%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP001^5 : 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 : n017.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 08:03:48 AM UTC 2026
% Result : Theorem 0.22s 0.29s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 1
% Syntax : Number of formulae : 20 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 87 ( 47 equ; 0 cnn)
% Maximal formula atoms : 5 ( 4 avg)
% Number of connectives : 214 ( 8 ~; 0 |; 25 &; 178 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 72 ( 0 ^; 66 !; 6 ?; 72 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cP: $i > $i > $i ).
thf(f1,conjecture,
( ( ! [X2: $i] :
( ( cP @ X2 @ X2 )
= e )
& ! [X1: $i] :
( ( cP @ X1 @ e )
= X1 )
& ! [X0: $i] :
( ( cP @ e @ X0 )
= X0 )
& ! [X2: $i,X1: $i,X0: $i] :
( ( cP @ ( cP @ X0 @ X1 ) @ X2 )
= ( cP @ X0 @ ( cP @ X1 @ X2 ) ) ) )
=> ! [X4: $i,X3: $i] :
( ( cP @ X3 @ X4 )
= ( cP @ X4 @ X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cGRP_COMM2) ).
thf(f2,negated_conjecture,
~ ( ( ! [X2: $i] :
( ( cP @ X2 @ X2 )
= e )
& ! [X1: $i] :
( ( cP @ X1 @ e )
= X1 )
& ! [X0: $i] :
( ( cP @ e @ X0 )
= X0 )
& ! [X2: $i,X1: $i,X0: $i] :
( ( cP @ ( cP @ X0 @ X1 ) @ X2 )
= ( cP @ X0 @ ( cP @ X1 @ X2 ) ) ) )
=> ! [X4: $i,X3: $i] :
( ( cP @ X3 @ X4 )
= ( cP @ X4 @ X3 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ( ! [X2: $i] :
( ( cP @ e @ X2 )
= X2 )
& ! [X1: $i] :
( ( cP @ X1 @ e )
= X1 )
& ! [X5: $i,X3: $i,X4: $i] :
( ( cP @ X5 @ ( cP @ X4 @ X3 ) )
= ( cP @ ( cP @ X5 @ X4 ) @ X3 ) )
& ! [X0: $i] :
( e
= ( cP @ X0 @ X0 ) ) )
=> ! [X6: $i,X7: $i] :
( ( cP @ X7 @ X6 )
= ( cP @ X6 @ X7 ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
( ? [X6: $i,X7: $i] :
( ( cP @ X7 @ X6 )
!= ( cP @ X6 @ X7 ) )
& ! [X2: $i] :
( ( cP @ e @ X2 )
= X2 )
& ! [X1: $i] :
( ( cP @ X1 @ e )
= X1 )
& ! [X5: $i,X3: $i,X4: $i] :
( ( cP @ X5 @ ( cP @ X4 @ X3 ) )
= ( cP @ ( cP @ X5 @ X4 ) @ X3 ) )
& ! [X0: $i] :
( e
= ( cP @ X0 @ X0 ) ) ),
inference(ennf_transformation,[],[f3]) ).
thf(f5,plain,
( ! [X2: $i] :
( ( cP @ e @ X2 )
= X2 )
& ! [X1: $i] :
( ( cP @ X1 @ e )
= X1 )
& ! [X5: $i,X3: $i,X4: $i] :
( ( cP @ X5 @ ( cP @ X4 @ X3 ) )
= ( cP @ ( cP @ X5 @ X4 ) @ X3 ) )
& ? [X6: $i,X7: $i] :
( ( cP @ X7 @ X6 )
!= ( cP @ X6 @ X7 ) )
& ! [X0: $i] :
( e
= ( cP @ X0 @ X0 ) ) ),
inference(flattening,[],[f4]) ).
thf(f6,plain,
( ! [X0: $i] :
( ( cP @ e @ X0 )
= X0 )
& ! [X1: $i] :
( ( cP @ X1 @ e )
= X1 )
& ! [X2: $i,X3: $i,X4: $i] :
( ( cP @ ( cP @ X2 @ X4 ) @ X3 )
= ( cP @ X2 @ ( cP @ X4 @ X3 ) ) )
& ? [X5: $i,X6: $i] :
( ( cP @ X5 @ X6 )
!= ( cP @ X6 @ X5 ) )
& ! [X7: $i] :
( e
= ( cP @ X7 @ X7 ) ) ),
inference(rectify,[],[f5]) ).
