%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV057^5 : 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 : n020.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 08:37:33 AM UTC 2026
% Result : Theorem 0.20s 0.29s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV057^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n020.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 15:06:35 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running higher-order theorem proving
% 0.08/0.22 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
% 0.20/0.29 % (1165141)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.29 % (1165150)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3776956211:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.29 % (1165150)Refutation not found, incomplete strategy
% 0.20/0.29 % (1165150)------------------------------
% 0.20/0.29 % (1165150)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (1165150)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (1165150)CaDiCaL version: 2.1.3
% 0.20/0.29 % (1165150)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.29 % (1165150)Time elapsed: 0.001 s
% 0.20/0.29 % (1165150)Peak memory usage: 12 MB
% 0.20/0.29 % (1165150)Instructions burned: 2 (million)
% 0.20/0.29 % (1165150)------------------------------
% 0.20/0.29 % (1165150)------------------------------
% 0.20/0.29 % (1165152)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.29 % (1165152)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
% 0.20/0.29 % (1165146)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2022066788:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.29 % (1165147)lrs+10_16_si=on:nwc=1.5:random_seed=13424919:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.29 % (1165148)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3023472800:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.29 % (1165149)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=2413412165: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)
% 0.20/0.29 % (1165151)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2551921189:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.29 % (1165152)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=3435811442:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.29 % (1165148)Refutation not found, incomplete strategy
% 0.20/0.29 % (1165148)------------------------------
% 0.20/0.29 % (1165148)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (1165148)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (1165148)CaDiCaL version: 2.1.3
% 0.20/0.29 % (1165148)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.29 % (1165148)Time elapsed: 0.003 s
% 0.20/0.29 % (1165148)Peak memory usage: 12 MB
% 0.20/0.29 % (1165148)Instructions burned: 3 (million)
% 0.20/0.29 % (1165149)Refutation not found, incomplete strategy
% 0.20/0.29 % (1165149)------------------------------
% 0.20/0.29 % (1165149)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (1165149)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (1165149)CaDiCaL version: 2.1.3
% 0.20/0.29 % (1165149)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.29 % (1165149)Time elapsed: 0.002 s
% 0.20/0.29 % (1165149)Peak memory usage: 12 MB
% 0.20/0.29 % (1165149)Instructions burned: 3 (million)
% 0.20/0.29 % (1165146)Refutation not found, incomplete strategy
% 0.20/0.29 % (1165146)------------------------------
% 0.20/0.29 % (1165146)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (1165146)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (1165146)CaDiCaL version: 2.1.3
% 0.20/0.29 % (1165146)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.29 % (1165146)Time elapsed: 0.003 s
% 0.20/0.29 % (1165146)Peak memory usage: 12 MB
% 0.20/0.29 % (1165146)Instructions burned: 4 (million)
% 0.20/0.29 % (1165148)------------------------------
% 0.20/0.29 % (1165148)------------------------------
% 0.20/0.29 % (1165149)------------------------------
% 0.20/0.29 % (1165149)------------------------------
% 0.20/0.29 % (1165146)------------------------------
% 0.20/0.29 % (1165146)------------------------------
% 0.20/0.29 % (1165154)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2862980060:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.20/0.29 % (1165154)Instruction limit reached!
% 0.20/0.29 % (1165154)------------------------------
% 0.20/0.29 % (1165154)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (1165154)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (1165154)CaDiCaL version: 2.1.3
% 0.20/0.29 % (1165154)Termination reason: Instruction limit
% 0.20/0.29 % (1165154)Termination phase: Saturation
% 0.20/0.29 % (1165154)Time elapsed: 0.001 s
% 0.20/0.29 % (1165154)Peak memory usage: 12 MB
% 0.20/0.29 % (1165154)Instructions burned: 2 (million)
% 0.20/0.29 % (1165147)Instruction limit reached!
