%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM696_8 : TPTP v9.3.1. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 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 : Tue Sep 29 12:25:25 PM UTC 2026
% Result : Theorem 0.16s 0.47s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 32 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 49 ( 48 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 53 ( 36 ~; 9 |; 1 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 54 ( 50 !; 4 ?; 54 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
nat: $tType ).
tff(func_def_0,type,
x: nat ).
tff(func_def_1,type,
y: nat ).
tff(func_def_2,type,
pl: ( nat * nat ) > nat ).
tff(func_def_3,type,
n_1: nat ).
tff(func_def_6,type,
sK0: nat ).
tff(func_def_7,type,
sK1: nat > nat ).
tff(func_def_8,type,
sK2: ( nat * nat * nat ) > nat ).
tff(f1,axiom,
~ ! [X0: nat] : ( y != pl(x,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m) ).
tff(f3,axiom,
! [X0: nat] :
( ~ ~ ! [X1: nat] : ( X0 != pl(n_1,X1) )
=> ( X0 = n_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz24) ).
tff(f4,axiom,
! [X0: nat,X1: nat,X2: nat] :
( ~ ! [X3: nat] : ( X0 != pl(X1,X3) )
=> ~ ! [X3: nat] : ( pl(X0,X2) != pl(pl(X1,X2),X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz19a) ).
tff(f5,axiom,
! [X0: nat,X1: nat] : ( pl(X0,X1) = pl(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz6) ).
tff(f6,conjecture,
( ~ ~ ! [X0: nat] : ( y != pl(pl(x,n_1),X0) )
=> ( y = pl(x,n_1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz25) ).
tff(f7,negated_conjecture,
~ ( ~ ~ ! [X0: nat] : ( y != pl(pl(x,n_1),X0) )
=> ( y = pl(x,n_1) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
tff(f11,plain,
! [X0: nat] :
( ! [X1: nat] : ( X0 != pl(n_1,X1) )
=> ( X0 = n_1 ) ),
inference(flattening,[],[f3]) ).
tff(f12,plain,
! [X0: nat,X1: nat,X2: nat] :
( ~ ! [X3: nat] : ( X0 != pl(X1,X3) )
=> ~ ! [X4: nat] : ( pl(X0,X2) != pl(pl(X1,X2),X4) ) ),
inference(rectify,[],[f4]) ).
tff(f13,plain,
~ ( ! [X0: nat] : ( y != pl(pl(x,n_1),X0) )
=> ( y = pl(x,n_1) ) ),
inference(flattening,[],[f7]) ).
tff(f14,plain,
? [X0: nat] : ( y = pl(x,X0) ),
inference(ennf_transformation,[],[f1]) ).
tff(f16,plain,
! [X0: nat] :
( ( X0 = n_1 )
| ? [X1: nat] : ( pl(n_1,X1) = X0 ) ),
inference(ennf_transformation,[],[f11]) ).
tff(f17,plain,
! [X0: nat,X1: nat,X2: nat] :
( ? [X4: nat] : ( pl(X0,X2) = pl(pl(X1,X2),X4) )
| ! [X3: nat] : ( X0 != pl(X1,X3) ) ),
inference(ennf_transformation,[],[f12]) ).
tff(f18,plain,
( ( y != pl(x,n_1) )
& ! [X0: nat] : ( y != pl(pl(x,n_1),X0) ) ),
inference(ennf_transformation,[],[f13]) ).
tff(f19,plain,
y = pl(x,sK0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f14]) ).
tff(f20,plain,
! [X0: nat] :
( ( X0 = n_1 )
| ( pl(n_1,sK1(X0)) = X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X1,sK1(X0))],[f16]) ).
tff(f21,plain,
! [X0: nat,X1: nat,X2: nat] :
( ? [X3: nat] : ( pl(X0,X2) = pl(pl(X1,X2),X3) )
| ! [X4: nat] : ( pl(X1,X4) != X0 ) ),
inference(rectify,[],[f17]) ).
tff(f22,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( pl(X0,X2) = pl(pl(X1,X2),sK2(X0,X1,X2)) )
| ! [X4: nat] : ( pl(X1,X4) != X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X3,sK2(X0,X1,X2))],[f21]) ).