thf(f7,plain,
( ! [X0: $i] :
( ( cP @ e @ X0 )
= X0 )
& ! [X1: $i] :
( ( cP @ X1 @ e )
= X1 )
& ! [X2: $i,X3: $i,X4: $i] :
( ( cP @ ( cP @ X2 @ X4 ) @ X3 )
= ( cP @ X2 @ ( cP @ X4 @ X3 ) ) )
& ( ( cP @ sK1 @ sK0 )
!= ( cP @ sK0 @ sK1 ) )
& ! [X7: $i] :
( e
= ( cP @ X7 @ X7 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X5,sK0),skolemize(X6,sK1)],[f6]) ).
thf(f8,plain,
! [X7: $i] :
( e
= ( cP @ X7 @ X7 ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f9,plain,
( ( cP @ sK1 @ sK0 )
!= ( cP @ sK0 @ sK1 ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f10,plain,
! [X2: $i,X3: $i,X4: $i] :
( ( cP @ ( cP @ X2 @ X4 ) @ X3 )
= ( cP @ X2 @ ( cP @ X4 @ X3 ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f11,plain,
! [X1: $i] :
( ( cP @ X1 @ e )
= X1 ),
inference(cnf_transformation,[],[f7]) ).
thf(f12,plain,
! [X0: $i] :
( ( cP @ e @ X0 )
= X0 ),
inference(cnf_transformation,[],[f7]) ).
thf(f13,plain,
! [X0: $i,X1: $i] :
( ( cP @ X0 @ ( cP @ X0 @ X1 ) )
= ( cP @ e @ X1 ) ),
inference(constrained_superposition,[],[f10,f8]) ).
thf(f17,plain,
! [X0: $i,X1: $i] :
( e
= ( cP @ X0 @ ( cP @ X1 @ ( cP @ X0 @ X1 ) ) ) ),
inference(constrained_superposition,[],[f10,f8]) ).
thf(f22,plain,
! [X0: $i,X1: $i] :
( ( cP @ X0 @ ( cP @ X0 @ X1 ) )
= X1 ),
inference(forward_demodulation,[],[f13,f12]) ).
thf(f49,plain,
! [X0: $i,X1: $i] :
( ( cP @ X0 @ e )
= ( cP @ X1 @ ( cP @ X0 @ X1 ) ) ),
inference(constrained_superposition,[],[f22,f17]) ).
thf(f62,plain,
! [X0: $i,X1: $i] :
( ( cP @ X1 @ ( cP @ X0 @ X1 ) )
= X0 ),
inference(forward_demodulation,[],[f49,f11]) ).
thf(f78,plain,
! [X0: $i,X1: $i] :
( ( cP @ X0 @ X1 )
= ( cP @ X1 @ X0 ) ),
inference(constrained_superposition,[],[f22,f62]) ).
thf(f112,plain,
( ( cP @ sK0 @ sK1 )
!= ( cP @ sK0 @ sK1 ) ),
inference(constrained_superposition,[],[f9,f78]) ).
thf(f113,plain,
$false,
inference(trivial_inequality_removal,[],[f112]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP001^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n017.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 19:04:08 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 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
% 0.22/0.29 % (759286)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.29 % (759291)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=4119518339:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.29 % (759291) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-759286-759291"...
% 0.22/0.29 % (759291)...printing done.
% 0.22/0.29 % (759297)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.29 % (759297)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
% 0.22/0.29 % (759291)Refutation found. Thanks to Tanya!
% 0.22/0.29 % SZS status Theorem for theBenchmark
% 0.22/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.29 % (759291)------------------------------
% 0.22/0.29 % (759291)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.29 % (759291)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.29 % (759291)CaDiCaL version: 2.1.3
% 0.22/0.29 % (759291)Termination reason: Refutation
% 0.22/0.29 % (759291)Time elapsed: 0.003 s
% 0.22/0.29 % (759291)Peak memory usage: 12 MB
% 0.22/0.29 % (759291)Instructions burned: 8 (million)
% 0.22/0.29 % (759286)Success in time 0.033 s
% 0.22/0.29 % Vampire exiting
%------------------------------------------------------------------------------