%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU995^5 : 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 : n008.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 08:32:06 AM UTC 2026
% Result : Theorem 0.22s 0.31s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 1
% Syntax : Number of formulae : 14 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 42 ( 21 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 92 ( 16 ~; 3 |; 3 &; 68 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 95 ( 95 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 3 con; 0-4 aty)
% Number of variables : 55 ( 8 ^; 45 !; 2 ?; 55 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_3,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_4,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_5,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_6,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(f1,conjecture,
( ( cU != cV )
=> ? [X0: ( $i > $i ) > ( $i > $i ) > $i > $i] :
~ ! [X2: $i > $i,X1: $i > $i] :
( ( X0 @ X1 @ X2 )
= ( X0 @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM24_pme) ).
thf(f2,negated_conjecture,
~ ( ( cU != cV )
=> ? [X0: ( $i > $i ) > ( $i > $i ) > $i > $i] :
~ ! [X2: $i > $i,X1: $i > $i] :
( ( X0 @ X1 @ X2 )
= ( X0 @ X2 @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
( ! [X0: ( $i > $i ) > ( $i > $i ) > $i > $i,X2: $i > $i,X1: $i > $i] :
( ( X0 @ X1 @ X2 )
= ( X0 @ X2 @ X1 ) )
& ( cU != cV ) ),
inference(ennf_transformation,[],[f2]) ).
thf(f4,plain,
( ( cU != cV )
& ! [X2: $i > $i,X0: ( $i > $i ) > ( $i > $i ) > $i > $i,X1: $i > $i] :
( ( X0 @ X1 @ X2 )
= ( X0 @ X2 @ X1 ) ) ),
inference(flattening,[],[f3]) ).
thf(f5,plain,
( ( cU != cV )
& ! [X0: $i > $i,X1: ( $i > $i ) > ( $i > $i ) > $i > $i,X2: $i > $i] :
( ( X1 @ X2 @ X0 )
= ( X1 @ X0 @ X2 ) ) ),
inference(rectify,[],[f4]) ).
thf(f6,plain,
! [X2: $i > $i,X0: $i > $i,X1: ( $i > $i ) > ( $i > $i ) > $i > $i] :
( ( X1 @ X2 @ X0 )
= ( X1 @ X0 @ X2 ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f7,plain,
cU != cV,
inference(cnf_transformation,[],[f5]) ).
thf(f8,plain,
! [X2: $i > $i,X3: $i,X0: $i > $i,X1: ( $i > $i ) > ( $i > $i ) > $i > $i] :
( ( X1 @ X2 @ X0 @ X3 )
= ( X1 @ X0 @ X2 @ X3 ) ),
inference(argument_congruence,[],[f6]) ).
thf(f16,plain,
! [X2: $i > $i,X3: $i,X0: ( $i > $i ) > ( $i > $i ) > $i > $i,X1: $i > $i,X6: $i > $i,X7: $i,X4: ( $i > $i ) > ( $i > $i ) > $i > $i,X5: $i > $i] :
( ( ( X0 @ X1 @ X2 @ X3 )
= ( X4 @ X5 @ X6 @ X7 ) )
| ( ( X0 @ X2 @ X1 @ X3 )
!= ( X4 @ X6 @ X5 @ X7 ) ) ),
inference(constrained_superposition,[],[f8,f8]) ).
thf(f79,plain,
! [X2: $i > $i,X3: $i,X0: ( $i > $i ) > ( $i > $i ) > $i > $i,X1: $i > $i,X8: $i > $i,X6: $i,X5: $i > $i] :
( ( cU
!= ( X0 @ X1 @ X2 @ X3 ) )
| ( ( X0 @ X2 @ X1 @ X3 )
!= ( ^ [Y0: $i > $i,Y1: $i > $i,Y2: $i] : cV
@ X5
@ X8
@ X6 ) ) ),
inference(constrained_superposition,[],[f7,f16]) ).
thf(f95,plain,
! [X2: $i > $i,X3: $i,X0: ( $i > $i ) > ( $i > $i ) > $i > $i,X1: $i > $i] :
( ( cU
!= ( X0 @ X1 @ X2 @ X3 ) )
| ( cV
!= ( X0 @ X2 @ X1 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f79]) ).
thf(f135,plain,
! [X2: $i,X0: ( $i > $i ) > ( $i > $i ) > $i > $i,X1: $i > $i] :
( cV
!= ( ^ [Y0: $i > $i,Y1: $i > $i,Y2: $i] : ( Y0 @ ( X0 @ Y0 @ Y1 @ Y2 ) )
@ X1
@ ^ [Y0: $i] : cU
@ X2 ) ),
inference(equality_resolution,[],[f95]) ).
thf(f148,plain,
! [X2: $i,X0: ( $i > $i ) > ( $i > $i ) > $i > $i,X1: $i > $i] :
( cV
!= ( X1
@ ( X0 @ X1
@ ^ [Y0: $i] : cU
@ X2 ) ) ),
inference(beta-eta_normalization,[],[f135]) ).