tff(f23,plain,
y = pl(x,sK0),
inference(cnf_transformation,[],[f19]) ).
tff(f25,plain,
! [X0: nat] :
( ( pl(n_1,sK1(X0)) = X0 )
| ( n_1 = X0 ) ),
inference(cnf_transformation,[],[f20]) ).
tff(f26,plain,
! [X2: nat,X0: nat,X1: nat,X4: nat] :
( ( pl(X0,X2) = pl(pl(X1,X2),sK2(X0,X1,X2)) )
| ( pl(X1,X4) != X0 ) ),
inference(cnf_transformation,[],[f22]) ).
tff(f27,plain,
! [X0: nat,X1: nat] : ( pl(X0,X1) = pl(X1,X0) ),
inference(cnf_transformation,[],[f5]) ).
tff(f28,plain,
! [X0: nat] : ( y != pl(pl(x,n_1),X0) ),
inference(cnf_transformation,[],[f18]) ).
tff(f29,plain,
y != pl(x,n_1),
inference(cnf_transformation,[],[f18]) ).
tff(f33,plain,
! [X2: nat,X1: nat,X4: nat] : ( pl(pl(X1,X4),X2) = pl(pl(X1,X2),sK2(pl(X1,X4),X1,X2)) ),
inference(equality_resolution,[],[f26]) ).
tff(f57,plain,
! [X0: nat] : ( y != pl(pl(n_1,x),X0) ),
inference(superposition,[],[f28,f27]) ).
tff(f940,plain,
! [X0: nat] : ( y != pl(pl(n_1,X0),x) ),
inference(superposition,[],[f57,f33]) ).
tff(f941,plain,
! [X0: nat] : ( y != pl(x,pl(n_1,X0)) ),
inference(forward_demodulation,[],[f940,f27]) ).
tff(f948,plain,
! [X0: nat] :
( ( y != pl(x,X0) )
| ( n_1 = X0 ) ),
inference(superposition,[],[f941,f25]) ).
tff(f963,plain,
( ( y != y )
| ( n_1 = sK0 ) ),
inference(superposition,[],[f948,f23]) ).
tff(f966,plain,
n_1 = sK0,
inference(trivial_inequality_removal,[],[f963]) ).
tff(f972,plain,
y = pl(x,n_1),
inference(superposition,[],[f23,f966]) ).
tff(f973,plain,
$false,
inference(forward_subsumption_resolution,[],[f972,f29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM696_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n017.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 21:03:20 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.41 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
% 0.16/0.47 % (2932884)Will run a generic schedule for satisfiability detection.
% 0.16/0.47 % (2932891)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3805352915:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.47 % (2932890)% WARNING: option uhcvi not known.
% 0.16/0.47 % (2932889)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3921223859_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.47 % (2932890)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1998529478:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.47 % (2932892)dis+10_1_sil=32000:sp=arity:random_seed=1979552593:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.47 % (2932893)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1470228896:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.47 % (2932894)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1272091378:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.47 % (2932895)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3877471569:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.47 % Detected minimum model sizes of [1,1]
% 0.16/0.47 % Detected maximum model sizes of [max,2]
% 0.16/0.47 % TRYING [1,1]
% 0.16/0.47 % TRYING [1,2]
% 0.16/0.47 % TRYING [2,2]
% 0.16/0.47 % TRYING [3,2]
% 0.16/0.47 % TRYING [4,2]
% 0.16/0.47 % (2932891) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2932884-2932891"...
% 0.16/0.47 % (2932891)...printing done.
% 0.16/0.47 % (2932891)Refutation found. Thanks to Tanya!
% 0.16/0.47 % SZS status Theorem for theBenchmark
% 0.16/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.47 % (2932891)------------------------------
% 0.16/0.47 % (2932891)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.47 % (2932891)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.47 % (2932891)CaDiCaL version: 2.1.3
% 0.16/0.47 % (2932891)Termination reason: Refutation
% 0.16/0.47 % (2932891)Time elapsed: 0.021 s
% 0.16/0.47 % (2932891)Peak memory usage: 12 MB
% 0.16/0.47 % (2932891)Instructions burned: 82 (million)
% 0.16/0.47 % (2932884)Success in time 0.048 s
% 0.16/0.47 % Vampire exiting
%------------------------------------------------------------------------------