% 0.20/0.29 % (1165147)------------------------------
% 0.20/0.29 % (1165147)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (1165147)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (1165147)CaDiCaL version: 2.1.3
% 0.20/0.29 % (1165147)Termination reason: Instruction limit
% 0.20/0.29 % (1165147)Termination phase: Saturation
% 0.20/0.29 % (1165147)Time elapsed: 0.010 s
% 0.20/0.29 % (1165147)Peak memory usage: 12 MB
% 0.20/0.29 % (1165147)Instructions burned: 18 (million)
% 0.20/0.29 % (1165163)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.20/0.29 % (1165165)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
% 0.20/0.29 % (1165165)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.20/0.29 % (1165162)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2155343678:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.20/0.29 % (1165163)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1489205341:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.20/0.29 % (1165164)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1506293004:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.20/0.29 % (1165165)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=401959769:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.20/0.29 % (1165151) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1165141-1165151"...
% 0.20/0.29 % (1165162)Instruction limit reached!
% 0.20/0.29 % (1165162)------------------------------
% 0.20/0.29 % (1165162)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (1165162)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (1165162)CaDiCaL version: 2.1.3
% 0.20/0.29 % (1165162)Termination reason: Instruction limit
% 0.20/0.29 % (1165162)Termination phase: Saturation
% 0.20/0.29 % (1165162)Time elapsed: 0.004 s
% 0.20/0.29 % (1165162)Peak memory usage: 12 MB
% 0.20/0.29 % (1165162)Instructions burned: 5 (million)
% 0.20/0.29 % (1165163)Instruction limit reached!
% 0.20/0.29 % (1165163)------------------------------
% 0.20/0.29 % (1165163)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (1165163)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (1165163)CaDiCaL version: 2.1.3
% 0.20/0.29 % (1165163)Termination reason: Instruction limit
% 0.20/0.29 % (1165163)Termination phase: Saturation
% 0.20/0.29 % (1165163)Time elapsed: 0.004 s
% 0.20/0.29 % (1165163)Peak memory usage: 12 MB
% 0.20/0.29 % (1165163)Instructions burned: 7 (million)
% 0.20/0.29 % (1165151)...printing done.
% 0.20/0.29 % (1165166)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=397224899:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.20/0.29 % (1165151)Refutation found. Thanks to Tanya!
% 0.20/0.29 % SZS status Theorem for theBenchmark
% 0.20/0.29 % SZS output start Proof for theBenchmark
% 0.20/0.29 thf(type_def_5, type, a: $tType).
% 0.20/0.29 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.29 thf(func_def_3, type, sK0: (a > $o)).
% 0.20/0.29 thf(func_def_4, type, sK1: ((a > a) > a)).
% 0.20/0.29 thf(func_def_5, type, sK2: (a > (a > a) > a)).
% 0.20/0.29 thf(func_def_6, type, sK3: ((a > a) > a)).
% 0.20/0.29 thf(func_def_7, type, db0: !>[X0: $tType]:(X0)).
% 0.20/0.29 thf(func_def_8, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.20/0.29 thf(func_def_9, type, db1: !>[X0: $tType]:(X0)).
% 0.20/0.29 thf(func_def_11, type, sK5: a).
% 0.20/0.29 thf(func_def_12, type, sK6: a).
% 0.20/0.29 thf(func_def_13, type, sK7: a).
% 0.20/0.29 thf(func_def_14, type, sK8: (a > (a > a > a > a) > a)).
% 0.20/0.29 thf(func_def_15, type, sK9: (a > (a > a > a > a) > a)).
% 0.20/0.29 thf(func_def_16, type, sK10: a).
% 0.20/0.29 thf(func_def_17, type, sK11: ((a > a > a) > a)).
% 0.20/0.29 thf(f1,conjecture,(
% 0.20/0.29 ! [X0 : (a > $o)] : ? [X1 : (a > a)] : (! [X3 : a] : ((X0 @ X3) => ? [X2 : a] : ((X3 = ((X1 @ X2))) & ! [X4 : a] : (((X3 = ((X1 @ X4))) & (X0 @ X4)) => (X4 = X2)) & (X0 @ X2))) & ! [X2 : a] : ((X0 @ X2) => (X0 @ (X1 @ X2))))),
% 0.20/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cEQP1_1A_pme)).
