%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWV050+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n001.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 01:20:04 PM UTC 2026
% Result : Theorem 0.21s 0.27s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 36 ( 23 unt; 3 def)
% Number of atoms : 64 ( 43 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 46 ( 18 ~; 13 |; 10 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 4 prp; 0-2 aty)
% Number of functors : 23 ( 23 usr; 15 con; 0-3 aty)
% Number of variables : 9 ( 0 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f26,axiom,
! [X0] : sum(n0,tptp_minus_1,X0) = n0,
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',sum_plus_base) ).
fof(f28,axiom,
succ(tptp_minus_1) = n0,
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',succ_tptp_minus_1) ).
fof(f29,axiom,
! [X0] : plus(X0,n1) = succ(X0),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',succ_plus_1_r) ).
fof(f39,axiom,
! [X0] : minus(X0,n1) = pred(X0),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',pred_minus_1) ).
fof(f40,axiom,
! [X0] : pred(succ(X0)) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',pred_succ) ).
fof(f53,conjecture,
( ( pv86 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(mu,pv87),a_select2(muold,pv87))),plus(abs(a_select2(mu,pv87)),abs(a_select2(muold,pv87)))))
& pv88 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89))))) )
=> ( n0 = sum(n0,minus(n0,n1),divide(abs(minus(a_select2(sigma,pv91),a_select2(sigmaold,pv91))),plus(abs(a_select2(sigma,pv91)),abs(a_select2(sigmaold,pv91)))))
& pv86 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(mu,pv87),a_select2(muold,pv87))),plus(abs(a_select2(mu,pv87)),abs(a_select2(muold,pv87)))))
& pv88 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89))))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cl5_nebula_norm_0022) ).
fof(f54,negated_conjecture,
~ ( ( pv86 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(mu,pv87),a_select2(muold,pv87))),plus(abs(a_select2(mu,pv87)),abs(a_select2(muold,pv87)))))
& pv88 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89))))) )
=> ( n0 = sum(n0,minus(n0,n1),divide(abs(minus(a_select2(sigma,pv91),a_select2(sigmaold,pv91))),plus(abs(a_select2(sigma,pv91)),abs(a_select2(sigmaold,pv91)))))
& pv86 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(mu,pv87),a_select2(muold,pv87))),plus(abs(a_select2(mu,pv87)),abs(a_select2(muold,pv87)))))
& pv88 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89))))) ) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f136,plain,
( ( n0 != sum(n0,minus(n0,n1),divide(abs(minus(a_select2(sigma,pv91),a_select2(sigmaold,pv91))),plus(abs(a_select2(sigma,pv91)),abs(a_select2(sigmaold,pv91)))))
| pv86 != sum(n0,minus(n5,n1),divide(abs(minus(a_select2(mu,pv87),a_select2(muold,pv87))),plus(abs(a_select2(mu,pv87)),abs(a_select2(muold,pv87)))))
| pv88 != sum(n0,minus(n5,n1),divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89))))) )
& pv86 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(mu,pv87),a_select2(muold,pv87))),plus(abs(a_select2(mu,pv87)),abs(a_select2(muold,pv87)))))
& pv88 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89))))) ),
inference(ennf_transformation,[],[f54]) ).
fof(f137,plain,
( ( n0 != sum(n0,minus(n0,n1),divide(abs(minus(a_select2(sigma,pv91),a_select2(sigmaold,pv91))),plus(abs(a_select2(sigma,pv91)),abs(a_select2(sigmaold,pv91)))))
| pv86 != sum(n0,minus(n5,n1),divide(abs(minus(a_select2(mu,pv87),a_select2(muold,pv87))),plus(abs(a_select2(mu,pv87)),abs(a_select2(muold,pv87)))))
| pv88 != sum(n0,minus(n5,n1),divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89))))) )
& pv86 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(mu,pv87),a_select2(muold,pv87))),plus(abs(a_select2(mu,pv87)),abs(a_select2(muold,pv87)))))
& pv88 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89))))) ),
inference(flattening,[],[f136]) ).
fof(f267,plain,
! [X0] : n0 = sum(n0,tptp_minus_1,X0),
inference(cnf_transformation,[],[f26]) ).
fof(f269,plain,
n0 = succ(tptp_minus_1),
inference(cnf_transformation,[],[f28]) ).
fof(f270,plain,
! [X0] : succ(X0) = plus(X0,n1),
inference(cnf_transformation,[],[f29]) ).
fof(f280,plain,
! [X0] : minus(X0,n1) = pred(X0),
inference(cnf_transformation,[],[f39]) ).
fof(f281,plain,
! [X0] : pred(succ(X0)) = X0,
inference(cnf_transformation,[],[f40]) ).
fof(f300,plain,
pv88 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89))))),
inference(cnf_transformation,[],[f137]) ).
fof(f301,plain,
pv86 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(mu,pv87),a_select2(muold,pv87))),plus(abs(a_select2(mu,pv87)),abs(a_select2(muold,pv87))))),
inference(cnf_transformation,[],[f137]) ).
