% 0.21/0.31 % (1463810)Termination phase: Saturation
% 0.21/0.31 % (1463810)Time elapsed: 0.007 s
% 0.21/0.31 % (1463810)Peak memory usage: 12 MB
% 0.21/0.31 % (1463810)Instructions burned: 29 (million)
% 0.21/0.31 % (1463806) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1463764-1463806"...
% 0.21/0.31 % (1463811)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=1422266836:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.21/0.31 % (1463806)...printing done.
% 0.21/0.31 % (1463806)Refutation found. Thanks to Tanya!
% 0.21/0.31 % SZS status Theorem for theBenchmark
% 0.21/0.31 % SZS output start Proof for theBenchmark
% 0.21/0.31 thf(type_def_5, type, b: $tType).
% 0.21/0.31 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.31 thf(func_def_3, type, diff: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > X1) > X0))).
% 0.21/0.31 thf(func_def_4, type, vEPSILON: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.21/0.31 thf(func_def_5, type, sK0: (((b > $o) > b) > b > $o)).
% 0.21/0.31 thf(func_def_6, type, sK1: (((b > $o) > b) > b)).
% 0.21/0.31 thf(func_def_7, type, sK2: (((b > $o) > b > $o) > (b > $o) > b)).
% 0.21/0.31 thf(func_def_8, type, sK3: (((b > $o) > b > $o) > b > $o)).
% 0.21/0.31 thf(func_def_9, type, vNOT: ($o > $o)).
% 0.21/0.31 thf(func_def_10, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.21/0.31 thf(func_def_11, type, db0: !>[X0: $tType]:(X0)).
% 0.21/0.31 thf(func_def_12, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.21/0.31 thf(f1,conjecture,(
% 0.21/0.31 ! [X0 : ((b > $o) > b > $o)] : (! [X1 : (b > $o)] : ? [X2 : b] : (X0 @ X1 @ X2) => ? [X3 : ((b > $o) > b)] : ! [X1 : (b > $o)] : (X0 @ X1 @ (X3 @ X1))) => ? [X4 : ((b > $o) > b)] : ! [X5 : (b > $o)] : (? [X6 : b] : (X5 @ X6) => (X5 @ (X4 @ X5)))),
% 0.21/0.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cX5310)).
% 0.21/0.31 thf(f2,negated_conjecture,(
% 0.21/0.31 ~(! [X0 : ((b > $o) > b > $o)] : (! [X1 : (b > $o)] : ? [X2 : b] : (X0 @ X1 @ X2) => ? [X3 : ((b > $o) > b)] : ! [X1 : (b > $o)] : (X0 @ X1 @ (X3 @ X1))) => ? [X4 : ((b > $o) > b)] : ! [X5 : (b > $o)] : (? [X6 : b] : (X5 @ X6) => (X5 @ (X4 @ X5))))),
% 0.21/0.31 inference(negated_conjecture,[status(cth)],[f1])).
% 0.21/0.31 thf(f3,plain,(
% 0.21/0.31 ~(! [X0 : ((b > $o) > b > $o)] : (! [X1 : (b > $o)] : ? [X2 : b] : (X0 @ X1 @ X2) => ? [X3 : ((b > $o) > b)] : ! [X4 : (b > $o)] : (X0 @ X4 @ (X3 @ X4))) => ? [X5 : ((b > $o) > b)] : ! [X6 : (b > $o)] : (? [X7 : b] : (X6 @ X7) => (X6 @ (X5 @ X6))))),
% 0.21/0.31 inference(rectify,[],[f2])).
% 0.21/0.31 thf(f4,plain,(
% 0.21/0.31 ~(! [X0 : ((b > $o) > b > $o)] : (! [X1 : (b > $o)] : ? [X2 : b] : (((X0 @ X1 @ X2)) = $true) => ? [X3 : ((b > $o) > b)] : ! [X4 : (b > $o)] : (((X0 @ X4 @ (X3 @ X4))) = $true)) => ? [X5 : ((b > $o) > b)] : ! [X6 : (b > $o)] : (? [X7 : b] : (((X6 @ X7)) = $true) => (((X6 @ (X5 @ X6))) = $true)))),
% 0.21/0.31 inference(fool_elimination,[],[f3])).