% 0.20/0.29 thf(f2,negated_conjecture,(
% 0.20/0.29 ~ ! [X0 : (a > $o)] : ? [X1 : (a > a)] : (! [X3 : a] : ((X0 @ X3) => ? [X2 : a] : ((X3 = ((X1 @ X2))) & ! [X4 : a] : (((X3 = ((X1 @ X4))) & (X0 @ X4)) => (X4 = X2)) & (X0 @ X2))) & ! [X2 : a] : ((X0 @ X2) => (X0 @ (X1 @ X2))))),
% 0.20/0.29 inference(negated_conjecture,[status(cth)],[f1])).
% 0.20/0.29 thf(f3,plain,(
% 0.20/0.29 ~ ! [X0 : (a > $o)] : ? [X1 : (a > a)] : (! [X2 : a] : ((X0 @ X2) => ? [X3 : a] : ((((X1 @ X3)) = X2) & ! [X4 : a] : (((((X1 @ X4)) = X2) & (X0 @ X4)) => (X3 = X4)) & (X0 @ X3))) & ! [X5 : a] : ((X0 @ X5) => (X0 @ (X1 @ X5))))),
% 0.20/0.29 inference(rectify,[],[f2])).
% 0.20/0.29 thf(f4,plain,(
% 0.20/0.29 ~ ! [X0 : (a > $o)] : ? [X1 : (a > a)] : (! [X5 : a] : ((((X0 @ X5)) = $true) => (((X0 @ (X1 @ X5))) = $true)) & ! [X2 : a] : ((((X0 @ X2)) = $true) => ? [X3 : a] : ((((X1 @ X3)) = X2) & ! [X4 : a] : (((((X0 @ X4)) = $true) & (((X1 @ X4)) = X2)) => (X3 = X4)) & (((X0 @ X3)) = $true))))),
% 0.20/0.29 inference(fool_elimination,[],[f3])).
% 0.20/0.29 thf(f5,plain,(
% 0.20/0.29 ? [X0 : (a > $o)] : ! [X1 : (a > a)] : (? [X5 : a] : ((((X0 @ (X1 @ X5))) != $true) & (((X0 @ X5)) = $true)) | ? [X2 : a] : (! [X3 : a] : ((((X1 @ X3)) != X2) | ? [X4 : a] : ((X3 != X4) & ((((X0 @ X4)) = $true) & (((X1 @ X4)) = X2))) | (((X0 @ X3)) != $true)) & (((X0 @ X2)) = $true)))),
% 0.20/0.29 inference(ennf_transformation,[],[f4])).
% 0.20/0.29 thf(f6,plain,(
% 0.20/0.29 ? [X0 : (a > $o)] : ! [X1 : (a > a)] : (? [X2 : a] : ((((X0 @ X2)) = $true) & ! [X3 : a] : (? [X4 : a] : ((X3 != X4) & (((X0 @ X4)) = $true) & (((X1 @ X4)) = X2)) | (((X0 @ X3)) != $true) | (((X1 @ X3)) != X2))) | ? [X5 : a] : ((((X0 @ (X1 @ X5))) != $true) & (((X0 @ X5)) = $true)))),
% 0.20/0.29 inference(flattening,[],[f5])).
% 0.20/0.29 thf(f7,plain,(
% 0.20/0.29 ! [X1 : (a > a)] : (((((sK0 @ (sK1 @ X1))) = $true) & ! [X3 : a] : (((((sK2 @ X3 @ X1)) != X3) & (((sK0 @ (sK2 @ X3 @ X1))) = $true) & (((sK1 @ X1)) = ((X1 @ (sK2 @ X3 @ X1))))) | (((sK0 @ X3)) != $true) | (((sK1 @ X1)) != ((X1 @ X3))))) | ((((sK0 @ (X1 @ (sK3 @ X1)))) != $true) & (((sK0 @ (sK3 @ X1))) = $true)))),
% 0.20/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,vAPP,vAPP,vAPP]),skolemize(X0,sK0),skolemize(X5,sK3 @ X1),skolemize(X5,sK3 @ X1),skolemize(X5,sK3 @ X1)],[f6])).
