%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM709^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 : Wed Sep 30 08:19:23 AM UTC 2026
% Result : Theorem 0.08s 0.17s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 2
% Syntax : Number of formulae : 8 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 8 ( 7 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 52 ( 4 ~; 0 |; 0 &; 48 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 4 ( 0 ^; 4 !; 0 ?; 4 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
nat: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
x: nat ).
thf(func_def_1,type,
y: nat ).
thf(func_def_2,type,
pl: nat > nat > nat ).
thf(func_def_3,type,
ts: nat > nat > nat ).
thf(func_def_4,type,
suc: nat > nat ).
thf(f1,axiom,
! [X0: nat,X1: nat] :
( ( ts @ ( suc @ X0 ) @ X1 )
= ( pl @ ( ts @ X0 @ X1 ) @ X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz28d) ).
thf(f2,conjecture,
( ( pl @ ( ts @ x @ y ) @ y )
= ( ts @ ( suc @ x ) @ y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz28h) ).
thf(f3,negated_conjecture,
( ( pl @ ( ts @ x @ y ) @ y )
!= ( ts @ ( suc @ x ) @ y ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f4,plain,
( ( pl @ ( ts @ x @ y ) @ y )
!= ( ts @ ( suc @ x ) @ y ) ),
inference(flattening,[],[f3]) ).
thf(f5,plain,
! [X0: nat,X1: nat] :
( ( ts @ ( suc @ X0 ) @ X1 )
= ( pl @ ( ts @ X0 @ X1 ) @ X1 ) ),
inference(cnf_transformation,[],[f1]) ).
thf(f6,plain,
( ( pl @ ( ts @ x @ y ) @ y )
!= ( ts @ ( suc @ x ) @ y ) ),
inference(cnf_transformation,[],[f4]) ).
thf(f7,plain,
( ( ts @ ( suc @ x ) @ y )
!= ( ts @ ( suc @ x ) @ y ) ),
inference(constrained_superposition,[],[f6,f5]) ).
thf(f8,plain,
$false,
inference(trivial_inequality_removal,[],[f7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM709^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 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 12:42:49 UTC 2026
% 0.00/0.11 % CPUTime :
% 0.00/0.11 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.13 Running first-order model finding
% 0.08/0.13 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.17 % (51174)Will run a generic schedule for satisfiability detection.
% 0.08/0.17 % (51180)% WARNING: option uhcvi not known.
% 0.08/0.17 % (51183)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1220245286:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.08/0.17 % (51182)dis+10_1_sil=32000:sp=arity:random_seed=1994935611:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.08/0.17 % (51179)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1971885753_2999 on theBenchmark for (2999ds/0Mi)
% 0.08/0.17 % (51181)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3797026954:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.08/0.17 % (51184)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4274861835:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.08/0.17 % (51180)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4143085975:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.08/0.17 % (51183)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.08/0.17 % (51185)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2772269458:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.08/0.17 % (51180)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.08/0.17 % Exception at run slice level
% 0.08/0.17 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.08/0.17 % (51180)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.08/0.17 % (51183) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-51174-51183"...
% 0.08/0.17 % (51182) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-51174-51182"...
% 0.08/0.17 % (51180) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-51174-51180"...
% 0.08/0.17 % (51184) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-51174-51184"...
% 0.08/0.17 % (51181) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-51174-51181"...
% 0.08/0.17 % (51185) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-51174-51185"...
% 0.08/0.17 % (51183)...printing done.
% 0.08/0.17 % (51180)...printing done.
% 0.08/0.17 % (51184)...printing done.
% 0.08/0.17 % (51182)...printing done.
% 0.08/0.17 % (51181)...printing done.
% 0.08/0.17 % (51185)...printing done.
% 0.08/0.17 % (51183)Refutation found. Thanks to Tanya!
% 0.08/0.17 % SZS status Theorem for theBenchmark
% 0.08/0.17 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.17 % (51183)------------------------------
% 0.08/0.17 % (51183)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.17 % (51183)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.17 % (51183)CaDiCaL version: 2.1.3
% 0.08/0.17 % (51183)Termination reason: Refutation
% 0.08/0.17 % (51183)Time elapsed: 0.001 s
% 0.08/0.17 % (51183)Peak memory usage: 11 MB
% 0.08/0.17 % (51183)Instructions burned: 1 (million)
% 0.08/0.17 % (51174)Success in time 0.034 s
% 0.08/0.17 % Vampire exiting
%------------------------------------------------------------------------------