%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM960_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 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 : Tue Sep 29 12:26:17 PM UTC 2026
% Result : Theorem 0.07s 0.41s
% Output : Refutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 39 ( 30 unt; 0 typ; 0 def)
% Number of atoms : 49 ( 12 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 25 ( 15 ~; 6 |; 2 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 17 ( 15 usr; 1 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 9 con; 0-3 aty)
% Number of variables : 22 ( 22 !; 0 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
bool: $tType ).
tff(type_def_6,type,
int: $tType ).
tff(type_def_7,type,
nat: $tType ).
tff(func_def_0,type,
minus_minus:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_1,type,
one_one:
!>[X0: $tType] : X0 ).
tff(func_def_2,type,
plus_plus:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_3,type,
times_times:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_4,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_5,type,
bit0: int > int ).
tff(func_def_6,type,
bit1: int > int ).
tff(func_def_7,type,
pls: int ).
tff(func_def_8,type,
number_number_of:
!>[X0: $tType] : ( int > X0 ) ).
tff(func_def_9,type,
power_power:
!>[X0: $tType] : ( ( X0 * nat ) > X0 ) ).
tff(func_def_10,type,
fFalse: bool ).
tff(func_def_11,type,
fTrue: bool ).
tff(func_def_12,type,
m: int ).
tff(func_def_13,type,
s1: int ).
tff(func_def_14,type,
s: int ).
tff(func_def_15,type,
t: int ).
tff(func_def_16,type,
sK0: int ).
tff(func_def_17,type,
sK1: int ).
tff(pred_def_1,type,
number:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
ring:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
semiring:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
number_ring:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
ring_char_0:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
linorder:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
number_semiring:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
linordered_idom:
!>[X0: $tType] : $o ).
tff(pred_def_9,type,
linord219039673up_add:
!>[X0: $tType] : $o ).
tff(pred_def_10,type,
zcong: ( int * int * int ) > $o ).
tff(pred_def_11,type,
zprime: int > $o ).
tff(pred_def_12,type,
ord_less:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_13,type,
ord_less_eq:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_14,type,
twoSqu1567020053sum2sq: int > $o ).
tff(pred_def_15,type,
pp: bool > $o ).
tff(f1,axiom,
( ord_less_eq(int,zero_zero(int),s)
& ord_less(int,s,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
& zcong(s1,s,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_s0p) ).
tff(f11,axiom,
! [X0: $tType] :
( number_ring(X0)
=> ( number_number_of(X0,bit1(pls)) = one_one(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_numeral__1__eq__1) ).
tff(f35,axiom,
! [X0: int,X1: int] : ( times_times(int,bit0(X1),X0) = bit0(times_times(int,X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_mult__Bit0) ).
tff(f58,axiom,
! [X0: int,X1: int] : ( plus_plus(int,bit0(X1),bit1(X0)) = bit1(plus_plus(int,X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_add__Bit0__Bit1) ).
tff(f64,axiom,
! [X0: int,X1: int] :
( ord_less_eq(int,X1,minus_minus(int,X0,one_one(int)))
<=> ord_less(int,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_zle__diff1__eq) ).
tff(f91,axiom,
! [X0: int] : ( number_number_of(int,X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_number__of__is__id) ).
tff(f104,axiom,
number_ring(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__ring) ).
tff(f115,conjecture,
ord_less_eq(int,s,minus_minus(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),one_one(int))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(f116,negated_conjecture,
~ ord_less_eq(int,s,minus_minus(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),one_one(int))),
inference(negated_conjecture,[status(cth)],[f115]) ).
tff(f117,plain,
~ ord_less_eq(int,s,minus_minus(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),one_one(int))),
inference(flattening,[],[f116]) ).
tff(f127,plain,
! [X0: $tType] :
( ( number_number_of(X0,bit1(pls)) = one_one(X0) )
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f11]) ).
tff(f174,plain,
ord_less(int,s,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))),
inference(cnf_transformation,[],[f1]) ).
tff(f186,plain,
! [X0: $tType] :
( ~ number_ring(X0)
| ( one_one(X0) = number_number_of(X0,bit1(pls)) ) ),
inference(cnf_transformation,[],[f127]) ).
tff(f220,plain,
! [X0: int,X1: int] : ( bit0(times_times(int,X1,X0)) = times_times(int,bit0(X1),X0) ),
inference(cnf_transformation,[],[f35]) ).
tff(f253,plain,
! [X0: int,X1: int] : ( bit1(plus_plus(int,X1,X0)) = plus_plus(int,bit0(X1),bit1(X0)) ),
inference(cnf_transformation,[],[f58]) ).
tff(f264,plain,
! [X0: int,X1: int] :
( ~ ord_less(int,X1,X0)
| ord_less_eq(int,X1,minus_minus(int,X0,one_one(int))) ),
inference(cnf_transformation,[],[f64]) ).
tff(f315,plain,
! [X0: int] : ( number_number_of(int,X0) = X0 ),
inference(cnf_transformation,[],[f91]) ).
tff(f331,plain,
number_ring(int),
inference(cnf_transformation,[],[f104]) ).
tff(f342,plain,
~ ord_less_eq(int,s,minus_minus(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),one_one(int))),
inference(cnf_transformation,[],[f117]) ).
tff(f354,plain,
~ ord_less(int,s,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))),
inference(consistent_polarity_flipping,[],[f174]) ).
tff(f364,plain,
! [X0: $tType] :
( number_ring(X0)
| ( one_one(X0) = number_number_of(X0,bit1(pls)) ) ),
inference(consistent_polarity_flipping,[],[f186]) ).