thf(f228,plain,
$false,
inference(equality_resolution,[],[f148]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU995^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n008.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 14:56:54 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.24 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
% 0.22/0.31 % (3268717)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.31 % (3268724)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3211578725:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.31 % (3268724)Refutation not found, incomplete strategy
% 0.22/0.31 % (3268724)------------------------------
% 0.22/0.31 % (3268724)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.31 % (3268724)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.31 % (3268724)CaDiCaL version: 2.1.3
% 0.22/0.31 % (3268724)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.31 % (3268724)Time elapsed: 0.001 s
% 0.22/0.31 % (3268724)Peak memory usage: 12 MB
% 0.22/0.31 % (3268724)Instructions burned: 1 (million)
% 0.22/0.31 % (3268724)------------------------------
% 0.22/0.31 % (3268724)------------------------------
% 0.22/0.31 % (3268728)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.31 % (3268728)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
% 0.22/0.31 % (3268723)lrs+10_16_si=on:nwc=1.5:random_seed=336636744:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.31 % (3268722)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3326290766:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.31 % (3268726)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2561866677:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.31 % (3268725)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=1514082751: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)
% 0.22/0.31 % (3268727)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=873984309:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.31 % (3268726)Refutation not found, incomplete strategy
% 0.22/0.31 % (3268726)------------------------------
% 0.22/0.31 % (3268726)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.31 % (3268726)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.31 % (3268726)CaDiCaL version: 2.1.3
% 0.22/0.31 % (3268726)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.31 % (3268726)Time elapsed: 0.001 s
% 0.22/0.31 % (3268726)Peak memory usage: 11 MB
% 0.22/0.31 % (3268722)Refutation not found, incomplete strategy
% 0.22/0.31 % (3268722)------------------------------
% 0.22/0.31 % (3268722)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.31 % (3268722)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.31 % (3268722)CaDiCaL version: 2.1.3
% 0.22/0.31 % (3268722)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.31 % (3268722)Time elapsed: 0.001 s
% 0.22/0.31 % (3268722)Peak memory usage: 12 MB
% 0.22/0.31 % (3268722)Instructions burned: 1 (million)
% 0.22/0.31 % (3268725)Refutation not found, incomplete strategy
% 0.22/0.31 % (3268725)------------------------------
% 0.22/0.31 % (3268725)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.31 % (3268725)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.31 % (3268725)CaDiCaL version: 2.1.3
% 0.22/0.31 % (3268725)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.31 % (3268725)Time elapsed: 0.001 s
% 0.22/0.31 % (3268725)Peak memory usage: 12 MB
% 0.22/0.31 % (3268725)Instructions burned: 1 (million)
% 0.22/0.31 % (3268726)------------------------------
% 0.22/0.31 % (3268726)------------------------------
% 0.22/0.31 % (3268722)------------------------------
% 0.22/0.31 % (3268722)------------------------------
% 0.22/0.31 % (3268725)------------------------------
% 0.22/0.31 % (3268725)------------------------------
% 0.22/0.31 % (3268728)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=1190813831:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.31 % (3268730)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2393998465:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.22/0.31 % (3268728)Refutation not found, incomplete strategy
% 0.22/0.31 % (3268728)------------------------------
% 0.22/0.31 % (3268728)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.31 % (3268728)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.31 % (3268728)CaDiCaL version: 2.1.3
% 0.22/0.31 % (3268728)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.31 % (3268728)Time elapsed: 0.001 s
% 0.22/0.31 % (3268728)Peak memory usage: 12 MB
% 0.22/0.31 % (3268728)Instructions burned: 1 (million)
% 0.22/0.31 % (3268728)------------------------------
% 0.22/0.31 % (3268728)------------------------------
% 0.22/0.31 % (3268730)Instruction limit reached!
% 0.22/0.31 % (3268730)------------------------------
% 0.22/0.31 % (3268730)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.31 % (3268730)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.31 % (3268730)CaDiCaL version: 2.1.3
% 0.22/0.31 % (3268730)Termination reason: Instruction limit
% 0.22/0.31 % (3268730)Termination phase: Saturation
% 0.22/0.31 % (3268730)Time elapsed: 0.002 s
% 0.22/0.31 % (3268730)Peak memory usage: 12 MB
% 0.22/0.31 % (3268730)Instructions burned: 6 (million)
% 0.22/0.31 % (3268723)Instruction limit reached!
% 0.22/0.31 % (3268723)------------------------------
% 0.22/0.31 % (3268723)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.31 % (3268723)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.31 % (3268723)CaDiCaL version: 2.1.3
% 0.22/0.31 % (3268723)Termination reason: Instruction limit
% 0.22/0.31 % (3268723)Termination phase: Saturation
% 0.22/0.31 % (3268723)Time elapsed: 0.010 s
% 0.22/0.31 % (3268723)Peak memory usage: 12 MB
% 0.22/0.31 % (3268723)Instructions burned: 26 (million)
% 0.22/0.31 % (3268737)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.22/0.31 % (3268736)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1385612936:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.22/0.31 % (3268743)lrs+10_1_si=on:cs=on:random_seed=2951872377:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.22/0.31 % (3268727) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3268717-3268727"...
% 0.22/0.31 % (3268741)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
% 0.22/0.31 % (3268741)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.22/0.31 % (3268737)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=703508781:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.22/0.31 % (3268727)...printing done.
% 0.22/0.31 % (3268739)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2998972814:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.22/0.31 % (3268727)Refutation found. Thanks to Tanya!
% 0.22/0.31 % SZS status Theorem for theBenchmark
% 0.22/0.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.31 % (3268727)------------------------------
% 0.22/0.31 % (3268727)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.31 % (3268727)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.31 % (3268727)CaDiCaL version: 2.1.3
% 0.22/0.31 % (3268727)Termination reason: Refutation
% 0.22/0.31 % (3268727)Time elapsed: 0.021 s
% 0.22/0.31 % (3268727)Peak memory usage: 12 MB
% 0.22/0.31 % (3268727)Instructions burned: 42 (million)
% 0.22/0.31 % (3268717)Success in time 0.058 s
% 0.22/0.31 % Vampire exiting
%------------------------------------------------------------------------------