%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO038-1.003.003 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 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 02:24:47 PM UTC 2026
% Result : Unsatisfiable 4.04s 1.44s
% Output : Refutation 4.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of formulae : 61 ( 22 unt; 6 def)
% Number of atoms : 102 ( 9 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 81 ( 40 ~; 35 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 7 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 14 ( 0 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : f(X0,one) = s(one),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
fof(f2,axiom,
! [X0] : f(one,s(X0)) = s(s(f(one,X0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
fof(f3,axiom,
! [X0,X1] : f(s(X0),s(X1)) = f(X0,f(s(X0),X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
fof(f4,axiom,
d(one),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).
fof(f5,axiom,
! [X0] :
( d(s(X0))
| ~ d(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax5) ).
fof(f6,negated_conjecture,
~ d(f(s(s(one)),s(s(one)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
fof(f7,plain,
f(one,s(one)) = s(s(s(one))),
inference(superposition,[],[f2,f1]) ).
fof(f8,plain,
! [X0] :
( ~ d(s(f(one,X0)))
| d(f(one,s(X0))) ),
inference(superposition,[],[f5,f2]) ).
fof(f10,plain,
! [X0] : f(s(X0),s(one)) = f(X0,s(one)),
inference(superposition,[],[f3,f1]) ).
fof(f14,plain,
( d(f(one,s(one)))
| ~ d(s(s(one))) ),
inference(superposition,[],[f5,f7]) ).
fof(f16,definition,
( spl0_1
<=> d(s(s(one))) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f18,plain,
( ~ d(s(s(one)))
| spl0_1 ),
inference(avatar_component_clause,[],[f16]) ).
fof(f20,definition,
( spl0_2
<=> d(f(one,s(one))) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f22,plain,
( d(f(one,s(one)))
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f20]) ).
fof(f23,plain,
( ~ spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f14,f20,f16]) ).
fof(f24,plain,
! [X0] :
( d(f(one,s(X0)))
| ~ d(f(one,X0)) ),
inference(resolution,[],[f8,f5]) ).
fof(f27,plain,
( ~ d(s(one))
| spl0_1 ),
inference(resolution,[],[f18,f5]) ).
fof(f30,plain,
! [X0] : f(s(X0),s(s(one))) = f(X0,f(X0,s(one))),
inference(superposition,[],[f3,f10]) ).
fof(f36,plain,
( ~ d(one)
| spl0_1 ),
inference(resolution,[],[f27,f5]) ).
fof(f37,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f36,f4]) ).
fof(f38,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f37]) ).
fof(f75,plain,
! [X0] :
( ~ d(f(one,s(f(one,X0))))
| d(f(one,f(one,s(X0)))) ),
inference(superposition,[],[f24,f2]) ).
fof(f77,plain,
( d(f(one,f(one,s(one))))
| ~ d(f(one,s(s(one)))) ),
inference(superposition,[],[f24,f7]) ).
fof(f79,definition,
( spl0_3
<=> d(f(one,s(s(one)))) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f81,plain,
( ~ d(f(one,s(s(one))))
| spl0_3 ),
inference(avatar_component_clause,[],[f79]) ).
fof(f83,definition,
( spl0_4
<=> d(f(one,f(one,s(one)))) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f85,plain,
( d(f(one,f(one,s(one))))
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f83]) ).
fof(f86,plain,
( ~ spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f77,f83,f79]) ).
fof(f87,plain,
! [X0] : f(s(s(X0)),s(s(one))) = f(s(X0),f(X0,s(one))),
inference(superposition,[],[f30,f10]) ).
fof(f89,plain,
! [X0] : f(s(X0),s(s(s(one)))) = f(X0,f(X0,f(X0,s(one)))),
inference(superposition,[],[f3,f30]) ).
fof(f96,plain,
! [X0] : f(X0,f(X0,f(X0,s(one)))) = f(s(X0),f(one,s(one))),
inference(forward_demodulation,[],[f89,f7]) ).
fof(f99,plain,
( ~ d(f(one,s(one)))
| spl0_3 ),
inference(resolution,[],[f81,f24]) ).
fof(f100,plain,
( $false
| ~ spl0_2
| spl0_3 ),
inference(forward_subsumption_resolution,[],[f99,f22]) ).
fof(f101,plain,
( ~ spl0_2
| spl0_3 ),
inference(avatar_contradiction_clause,[],[f100]) ).
fof(f329,plain,
! [X0] :
( d(f(one,f(one,s(X0))))
| ~ d(f(one,f(one,X0))) ),
inference(resolution,[],[f75,f24]) ).
fof(f485,plain,
( d(f(one,f(one,f(one,s(one)))))
| ~ d(f(one,f(one,s(s(one))))) ),
inference(superposition,[],[f329,f7]) ).
fof(f488,plain,
( d(f(s(one),f(one,s(one))))
| ~ d(f(one,f(one,s(s(one))))) ),
inference(forward_demodulation,[],[f485,f96]) ).
fof(f531,definition,
( spl0_12
<=> d(f(one,f(one,s(s(one))))) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f533,plain,
( ~ d(f(one,f(one,s(s(one)))))
| spl0_12 ),
inference(avatar_component_clause,[],[f531]) ).
