%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : QUA004^1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 08:21:23 AM UTC 2026
% Result : Theorem 0.21s 0.28s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 25 ( 25 unt; 0 typ; 0 def)
% Number of atoms : 72 ( 37 equ; 2 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 76 ( 8 ~; 7 |; 0 &; 61 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 23 usr; 3 con; 0-4 aty)
% Number of variables : 53 ( 46 ^; 6 !; 1 ?; 53 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
emptyset: $i > $o ).
thf(func_def_1,type,
union: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_3,type,
singleton: $i > $i > $o ).
thf(func_def_5,type,
sup: ( $i > $o ) > $i ).
thf(func_def_6,type,
supset: ( ( $i > $o ) > $o ) > $i > $o ).
thf(func_def_7,type,
unionset: ( ( $i > $o ) > $o ) > $i > $o ).
thf(func_def_8,type,
addition: $i > $i > $i ).
thf(func_def_9,type,
leq: $i > $i > $o ).
thf(func_def_10,type,
multiplication: $i > $i > $i ).
thf(func_def_11,type,
crossmult: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_13,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_16,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_17,type,
vAND: $o > $o > $o ).
thf(func_def_18,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_19,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_22,type,
vOR: $o > $o > $o ).
thf(func_def_23,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_24,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_26,type,
vNOT: $o > $o ).
thf(f2,axiom,
( union
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/QUA001^0.ax',union_def) ).
thf(f3,axiom,
( ( ^ [X0: $i,X1: $i] : ( X1 = X0 ) )
= singleton ),
file('/export/starexec/sandbox/benchmark/Axioms/QUA001^0.ax',singleton_def) ).
thf(f5,axiom,
! [X0: $i] :
( ( sup @ ( singleton @ X0 ) )
= X0 ),
file('/export/starexec/sandbox/benchmark/Axioms/QUA001^0.ax',sup_singleset) ).
thf(f9,axiom,
( ( ^ [X0: $i,X1: $i] : ( sup @ ( union @ ( singleton @ X0 ) @ ( singleton @ X1 ) ) ) )
= addition ),
file('/export/starexec/sandbox/benchmark/Axioms/QUA001^0.ax',addition_def) ).
thf(f15,conjecture,
! [X0: $i] :
( ( addition @ X0 @ X0 )
= X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',addition_idemp) ).
thf(f16,negated_conjecture,
~ ! [X0: $i] :
( ( addition @ X0 @ X0 )
= X0 ),
inference(negated_conjecture,[status(cth)],[f15]) ).
thf(f17,plain,
( addition
= ( ^ [Y0: $i,Y1: $i] : ( sup @ ( union @ ( singleton @ Y0 ) @ ( singleton @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f25,plain,
( union
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f26,plain,
( union
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f25]) ).
thf(f29,plain,
( singleton
= ( ^ [Y0: $i,Y1: $i] : ( Y0 = Y1 ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f30,plain,
? [X0: $i] :
( ( addition @ X0 @ X0 )
!= X0 ),
inference(ennf_transformation,[],[f16]) ).
thf(f31,plain,
( ( addition @ sK0 @ sK0 )
!= sK0 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f30]) ).
thf(f33,plain,
! [X0: $i] :
( ( sup @ ( singleton @ X0 ) )
= X0 ),
inference(cnf_transformation,[],[f5]) ).
thf(f34,plain,
( ( addition @ sK0 @ sK0 )
!= sK0 ),
inference(cnf_transformation,[],[f31]) ).
thf(f35,plain,
( singleton
= ( ^ [Y0: $i,Y1: $i] : ( Y0 = Y1 ) ) ),
inference(cnf_transformation,[],[f29]) ).
thf(f42,plain,
( union
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f26]) ).
thf(f44,plain,
( addition
= ( ^ [Y0: $i,Y1: $i] : ( sup @ ( union @ ( singleton @ Y0 ) @ ( singleton @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f51,plain,
( addition
= ( ^ [Y0: $i,Y1: $i] :
( sup
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i,Y3: $i] : ( Y2 = Y3 )
@ Y0 )
@ ( ^ [Y2: $i,Y3: $i] : ( Y2 = Y3 )
@ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f44,f42,f35,f35]) ).
thf(f52,plain,
! [X0: $i] :
( ( sup
@ ( ^ [Y0: $i,Y1: $i] : ( Y0 = Y1 )
@ X0 ) )
= X0 ),
inference(definition_unfolding,[],[f33,f35]) ).
thf(f53,plain,
( ( ^ [Y0: $i,Y1: $i] :
( sup
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i,Y3: $i] : ( Y2 = Y3 )
@ Y0 )
@ ( ^ [Y2: $i,Y3: $i] : ( Y2 = Y3 )
@ Y1 ) ) )
@ sK0
@ sK0 )
!= sK0 ),
inference(definition_unfolding,[],[f34,f51]) ).
thf(f61,plain,
! [X0: $i] :
( ( sup @ ( (=) @ X0 ) )
= X0 ),
inference(beta-eta_normalization,[],[f52]) ).
thf(f63,plain,
( ( sup
@ ^ [Y0: $i] :
( ( sK0 = Y0 )
| ( sK0 = Y0 ) ) )
!= sK0 ),
inference(beta-eta_normalization,[],[f53]) ).
thf(f64,plain,
( ( sup
@ ^ [Y0: $i] : ( sK0 = Y0 ) )
!= sK0 ),
inference(boolean_simplification,[],[f63]) ).
thf(f65,plain,
( ( sup @ ( (=) @ sK0 ) )
!= sK0 ),
inference(beta-eta_normalization,[],[f64]) ).
thf(f67,plain,
$false,
inference(forward_subsumption_resolution,[],[f65,f61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : QUA004^1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n004.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % 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 13:29:00 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.23 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
% 0.21/0.28 % (1273302)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.28 % (1273308)lrs+10_16_si=on:nwc=1.5:random_seed=2166678854:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.28 % (1273308) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1273302-1273308"...
% 0.21/0.28 % (1273308)...printing done.
% 0.21/0.28 % (1273308)Refutation found. Thanks to Tanya!
% 0.21/0.28 % SZS status Theorem for theBenchmark
% 0.21/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.28 % (1273308)------------------------------
% 0.21/0.28 % (1273308)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (1273308)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (1273308)CaDiCaL version: 2.1.3
% 0.21/0.28 % (1273308)Termination reason: Refutation
% 0.21/0.28 % (1273308)Time elapsed: 0.002 s
% 0.21/0.28 % (1273308)Peak memory usage: 12 MB
% 0.21/0.28 % (1273308)Instructions burned: 5 (million)
% 0.21/0.28 % (1273302)Success in time 0.032 s
% 0.21/0.28 % Vampire exiting
%------------------------------------------------------------------------------