% 0.21/0.31 thf(f6,plain,(
% 0.21/0.31 ( ! [X0 : $tType,X2 : X0,X1 : (X0 > $o)] : ((((X1 @ (vEPSILON @ X0 @ X1))) = $true) | ($false = ((X1 @ X2)))) )),
% 0.21/0.31 introduced(theory,[Hilbert's_choice_axiom_instance])).
% 0.21/0.31 thf(f7,plain,(
% 0.21/0.31 ! [X5 : ((b > $o) > b)] : ? [X6 : (b > $o)] : (? [X7 : b] : (((X6 @ X7)) = $true) & (((X6 @ (X5 @ X6))) != $true)) & ! [X0 : ((b > $o) > b > $o)] : (? [X3 : ((b > $o) > b)] : ! [X4 : (b > $o)] : (((X0 @ X4 @ (X3 @ X4))) = $true) | ? [X1 : (b > $o)] : ! [X2 : b] : (((X0 @ X1 @ X2)) != $true))),
% 0.21/0.31 inference(ennf_transformation,[],[f4])).
% 0.21/0.31 thf(f8,plain,(
% 0.21/0.31 ! [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)] : ! [X5 : (b > $o)] : (((X3 @ X5 @ (X4 @ X5))) = $true) | ? [X6 : (b > $o)] : ! [X7 : b] : (((X3 @ X6 @ X7)) != $true))),
% 0.21/0.31 inference(rectify,[],[f7])).
% 0.21/0.31 thf(f9,plain,(
% 0.21/0.31 ! [X0 : ((b > $o) > b)] : ((((sK0 @ X0 @ (sK1 @ X0))) = $true) & (((sK0 @ X0 @ (X0 @ (sK0 @ X0)))) != $true)) & ! [X3 : ((b > $o) > b > $o)] : (! [X5 : (b > $o)] : (((X3 @ X5 @ (sK2 @ X3 @ X5))) = $true) | ! [X7 : b] : (((X3 @ (sK3 @ X3) @ X7)) != $true))),
% 0.21/0.31 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,vAPP,vAPP]),skolemize(X6,sK3 @ X3),skolemize(X6,sK3 @ X3),skolemize(X6,sK3 @ X3),skolemize(X6,sK3 @ X3)],[f8])).
% 0.21/0.31 thf(f11,plain,(
% 0.21/0.31 ( ! [X0 : ((b > $o) > b)] : ((((sK0 @ X0 @ (X0 @ (sK0 @ X0)))) != $true)) )),
% 0.21/0.31 inference(cnf_transformation,[],[f9])).
% 0.21/0.31 thf(f12,plain,(
% 0.21/0.31 ( ! [X0 : ((b > $o) > b)] : ((((sK0 @ X0 @ (sK1 @ X0))) = $true)) )),
% 0.21/0.31 inference(cnf_transformation,[],[f9])).
% 0.21/0.31 thf(f30,plain,(
% 0.21/0.31 ( ! [X0 : b] : (($true != $true) | (((sK0 @ vEPSILON @ b @ X0)) = $false)) )),
% 0.21/0.31 inference(superposition,[],[f11,f6])).
% 0.21/0.31 thf(f31,plain,(
% 0.21/0.31 ( ! [X0 : b] : ((((sK0 @ vEPSILON @ b @ X0)) = $false)) )),
% 0.21/0.31 inference(trivial_inequality_removal,[],[f30])).
% 0.21/0.31 thf(f32,plain,(
% 0.21/0.31 ($false = $true)),
% 0.21/0.31 inference(superposition,[],[f31,f12])).
% 0.21/0.31 thf(f37,plain,(
% 0.21/0.31 $false),
% 0.21/0.31 inference(trivial_inequality_removal,[],[f32])).
% 0.21/0.31 % SZS output end Proof for theBenchmark
% 0.21/0.31 % (1463806)------------------------------
% 0.21/0.31 % (1463806)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (1463806)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (1463806)CaDiCaL version: 2.1.3
% 0.21/0.31 % (1463806)Termination reason: Refutation
% 0.21/0.31 % (1463806)Time elapsed: 0.003 s
% 0.21/0.31 % (1463806)Peak memory usage: 12 MB
% 0.21/0.31 % (1463806)Instructions burned: 3 (million)
% 0.21/0.31 % (1463764)Success in time 0.063 s
% 0.21/0.31 % Vampire exiting
%------------------------------------------------------------------------------