fof(f535,definition,
( spl0_13
<=> d(f(s(one),f(one,s(one)))) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f537,plain,
( d(f(s(one),f(one,s(one))))
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f535]) ).
fof(f538,plain,
( ~ spl0_12
| spl0_13 ),
inference(avatar_split_clause,[],[f488,f535,f531]) ).
fof(f592,plain,
( ~ d(f(one,f(one,s(one))))
| spl0_12 ),
inference(resolution,[],[f533,f329]) ).
fof(f593,plain,
( $false
| ~ spl0_4
| spl0_12 ),
inference(forward_subsumption_resolution,[],[f592,f85]) ).
fof(f594,plain,
( ~ spl0_4
| spl0_12 ),
inference(avatar_contradiction_clause,[],[f593]) ).
fof(f870,plain,
~ d(f(s(one),f(one,s(one)))),
inference(superposition,[],[f6,f87]) ).
fof(f889,plain,
( $false
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f870,f537]) ).
fof(f890,plain,
~ spl0_13,
inference(avatar_contradiction_clause,[],[f889]) ).
cnf(s1,plain,
( ~ spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f23]) ).
cnf(s2,plain,
spl0_1,
inference(sat_conversion,[],[f38]) ).
cnf(s3,plain,
( ~ spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f86]) ).
cnf(s4,plain,
( ~ spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f101]) ).
cnf(s10,plain,
( ~ spl0_12
| spl0_13 ),
inference(sat_conversion,[],[f538]) ).
cnf(s11,plain,
( ~ spl0_4
| spl0_12 ),
inference(sat_conversion,[],[f594]) ).
cnf(s12,plain,
~ spl0_13,
inference(sat_conversion,[],[f890]) ).
cnf(s13,plain,
~ spl0_12,
inference(rat,[],[s10,s12]) ).
cnf(s14,plain,
~ spl0_4,
inference(rat,[],[s11,s13]) ).
cnf(s15,plain,
~ spl0_3,
inference(rat,[],[s3,s14]) ).
cnf(s16,plain,
~ spl0_2,
inference(rat,[],[s4,s15]) ).
cnf(s17,plain,
$false,
inference(rat,[],[s1,s16,s2]) ).
fof(f904,plain,
$false,
inference(avatar_sat_refutation,[],[s17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO038-1.003.003 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.19 % Computer : n017.cluster.edu
% 0.06/0.19 % Model : x86_64 x86_64
% 0.06/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.19 % Memory : 8046.5625MB
% 0.06/0.19 % OS : Linux 6.8.0-71-generic
% 0.06/0.19 % CPULimit : 300
% 0.06/0.19 % WCLimit : 300
% 0.06/0.19 % DateTime : Mon Sep 28 17:17:21 UTC 2026
% 0.06/0.19 % CPUTime :
% 0.06/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.23 Running first-order theorem proving
% 0.06/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.04/1.44 % (3730925)Input is clausal, will run a generic CNF schedule.
% 4.04/1.44 % (3731006)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=127780333:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 4.04/1.44 % (3731007)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2642214404:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 4.04/1.44 % (3731005)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=1761801642:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 4.04/1.44 % (3731008)lrs+10_1_sil=8000:sp=occurrence:random_seed=2713922339:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 4.04/1.44 % (3731010)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4244052522:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 4.04/1.44 % (3731011)dis-21_1_sil=8000:lcm=predicate:random_seed=2272839774:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 4.04/1.44 % (3731011)Refutation not found, incomplete strategy
% 4.04/1.44 % (3731011)------------------------------
% 4.04/1.44 % (3731011)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.04/1.44 % (3731011)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.04/1.44 % (3731011)CaDiCaL version: 2.1.3
% 4.04/1.44 % (3731011)Termination reason: Refutation not found, incomplete strategy
% 4.04/1.44 % (3731011)Time elapsed: 0.001 s
% 4.04/1.44 % (3731011)Peak memory usage: 88 MB
% 4.04/1.44 % (3731008)First to succeed.
% 4.04/1.44 % (3731008)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3730925"
% 4.04/1.44 % (3731010)Also succeeded, but the first one will report.
% 4.04/1.44 % (3731009)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=4003310887:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 4.04/1.44 % (3731009)Also succeeded, but the first one will report.
% 4.04/1.44 % (3731008)Refutation found. Thanks to Tanya!
% 4.04/1.44 % SZS status Unsatisfiable for theBenchmark
% 4.04/1.44 % SZS output start Proof for theBenchmark
% See solution above
% 4.04/1.44 % (3731008)------------------------------
% 4.04/1.44 % (3731008)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.04/1.44 % (3731008)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.04/1.44 % (3731008)CaDiCaL version: 2.1.3
% 4.04/1.44 % (3731008)Termination reason: Refutation
% 4.04/1.44 % (3731008)Time elapsed: 0.033 s
% 4.04/1.44 % (3731008)Peak memory usage: 90 MB
% 4.04/1.44 % (3731008)Instructions burned: 52 (million)
% 4.04/1.44 % (3731008)------------------------------
% 4.04/1.44 % (3731008)------------------------------
% 4.04/1.44 % (3730925)Success in time 0.472 s
% 4.04/1.44 % Vampire exiting
%------------------------------------------------------------------------------