% 0.20/0.29 thf(f8,plain,(
% 0.20/0.29 ( ! [X3 : a,X1 : (a > a)] : ((((sK1 @ X1)) != ((X1 @ X3))) | (((sK0 @ X3)) != $true) | (((sK1 @ X1)) = ((X1 @ (sK2 @ X3 @ X1)))) | (((sK0 @ (sK3 @ X1))) = $true)) )),
% 0.20/0.29 inference(cnf_transformation,[],[f7])).
% 0.20/0.29 thf(f9,plain,(
% 0.20/0.29 ( ! [X3 : a,X1 : (a > a)] : ((((sK0 @ (X1 @ (sK3 @ X1)))) != $true) | (((sK1 @ X1)) = ((X1 @ (sK2 @ X3 @ X1)))) | (((sK1 @ X1)) != ((X1 @ X3))) | (((sK0 @ X3)) != $true)) )),
% 0.20/0.29 inference(cnf_transformation,[],[f7])).
% 0.20/0.29 thf(f12,plain,(
% 0.20/0.29 ( ! [X3 : a,X1 : (a > a)] : ((((sK2 @ X3 @ X1)) != X3) | (((sK0 @ (sK3 @ X1))) = $true) | (((sK1 @ X1)) != ((X1 @ X3))) | (((sK0 @ X3)) != $true)) )),
% 0.20/0.29 inference(cnf_transformation,[],[f7])).
% 0.20/0.29 thf(f13,plain,(
% 0.20/0.29 ( ! [X3 : a,X1 : (a > a)] : ((((sK2 @ X3 @ X1)) != X3) | (((sK0 @ X3)) != $true) | (((sK0 @ (X1 @ (sK3 @ X1)))) != $true) | (((sK1 @ X1)) != ((X1 @ X3)))) )),
% 0.20/0.29 inference(cnf_transformation,[],[f7])).
% 0.20/0.29 thf(f14,plain,(
% 0.20/0.29 ( ! [X1 : (a > a)] : ((((sK0 @ (sK3 @ X1))) = $true) | (((sK0 @ (sK1 @ X1))) = $true)) )),
% 0.20/0.29 inference(cnf_transformation,[],[f7])).
% 0.20/0.29 thf(f15,plain,(
% 0.20/0.29 ( ! [X1 : (a > a)] : ((((sK0 @ (X1 @ (sK3 @ X1)))) != $true) | (((sK0 @ (sK1 @ X1))) = $true)) )),
% 0.20/0.29 inference(cnf_transformation,[],[f7])).
% 0.20/0.29 thf(f18,plain,(
% 0.20/0.29 (((sK0 @ (sK1 @ (^[Y0 : a]: (Y0))))) = $true) | ($true != $true) | (((sK0 @ (sK1 @ (^[Y0 : a]: (Y0))))) = $true)),
% 0.20/0.29 inference(constrained_superposition,[],[f15,f14])).
% 0.20/0.29 thf(f21,plain,(
% 0.20/0.29 (((sK0 @ (sK1 @ (^[Y0 : a]: (Y0))))) = $true) | ($true != $true)),
% 0.20/0.29 inference(duplicate_literal_removal,[],[f18])).
% 0.20/0.29 thf(f22,plain,(
% 0.20/0.29 (((sK0 @ (sK1 @ (^[Y0 : a]: (Y0))))) = $true)),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f21])).
% 0.20/0.29 thf(f60,definition,(
% 0.20/0.29 spl4_7 <=> ($true = ((sK0 @ (sK3 @ (^[Y0 : a]: (Y0))))))),
% 0.20/0.29 introduced(definition,[new_symbols(definition,[spl4_7])],[avatar_definition])).
% 0.20/0.29 thf(f61,plain,(
% 0.20/0.29 ($true = ((sK0 @ (sK3 @ (^[Y0 : a]: (Y0)))))) | ~spl4_7),
% 0.20/0.29 inference(avatar_component_clause,[],[f60])).
