%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM696_8 : TPTP v9.3.1. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 12:16:33 PM UTC 2026
% Result : Theorem 0.17s 1.30s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 39 ( 23 unt; 0 typ; 2 def)
% Number of atoms : 55 ( 41 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 53 ( 37 ~; 8 |; 1 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 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 * nat ) > nat ).
tff(func_def_8,type,
sK2: nat > nat ).
tff(pred_def_1,type,
sP3: nat > $o ).
tff(pred_def_2,type,
sP4: nat > $o ).
tff(f1,axiom,
~ ! [X0: nat] : ( y != pl(x,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m) ).
tff(f3,axiom,
! [X0: nat] :
( ~ ~ ! [X1: nat] : ( X0 != pl(n_1,X1) )
=> ( X0 = n_1 ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',satz19a) ).
tff(f5,axiom,
! [X0: nat,X1: nat] : ( pl(X0,X1) = pl(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz6) ).
tff(f6,conjecture,
( ~ ~ ! [X0: nat] : ( y != pl(pl(x,n_1),X0) )
=> ( y = pl(x,n_1) ) ),
file('/export/starexec/sandbox/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(f10,plain,
~ ( ! [X0: nat] : ( y != pl(pl(x,n_1),X0) )
=> ( y = pl(x,n_1) ) ),
inference(flattening,[],[f7]) ).
tff(f11,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(f12,plain,
! [X0: nat] :
( ! [X1: nat] : ( X0 != pl(n_1,X1) )
=> ( X0 = n_1 ) ),
inference(flattening,[],[f3]) ).
tff(f13,plain,
( ( y != pl(x,n_1) )
& ! [X0: nat] : ( y != pl(pl(x,n_1),X0) ) ),
inference(ennf_transformation,[],[f10]) ).
tff(f14,plain,
? [X0: nat] : ( y = pl(x,X0) ),
inference(ennf_transformation,[],[f1]) ).
tff(f15,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,[],[f11]) ).
tff(f16,plain,
! [X0: nat] :
( ( X0 = n_1 )
| ? [X1: nat] : ( pl(n_1,X1) = X0 ) ),
inference(ennf_transformation,[],[f12]) ).
tff(f17,plain,
y = pl(x,sK0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f14]) ).
tff(f18,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,[],[f15]) ).
tff(f19,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( pl(X0,X2) = pl(pl(X1,X2),sK1(X0,X1,X2)) )
| ! [X4: nat] : ( pl(X1,X4) != X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1,X2))],[f18]) ).
tff(f20,plain,
! [X0: nat] :
( ( X0 = n_1 )
| ( pl(n_1,sK2(X0)) = X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X1,sK2(X0))],[f16]) ).
tff(f21,plain,
! [X0: nat] : ( y != pl(pl(x,n_1),X0) ),
inference(cnf_transformation,[],[f13]) ).
tff(f22,plain,
y != pl(x,n_1),
inference(cnf_transformation,[],[f13]) ).
tff(f23,plain,
y = pl(x,sK0),
inference(cnf_transformation,[],[f17]) ).
tff(f24,plain,
! [X0: nat,X1: nat] : ( pl(X0,X1) = pl(X1,X0) ),
inference(cnf_transformation,[],[f5]) ).
tff(f25,plain,
! [X2: nat,X0: nat,X1: nat,X4: nat] :
( ( pl(X0,X2) = pl(pl(X1,X2),sK1(X0,X1,X2)) )
| ( pl(X1,X4) != X0 ) ),
inference(cnf_transformation,[],[f19]) ).
tff(f26,plain,
! [X0: nat] :
( ( pl(n_1,sK2(X0)) = X0 )
| ( n_1 = X0 ) ),
inference(cnf_transformation,[],[f20]) ).
tff(f27,definition,
~ sP3(y),
introduced(definition,[new_symbols(definition,[sP3])],[inequality_splitting_name_introduction]) ).
tff(f28,plain,
sP3(pl(x,n_1)),
inference(inequality_splitting,[],[f22,f27]) ).
tff(f29,definition,
~ sP4(y),
introduced(definition,[new_symbols(definition,[sP4])],[inequality_splitting_name_introduction]) ).
