%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ALG286^5 : 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 : n012.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 07:45:21 AM UTC 2026
% Result : Theorem 0.09s 0.17s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 1
% Syntax : Number of formulae : 27 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 80 ( 79 equ; 0 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 212 ( 22 ~; 4 |; 35 &; 137 @)
% ( 6 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 41 ( 0 ^; 41 !; 0 ?; 41 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cZ: a ).
thf(func_def_1,type,
u: a ).
thf(func_def_2,type,
y: a ).
thf(func_def_3,type,
x: a ).
thf(func_def_4,type,
cP: a > a > a ).
thf(func_def_5,type,
cR: a > a ).
thf(func_def_6,type,
cL: a > a ).
thf(f1,conjecture,
( ( ( ( cL @ cZ )
= cZ )
& ( ( cR @ cZ )
= cZ )
& ! [X1: a,X0: a] :
( ( cR @ ( cP @ X0 @ X1 ) )
= X1 )
& ! [X0: a,X1: a] :
( ( cL @ ( cP @ X0 @ X1 ) )
= X0 )
& ! [X2: a] :
( ( X2
= ( cP @ ( cL @ X2 ) @ ( cR @ X2 ) ) )
<=> ( X2 != cZ ) ) )
=> ( ( u
= ( cP @ x @ y ) )
=> ( u != cZ ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cPU_PAIR_NOT_ZERO_pme) ).
thf(f2,negated_conjecture,
~ ( ( ( ( cL @ cZ )
= cZ )
& ( ( cR @ cZ )
= cZ )
& ! [X1: a,X0: a] :
( ( cR @ ( cP @ X0 @ X1 ) )
= X1 )
& ! [X0: a,X1: a] :
( ( cL @ ( cP @ X0 @ X1 ) )
= X0 )
& ! [X2: a] :
( ( X2
= ( cP @ ( cL @ X2 ) @ ( cR @ X2 ) ) )
<=> ( X2 != cZ ) ) )
=> ( ( u
= ( cP @ x @ y ) )
=> ( u != cZ ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ( ( ( cL @ cZ )
= cZ )
& ( ( cR @ cZ )
= cZ )
& ! [X0: a,X1: a] :
( ( cR @ ( cP @ X1 @ X0 ) )
= X0 )
& ! [X2: a,X3: a] :
( ( cL @ ( cP @ X2 @ X3 ) )
= X2 )
& ! [X4: a] :
( ( ( cP @ ( cL @ X4 ) @ ( cR @ X4 ) )
= X4 )
<=> ( cZ != X4 ) ) )
=> ( ( u
= ( cP @ x @ y ) )
=> ( u != cZ ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ( ! [X4: a] :
( ( cZ != X4 )
<=> ( ( cP @ ( cL @ X4 ) @ ( cR @ X4 ) )
= X4 ) )
& ( cZ
= ( cR @ cZ ) )
& ! [X2: a,X3: a] :
( ( cL @ ( cP @ X2 @ X3 ) )
= X2 )
& ( cZ
= ( cL @ cZ ) )
& ! [X0: a,X1: a] :
( ( cR @ ( cP @ X1 @ X0 ) )
= X0 ) )
=> ( ( u
= ( cP @ x @ y ) )
=> ( cZ != u ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ( cZ = u )
& ( u
= ( cP @ x @ y ) )
& ! [X4: a] :
( ( cZ != X4 )
<=> ( ( cP @ ( cL @ X4 ) @ ( cR @ X4 ) )
= X4 ) )
& ( cZ
= ( cR @ cZ ) )
& ! [X2: a,X3: a] :
( ( cL @ ( cP @ X2 @ X3 ) )
= X2 )
& ( cZ
= ( cL @ cZ ) )
& ! [X0: a,X1: a] :
( ( cR @ ( cP @ X1 @ X0 ) )
= X0 ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ( u
= ( cP @ x @ y ) )
& ( cZ
= ( cL @ cZ ) )
& ( cZ = u )
& ! [X0: a,X1: a] :
( ( cR @ ( cP @ X1 @ X0 ) )
= X0 )
& ( cZ
= ( cR @ cZ ) )
& ! [X2: a,X3: a] :
( ( cL @ ( cP @ X2 @ X3 ) )
= X2 )
& ! [X4: a] :
( ( cZ != X4 )
<=> ( ( cP @ ( cL @ X4 ) @ ( cR @ X4 ) )
= X4 ) ) ),
inference(flattening,[],[f5]) ).
thf(f7,plain,
( ( u
= ( cP @ x @ y ) )
& ( cZ
= ( cL @ cZ ) )
& ( cZ = u )
& ! [X0: a,X1: a] :
( ( cR @ ( cP @ X1 @ X0 ) )
= X0 )
& ( cZ
= ( cR @ cZ ) )
& ! [X2: a,X3: a] :
( ( cL @ ( cP @ X2 @ X3 ) )
= X2 )
& ! [X4: a] :
( ( ( cZ != X4 )
| ( ( cP @ ( cL @ X4 ) @ ( cR @ X4 ) )
!= X4 ) )
& ( ( ( cP @ ( cL @ X4 ) @ ( cR @ X4 ) )
= X4 )
| ( cZ = X4 ) ) ) ),
inference(nnf_transformation,[],[f6]) ).