% 0.20/0.29 thf(f119,plain,(
% 0.20/0.29 ( ! [X0 : (a > a)] : (((((^[Y0 : a]: (Y0)) @ (sK2 @ (sK1 @ X0) @ (^[Y0 : a]: (Y0))))) = ((sK1 @ (^[Y0 : a]: (Y0))))) | ($true = ((sK0 @ (sK3 @ (^[Y0 : a]: (Y0)))))) | ($true != ((sK0 @ (sK1 @ X0)))) | ((^[Y0 : a]: (Y0)) != X0)) )),
% 0.20/0.29 inference(equality_resolution,[],[f8])).
% 0.20/0.29 thf(f124,plain,(
% 0.20/0.29 ( ! [X0 : (a > a)] : (((^[Y0 : a]: (Y0)) != X0) | ($true != ((sK0 @ (sK1 @ X0)))) | ($true = ((sK0 @ (sK3 @ (^[Y0 : a]: (Y0)))))) | (((sK2 @ (sK1 @ X0) @ (^[Y0 : a]: (Y0)))) = ((sK1 @ (^[Y0 : a]: (Y0)))))) )),
% 0.20/0.29 inference(beta-eta_normalization,[],[f119])).
% 0.20/0.29 thf(f128,definition,(
% 0.20/0.29 spl4_14 <=> ! [X0 : (a > a)] : (((^[Y0 : a]: (Y0)) != X0) | (((sK2 @ (sK1 @ X0) @ (^[Y0 : a]: (Y0)))) = ((sK1 @ (^[Y0 : a]: (Y0))))) | ($true != ((sK0 @ (sK1 @ X0)))))),
% 0.20/0.29 introduced(definition,[new_symbols(definition,[spl4_14])],[avatar_definition])).
% 0.20/0.29 thf(f129,plain,(
% 0.20/0.29 ( ! [X0 : (a > a)] : (($true != ((sK0 @ (sK1 @ X0)))) | ((^[Y0 : a]: (Y0)) != X0) | (((sK2 @ (sK1 @ X0) @ (^[Y0 : a]: (Y0)))) = ((sK1 @ (^[Y0 : a]: (Y0)))))) ) | ~spl4_14),
% 0.20/0.29 inference(avatar_component_clause,[],[f128])).
% 0.20/0.29 thf(f130,plain,(
% 0.20/0.29 spl4_14 | spl4_7),
% 0.20/0.29 inference(avatar_split_clause,[],[f124,f60,f128])).
% 0.20/0.29 thf(f150,plain,(
% 0.20/0.29 ( ! [X0 : a] : (($true != ((sK0 @ X0))) | (((sK1 @ (^[Y0 : a]: (Y0)))) = (((^[Y0 : a]: (Y0)) @ (sK2 @ X0 @ (^[Y0 : a]: (Y0)))))) | ($true != $true) | ((((^[Y0 : a]: (Y0)) @ X0)) != ((sK1 @ (^[Y0 : a]: (Y0)))))) ) | ~spl4_7),
% 0.20/0.29 inference(constrained_superposition,[],[f9,f61])).
% 0.20/0.29 thf(f169,plain,(
% 0.20/0.29 ( ! [X0 : a] : (($true != ((sK0 @ X0))) | (((sK1 @ (^[Y0 : a]: (Y0)))) = (((^[Y0 : a]: (Y0)) @ (sK2 @ X0 @ (^[Y0 : a]: (Y0)))))) | ((((^[Y0 : a]: (Y0)) @ X0)) != ((sK1 @ (^[Y0 : a]: (Y0)))))) ) | ~spl4_7),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f150])).
% 0.20/0.29 thf(f170,plain,(
% 0.20/0.29 ( ! [X0 : a] : ((((sK1 @ (^[Y0 : a]: (Y0)))) != X0) | (((sK2 @ X0 @ (^[Y0 : a]: (Y0)))) = ((sK1 @ (^[Y0 : a]: (Y0))))) | ($true != ((sK0 @ X0)))) ) | ~spl4_7),
% 0.20/0.29 inference(beta-eta_normalization,[],[f169])).
% 0.20/0.29 thf(f300,plain,(
% 0.20/0.29 (((sK0 @ (sK1 @ (^[Y0 : a]: (Y0))))) != $true) | (((sK2 @ (sK1 @ (^[Y0 : a]: (Y0))) @ (^[Y0 : a]: (Y0)))) = ((sK1 @ (^[Y0 : a]: (Y0))))) | ~spl4_7),
% 0.20/0.29 inference(equality_resolution,[],[f170])).