fof(f302,plain,
( n0 != sum(n0,minus(n0,n1),divide(abs(minus(a_select2(sigma,pv91),a_select2(sigmaold,pv91))),plus(abs(a_select2(sigma,pv91)),abs(a_select2(sigmaold,pv91)))))
| pv86 != sum(n0,minus(n5,n1),divide(abs(minus(a_select2(mu,pv87),a_select2(muold,pv87))),plus(abs(a_select2(mu,pv87)),abs(a_select2(muold,pv87)))))
| pv88 != sum(n0,minus(n5,n1),divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89))))) ),
inference(cnf_transformation,[],[f137]) ).
fof(f341,plain,
n0 = plus(tptp_minus_1,n1),
inference(definition_unfolding,[],[f269,f270]) ).
fof(f351,plain,
! [X0] : minus(plus(X0,n1),n1) = X0,
inference(definition_unfolding,[],[f281,f280,f270]) ).
fof(f365,definition,
( spl31_1
<=> pv88 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89))))) ),
introduced(definition,[new_symbols(definition,[spl31_1])],[avatar_definition]) ).
fof(f369,definition,
( spl31_2
<=> pv86 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(mu,pv87),a_select2(muold,pv87))),plus(abs(a_select2(mu,pv87)),abs(a_select2(muold,pv87))))) ),
introduced(definition,[new_symbols(definition,[spl31_2])],[avatar_definition]) ).
fof(f373,definition,
( spl31_3
<=> n0 = sum(n0,minus(n0,n1),divide(abs(minus(a_select2(sigma,pv91),a_select2(sigmaold,pv91))),plus(abs(a_select2(sigma,pv91)),abs(a_select2(sigmaold,pv91))))) ),
introduced(definition,[new_symbols(definition,[spl31_3])],[avatar_definition]) ).
fof(f375,plain,
( n0 != sum(n0,minus(n0,n1),divide(abs(minus(a_select2(sigma,pv91),a_select2(sigmaold,pv91))),plus(abs(a_select2(sigma,pv91)),abs(a_select2(sigmaold,pv91)))))
| spl31_3 ),
inference(avatar_component_clause,[],[f373]) ).
fof(f376,plain,
( ~ spl31_1
| ~ spl31_2
| ~ spl31_3 ),
inference(avatar_split_clause,[],[f302,f373,f369,f365]) ).
fof(f377,plain,
spl31_1,
inference(avatar_split_clause,[],[f300,f365]) ).
fof(f378,plain,
spl31_2,
inference(avatar_split_clause,[],[f301,f369]) ).
fof(f405,plain,
tptp_minus_1 = minus(n0,n1),
inference(superposition,[],[f351,f341]) ).
fof(f422,plain,
( n0 != sum(n0,tptp_minus_1,divide(abs(minus(a_select2(sigma,pv91),a_select2(sigmaold,pv91))),plus(abs(a_select2(sigma,pv91)),abs(a_select2(sigmaold,pv91)))))
| spl31_3 ),
inference(superposition,[],[f375,f405]) ).
fof(f425,plain,
( $false
| spl31_3 ),
inference(forward_subsumption_resolution,[],[f422,f267]) ).
fof(f426,plain,
spl31_3,
inference(avatar_contradiction_clause,[],[f425]) ).
cnf(s1,plain,
( ~ spl31_1
| ~ spl31_2
| ~ spl31_3 ),
inference(sat_conversion,[],[f376]) ).
cnf(s2,plain,
spl31_1,
inference(sat_conversion,[],[f377]) ).
cnf(s3,plain,
spl31_2,
inference(sat_conversion,[],[f378]) ).
cnf(s4,plain,
spl31_3,
inference(sat_conversion,[],[f426]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s1,s4,s3,s2]) ).
fof(f427,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV050+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n001.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 09:53:02 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 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
% 0.21/0.27 % (255794)Will run a generic schedule for satisfiability detection.
% 0.21/0.27 % (255802)dis+10_1_sil=32000:sp=arity:random_seed=2430751051:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.21/0.27 % (255800)% WARNING: option uhcvi not known.
% 0.21/0.27 % (255802) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-255794-255802"...
% 0.21/0.27 % (255802)...printing done.
% 0.21/0.27 % (255802)Refutation found. Thanks to Tanya!
% 0.21/0.27 % SZS status Theorem for theBenchmark
% 0.21/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.27 % (255802)------------------------------
% 0.21/0.27 % (255802)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.27 % (255802)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.27 % (255802)CaDiCaL version: 2.1.3
% 0.21/0.27 % (255802)Termination reason: Refutation
% 0.21/0.27 % (255802)Time elapsed: 0.005 s
% 0.21/0.27 % (255802)Peak memory usage: 12 MB
% 0.21/0.27 % (255802)Instructions burned: 16 (million)
% 0.21/0.27 % (255794)Success in time 0.035 s
% 0.21/0.27 % Vampire exiting
%------------------------------------------------------------------------------