thf(f9,plain,
! [X4: a] :
( ( cZ != X4 )
| ( ( cP @ ( cL @ X4 ) @ ( cR @ X4 ) )
!= X4 ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f10,plain,
! [X2: a,X3: a] :
( ( cL @ ( cP @ X2 @ X3 ) )
= X2 ),
inference(cnf_transformation,[],[f7]) ).
thf(f11,plain,
( cZ
= ( cR @ cZ ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f12,plain,
! [X0: a,X1: a] :
( ( cR @ ( cP @ X1 @ X0 ) )
= X0 ),
inference(cnf_transformation,[],[f7]) ).
thf(f13,plain,
cZ = u,
inference(cnf_transformation,[],[f7]) ).
thf(f14,plain,
( cZ
= ( cL @ cZ ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f15,plain,
( u
= ( cP @ x @ y ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f16,plain,
( u
= ( cL @ u ) ),
inference(definition_unfolding,[],[f14,f13,f13]) ).
thf(f17,plain,
( u
= ( cR @ u ) ),
inference(definition_unfolding,[],[f11,f13,f13]) ).
thf(f18,plain,
! [X4: a] :
( ( u != X4 )
| ( ( cP @ ( cL @ X4 ) @ ( cR @ X4 ) )
!= X4 ) ),
inference(definition_unfolding,[],[f9,f13]) ).
thf(f20,plain,
( u
!= ( cP @ ( cL @ u ) @ ( cR @ u ) ) ),
inference(equality_resolution,[],[f18]) ).
thf(f21,plain,
( u
!= ( cP @ u @ ( cR @ u ) ) ),
inference(forward_demodulation,[],[f20,f16]) ).
thf(f22,plain,
( u
!= ( cP @ u @ u ) ),
inference(forward_demodulation,[],[f21,f17]) ).
thf(f23,plain,
( x
= ( cL @ u ) ),
inference(constrained_superposition,[],[f10,f15]) ).
thf(f24,plain,
u = x,
inference(forward_demodulation,[],[f23,f16]) ).
thf(f25,plain,
( y
= ( cR @ u ) ),
inference(constrained_superposition,[],[f12,f15]) ).
thf(f26,plain,
u = y,
inference(forward_demodulation,[],[f25,f17]) ).
thf(f27,plain,
( u
= ( cP @ u @ y ) ),
inference(constrained_superposition,[],[f15,f24]) ).
thf(f28,plain,
( u
= ( cP @ u @ u ) ),
inference(forward_demodulation,[],[f27,f26]) ).
thf(f29,plain,
$false,
inference(forward_subsumption_resolution,[],[f28,f22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : ALG286^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.00/0.11 % Computer : n012.cluster.edu
% 0.00/0.11 % Model : x86_64 x86_64
% 0.00/0.11 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.11 % Memory : 8046.5625MB
% 0.00/0.11 % OS : Linux 6.8.0-71-generic
% 0.00/0.11 % CPULimit : 300
% 0.00/0.11 % WCLimit : 300
% 0.00/0.11 % DateTime : Tue Sep 29 17:37:18 UTC 2026
% 0.00/0.11 % CPUTime :
% 0.00/0.11 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.13 Running higher-order theorem proving
% 0.09/0.14 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
% 0.09/0.17 % (435263)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.09/0.17 % (435274)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.09/0.17 % (435274)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
% 0.09/0.17 % (435269)lrs+10_16_si=on:nwc=1.5:random_seed=329478131:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.09/0.17 % (435270)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=327138634:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.09/0.17 % (435273)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3560107288:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.09/0.17 % (435272)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1191346229:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.09/0.17 % (435271)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=1538103867: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)
% 0.09/0.17 % (435274)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=7902424:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.09/0.17 % (435270) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-435263-435270"...
% 0.09/0.17 % (435272) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-435263-435272"...
% 0.09/0.17 % (435273) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-435263-435273"...
% 0.09/0.17 % (435269) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-435263-435269"...
% 0.09/0.17 % (435271) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-435263-435271"...
% 0.09/0.17 % (435272)...printing done.
% 0.09/0.17 % (435270)...printing done.
% 0.09/0.17 % (435273)...printing done.
% 0.09/0.17 % (435269)...printing done.
% 0.09/0.17 % (435271)...printing done.
% 0.09/0.17 % (435270)Refutation found. Thanks to Tanya!
% 0.09/0.17 % SZS status Theorem for theBenchmark
% 0.09/0.17 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.17 % (435270)------------------------------
% 0.09/0.17 % (435270)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.17 % (435270)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.17 % (435270)CaDiCaL version: 2.1.3
% 0.09/0.17 % (435270)Termination reason: Refutation
% 0.09/0.17 % (435270)Time elapsed: 0.001 s
% 0.09/0.17 % (435270)Peak memory usage: 12 MB
% 0.09/0.17 % (435270)Instructions burned: 2 (million)
% 0.09/0.17 % (435263)Success in time 0.025 s
% 0.09/0.17 % Vampire exiting
%------------------------------------------------------------------------------