tff(f421,plain,
! [X0: int,X1: int] :
( ord_less(int,X1,X0)
| ~ ord_less_eq(int,X1,minus_minus(int,X0,one_one(int))) ),
inference(consistent_polarity_flipping,[],[f264]) ).
tff(f478,plain,
~ number_ring(int),
inference(consistent_polarity_flipping,[],[f331]) ).
tff(f486,plain,
ord_less_eq(int,s,minus_minus(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),one_one(int))),
inference(consistent_polarity_flipping,[],[f342]) ).
tff(f496,plain,
ord_less_eq(int,s,minus_minus(int,plus_plus(int,times_times(int,bit0(bit0(bit1(pls))),m),one_one(int)),one_one(int))),
inference(superposition,[],[f486,f315]) ).
tff(f515,plain,
one_one(int) = number_number_of(int,bit1(pls)),
inference(resolution,[],[f364,f478]) ).
tff(f516,plain,
bit1(pls) = one_one(int),
inference(forward_demodulation,[],[f515,f315]) ).
tff(f598,plain,
ord_less_eq(int,s,minus_minus(int,plus_plus(int,bit0(times_times(int,bit0(bit1(pls)),m)),one_one(int)),one_one(int))),
inference(superposition,[],[f496,f220]) ).
tff(f599,plain,
ord_less_eq(int,s,minus_minus(int,plus_plus(int,bit0(times_times(int,bit0(bit1(pls)),m)),bit1(pls)),bit1(pls))),
inference(forward_demodulation,[],[f598,f516]) ).
tff(f604,plain,
ord_less_eq(int,s,minus_minus(int,plus_plus(int,bit0(bit0(times_times(int,bit1(pls),m))),bit1(pls)),bit1(pls))),
inference(forward_demodulation,[],[f599,f220]) ).
tff(f650,plain,
! [X0: int,X1: int] :
( ~ ord_less_eq(int,X1,minus_minus(int,X0,bit1(pls)))
| ord_less(int,X1,X0) ),
inference(forward_demodulation,[],[f421,f516]) ).
tff(f692,plain,
ord_less(int,s,plus_plus(int,bit0(bit0(times_times(int,bit1(pls),m))),bit1(pls))),
inference(resolution,[],[f650,f604]) ).
tff(f695,plain,
ord_less(int,s,bit1(plus_plus(int,bit0(times_times(int,bit1(pls),m)),pls))),
inference(forward_demodulation,[],[f692,f253]) ).
tff(f901,plain,
~ ord_less(int,s,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),bit1(pls))),
inference(forward_demodulation,[],[f354,f516]) ).
tff(f902,plain,
~ ord_less(int,s,plus_plus(int,times_times(int,bit0(bit0(bit1(pls))),m),bit1(pls))),
inference(forward_demodulation,[],[f901,f315]) ).
tff(f903,plain,
~ ord_less(int,s,plus_plus(int,bit0(times_times(int,bit0(bit1(pls)),m)),bit1(pls))),
inference(forward_demodulation,[],[f902,f220]) ).
tff(f904,plain,
~ ord_less(int,s,bit1(plus_plus(int,times_times(int,bit0(bit1(pls)),m),pls))),
inference(forward_demodulation,[],[f903,f253]) ).
tff(f905,plain,
~ ord_less(int,s,bit1(plus_plus(int,bit0(times_times(int,bit1(pls),m)),pls))),
inference(forward_demodulation,[],[f904,f220]) ).
tff(f906,plain,
$false,
inference(forward_subsumption_resolution,[],[f905,f695]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM960_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.34 % Computer : n012.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Sun Sep 27 21:47:20 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.34 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.36 Running first-order model finding
% 0.07/0.36 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.41 % (2781754)Will run a generic schedule for satisfiability detection.
% 0.07/0.41 % (2781760)% WARNING: option uhcvi not known.
% 0.07/0.41 % (2781764)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2452977740:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.07/0.41 % (2781760)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2729458289:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.07/0.41 % (2781765)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=600218152:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.07/0.41 % (2781759)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3109843992_2999 on theBenchmark for (2999ds/0Mi)
% 0.07/0.41 % (2781761)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2165106583:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.07/0.41 % (2781762)dis+10_1_sil=32000:sp=arity:random_seed=3403397747:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.07/0.41 % (2781763)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3857657684:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.07/0.41 % Exception at run slice level
% 0.07/0.41 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.07/0.41 % (2781760) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2781754-2781760"...
% 0.07/0.41 % (2781763) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2781754-2781763"...
% 0.07/0.41 % (2781760)...printing done.
% 0.07/0.41 % (2781760)Refutation found. Thanks to Tanya!
% 0.07/0.41 % SZS status Theorem for theBenchmark
% 0.07/0.41 % SZS output start Proof for theBenchmark
% See solution above
% 0.07/0.41 % (2781760)------------------------------
% 0.07/0.41 % (2781760)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.41 % (2781760)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.41 % (2781760)CaDiCaL version: 2.1.3
% 0.07/0.41 % (2781760)Termination reason: Refutation
% 0.07/0.41 % (2781760)Time elapsed: 0.016 s
% 0.07/0.41 % (2781760)Peak memory usage: 12 MB
% 0.07/0.41 % (2781760)Instructions burned: 27 (million)
% 0.07/0.41 % (2781754)Success in time 0.041 s
% 0.07/0.41 % Vampire exiting
%------------------------------------------------------------------------------