% 0.20/0.29 thf(f301,plain,(
% 0.20/0.29 (((sK2 @ (sK1 @ (^[Y0 : a]: (Y0))) @ (^[Y0 : a]: (Y0)))) = ((sK1 @ (^[Y0 : a]: (Y0))))) | ~spl4_7),
% 0.20/0.29 inference(forward_subsumption_resolution,[],[f300,f22])).
% 0.20/0.29 thf(f306,plain,(
% 0.20/0.29 ((((^[Y0 : a]: (Y0)) @ (sK1 @ (^[Y0 : a]: (Y0))))) != ((sK1 @ (^[Y0 : a]: (Y0))))) | (((sK0 @ (sK1 @ (^[Y0 : a]: (Y0))))) != $true) | (((sK1 @ (^[Y0 : a]: (Y0)))) != ((sK1 @ (^[Y0 : a]: (Y0))))) | (((sK0 @ ((^[Y0 : a]: (Y0)) @ (sK3 @ (^[Y0 : a]: (Y0)))))) != $true) | ~spl4_7),
% 0.20/0.29 inference(constrained_superposition,[],[f13,f301])).
% 0.20/0.29 thf(f321,plain,(
% 0.20/0.29 (((sK0 @ ((^[Y0 : a]: (Y0)) @ (sK3 @ (^[Y0 : a]: (Y0)))))) != $true) | ((((^[Y0 : a]: (Y0)) @ (sK1 @ (^[Y0 : a]: (Y0))))) != ((sK1 @ (^[Y0 : a]: (Y0))))) | (((sK0 @ (sK1 @ (^[Y0 : a]: (Y0))))) != $true) | ~spl4_7),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f306])).
% 0.20/0.29 thf(f322,plain,(
% 0.20/0.29 ($true != ((sK0 @ (sK3 @ (^[Y0 : a]: (Y0)))))) | (((sK0 @ (sK1 @ (^[Y0 : a]: (Y0))))) != $true) | (((sK1 @ (^[Y0 : a]: (Y0)))) != ((sK1 @ (^[Y0 : a]: (Y0))))) | ~spl4_7),
% 0.20/0.29 inference(beta-eta_normalization,[],[f321])).
% 0.20/0.29 thf(f323,plain,(
% 0.20/0.29 ($true != ((sK0 @ (sK3 @ (^[Y0 : a]: (Y0)))))) | (((sK0 @ (sK1 @ (^[Y0 : a]: (Y0))))) != $true) | ~spl4_7),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f322])).
% 0.20/0.29 thf(f333,plain,(
% 0.20/0.29 (((sK0 @ (sK1 @ (^[Y0 : a]: (Y0))))) != $true) | ~spl4_7),
% 0.20/0.29 inference(forward_subsumption_resolution,[],[f323,f61])).
% 0.20/0.29 thf(f334,plain,(
% 0.20/0.29 $false | ~spl4_7),
% 0.20/0.29 inference(forward_subsumption_resolution,[],[f333,f22])).
% 0.20/0.29 thf(f335,plain,(
% 0.20/0.29 ~spl4_7),
% 0.20/0.29 inference(avatar_contradiction_clause,[],[f334])).
% 0.20/0.29 thf(f336,plain,(
% 0.20/0.29 ($true != $true) | (((sK2 @ (sK1 @ (^[Y0 : a]: (Y0))) @ (^[Y0 : a]: (Y0)))) = ((sK1 @ (^[Y0 : a]: (Y0))))) | ((^[Y0 : a]: (Y0)) != (^[Y0 : a]: (Y0))) | ~spl4_14),
% 0.20/0.29 inference(constrained_superposition,[],[f129,f22])).
% 0.20/0.29 thf(f344,plain,(
% 0.20/0.29 (((sK2 @ (sK1 @ (^[Y0 : a]: (Y0))) @ (^[Y0 : a]: (Y0)))) = ((sK1 @ (^[Y0 : a]: (Y0))))) | ~spl4_14),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f336])).