tff(f30,plain,
! [X0: nat] : sP4(pl(pl(x,n_1),X0)),
inference(inequality_splitting,[],[f21,f29]) ).
tff(f31,plain,
! [X2: nat,X1: nat,X4: nat] : ( pl(pl(X1,X4),X2) = pl(pl(X1,X2),sK1(pl(X1,X4),X1,X2)) ),
inference(equality_resolution,[],[f25]) ).
tff(f32,plain,
~ sP3(pl(x,sK0)),
inference(forward_demodulation,[],[f27,f23]) ).
tff(f33,plain,
~ sP4(pl(x,sK0)),
inference(forward_demodulation,[],[f29,f23]) ).
tff(f34,plain,
! [X0: nat] : sP4(pl(pl(n_1,x),X0)),
inference(forward_demodulation,[],[f30,f24]) ).
tff(f35,plain,
sP3(pl(n_1,x)),
inference(forward_demodulation,[],[f28,f24]) ).
tff(f36,plain,
~ sP3(pl(sK0,x)),
inference(forward_demodulation,[],[f32,f24]) ).
tff(f37,plain,
~ sP4(pl(sK0,x)),
inference(forward_demodulation,[],[f33,f24]) ).
tff(f39,plain,
! [X0: nat] : sP4(pl(pl(n_1,X0),x)),
inference(superposition,[],[f34,f31]) ).
tff(f42,plain,
! [X0: nat] :
( sP4(pl(X0,x))
| ( n_1 = X0 ) ),
inference(superposition,[],[f39,f26]) ).
tff(f67,plain,
n_1 = sK0,
inference(resolution,[],[f42,f37]) ).
tff(f73,plain,
sP3(pl(sK0,x)),
inference(superposition,[],[f35,f67]) ).
tff(f79,plain,
$false,
inference(forward_subsumption_resolution,[],[f73,f36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM696_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.36 % Computer : n026.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Sun Sep 27 21:10:41 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 Running first-order theorem proving
% 0.12/0.40 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/1.30 % (3204095)Detected formulas, will run a generic FOF schedule.
% 0.17/1.30 % (3204103)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=92367765:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.17/1.30 % (3204103)First to succeed.
% 0.17/1.30 % (3204103)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3204095"
% 0.17/1.30 % (3204104)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1465547189:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.17/1.30 % (3204105)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2691228742:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.17/1.30 % (3204101)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=61680449:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.17/1.30 % (3204102)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=3751116680:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.17/1.30 % (3204100)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3013654327:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.17/1.30 % (3204104)Also succeeded, but the first one will report.
% 0.17/1.30 % (3204106)dis-21_1_sil=8000:lcm=predicate:random_seed=2193282906:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 0.17/1.30 % (3204106)Refutation not found, incomplete strategy
% 0.17/1.30 % (3204106)------------------------------
% 0.17/1.30 % (3204106)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.30 % (3204106)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.30 % (3204106)CaDiCaL version: 2.1.3
% 0.17/1.30 % (3204106)Termination reason: Refutation not found, incomplete strategy
% 0.17/1.30 % (3204106)Time elapsed: 0.001 s
% 0.17/1.30 % (3204106)Peak memory usage: 88 MB
% 0.17/1.30 % (3204105)Also succeeded, but the first one will report.
% 0.17/1.30 % (3204103)Refutation found. Thanks to Tanya!
% 0.17/1.30 % SZS status Theorem for theBenchmark
% 0.17/1.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/1.30 % (3204103)------------------------------
% 0.17/1.30 % (3204103)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.30 % (3204103)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.30 % (3204103)CaDiCaL version: 2.1.3
% 0.17/1.30 % (3204103)Termination reason: Refutation
% 0.17/1.30 % (3204103)Time elapsed: 0.002 s
% 0.17/1.30 % (3204103)Peak memory usage: 89 MB
% 0.17/1.30 % (3204103)Instructions burned: 3 (million)
% 0.17/1.30 % (3204103)------------------------------
% 0.17/1.30 % (3204103)------------------------------
% 0.17/1.30 % (3204095)Success in time 0.268 s
% 0.17/1.30 % Vampire exiting
%------------------------------------------------------------------------------