% 0.20/0.29 thf(f348,plain,(
% 0.20/0.29 ((((^[Y0 : a]: (Y0)) @ (sK1 @ (^[Y0 : a]: (Y0))))) != ((sK1 @ (^[Y0 : a]: (Y0))))) | ($true = ((sK0 @ (sK3 @ (^[Y0 : a]: (Y0)))))) | (((sK1 @ (^[Y0 : a]: (Y0)))) != ((sK1 @ (^[Y0 : a]: (Y0))))) | (((sK0 @ (sK1 @ (^[Y0 : a]: (Y0))))) != $true) | ~spl4_14),
% 0.20/0.30 inference(constrained_superposition,[],[f12,f344])).
% 0.20/0.30 thf(f361,plain,(
% 0.20/0.30 (((sK0 @ (sK1 @ (^[Y0 : a]: (Y0))))) != $true) | ((((^[Y0 : a]: (Y0)) @ (sK1 @ (^[Y0 : a]: (Y0))))) != ((sK1 @ (^[Y0 : a]: (Y0))))) | ($true = ((sK0 @ (sK3 @ (^[Y0 : a]: (Y0)))))) | ~spl4_14),
% 0.20/0.30 inference(trivial_inequality_removal,[],[f348])).
% 0.20/0.30 thf(f362,plain,(
% 0.20/0.30 (((sK0 @ (sK1 @ (^[Y0 : a]: (Y0))))) != $true) | (((sK1 @ (^[Y0 : a]: (Y0)))) != ((sK1 @ (^[Y0 : a]: (Y0))))) | ($true = ((sK0 @ (sK3 @ (^[Y0 : a]: (Y0)))))) | ~spl4_14),
% 0.20/0.30 inference(beta-eta_normalization,[],[f361])).
% 0.20/0.30 thf(f363,plain,(
% 0.20/0.30 ($true = ((sK0 @ (sK3 @ (^[Y0 : a]: (Y0)))))) | (((sK0 @ (sK1 @ (^[Y0 : a]: (Y0))))) != $true) | ~spl4_14),
% 0.20/0.30 inference(trivial_inequality_removal,[],[f362])).
% 0.20/0.30 thf(f374,plain,(
% 0.20/0.30 ($true = ((sK0 @ (sK3 @ (^[Y0 : a]: (Y0)))))) | ~spl4_14),
% 0.20/0.30 inference(forward_subsumption_resolution,[],[f363,f14])).
% 0.20/0.30 thf(f384,plain,(
% 0.20/0.30 spl4_7 | ~spl4_14),
% 0.20/0.30 inference(avatar_split_clause,[],[f374,f128,f60])).
% 0.20/0.30 cnf(s8, plain, spl4_7 | spl4_14, inference(sat_conversion,[],[f130])).
% 0.20/0.30 cnf(s19, plain, ~spl4_7, inference(sat_conversion,[],[f335])).
% 0.20/0.30 cnf(s22, plain, spl4_7 | ~spl4_14, inference(sat_conversion,[],[f384])).
% 0.20/0.30 cnf(s23, plain, ~spl4_14, inference(rat,[],[s22,s19])).
% 0.20/0.30 cnf(s24, plain, $false, inference(rat,[],[s8,s23,s19])).
% 0.20/0.30 thf(f385,plain,(
% 0.20/0.30 $false),
% 0.20/0.30 inference(avatar_sat_refutation,[],[s24])).
% 0.20/0.30 % SZS output end Proof for theBenchmark
% 0.20/0.30 % (1165151)------------------------------
% 0.20/0.30 % (1165151)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (1165151)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (1165151)CaDiCaL version: 2.1.3
% 0.20/0.30 % (1165151)Termination reason: Refutation
% 0.20/0.30 % (1165151)Time elapsed: 0.027 s
% 0.20/0.30 % (1165151)Peak memory usage: 13 MB
% 0.20/0.30 % (1165151)Instructions burned: 49 (million)
% 0.20/0.30 % (1165141)Success in time 0.064 s
% 0.20/0.30 % Vampire exiting
%------------------------------------------------------------------------------