%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWV488+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n020.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 01:24:25 PM UTC 2026
% Result : Theorem 0.20s 0.27s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 39 ( 16 unt; 2 def)
% Number of atoms : 155 ( 41 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 188 ( 72 ~; 62 |; 36 &)
% ( 2 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 45 ( 0 sgn 41 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f11,axiom,
real_zero != real_one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',real_constants) ).
fof(f12,axiom,
! [X0,X1] :
( ( int_leq(int_one,X0)
& int_leq(X0,n)
& int_leq(int_one,X1)
& int_leq(X1,n) )
=> ( ! [X2] :
( ( int_less(int_zero,X2)
& X0 = plus(X1,X2) )
=> ! [X3] :
( ( int_leq(int_one,X3)
& int_leq(X3,X1) )
=> a(plus(X3,X2),X3) = lu(plus(X3,X2),X3) ) )
& ! [X3] :
( ( int_leq(int_one,X3)
& int_leq(X3,X1) )
=> a(X3,X3) = real_one )
& ! [X2] :
( ( int_less(int_zero,X2)
& X1 = plus(X0,X2) )
=> ! [X3] :
( ( int_leq(int_one,X3)
& int_leq(X3,X0) )
=> a(X3,plus(X3,X2)) = real_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qil) ).
fof(f13,conjecture,
! [X0,X1] :
( ( int_leq(int_one,X0)
& int_leq(X0,X1)
& int_leq(X1,n) )
=> ( X0 = X1
=> a(X0,X1) != real_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lti) ).
fof(f14,negated_conjecture,
~ ! [X0,X1] :
( ( int_leq(int_one,X0)
& int_leq(X0,X1)
& int_leq(X1,n) )
=> ( X0 = X1
=> a(X0,X1) != real_zero ) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f15,plain,
! [X0,X1] :
( ( int_leq(int_one,X0)
& int_leq(X0,n)
& int_leq(int_one,X1)
& int_leq(X1,n) )
=> ( ! [X2] :
( ( int_less(int_zero,X2)
& X0 = plus(X1,X2) )
=> ! [X3] :
( ( int_leq(int_one,X3)
& int_leq(X3,X1) )
=> a(plus(X3,X2),X3) = lu(plus(X3,X2),X3) ) )
& ! [X4] :
( ( int_leq(int_one,X4)
& int_leq(X4,X1) )
=> real_one = a(X4,X4) )
& ! [X5] :
( ( int_less(int_zero,X5)
& plus(X0,X5) = X1 )
=> ! [X6] :
( ( int_leq(int_one,X6)
& int_leq(X6,X0) )
=> real_zero = a(X6,plus(X6,X5)) ) ) ) ),
inference(rectify,[],[f12]) ).
fof(f21,plain,
! [X0,X1] :
( ( ! [X2] :
( ! [X3] :
( a(plus(X3,X2),X3) = lu(plus(X3,X2),X3)
| ~ int_leq(int_one,X3)
| ~ int_leq(X3,X1) )
| ~ int_less(int_zero,X2)
| plus(X1,X2) != X0 )
& ! [X4] :
( real_one = a(X4,X4)
| ~ int_leq(int_one,X4)
| ~ int_leq(X4,X1) )
& ! [X5] :
( ! [X6] :
( real_zero = a(X6,plus(X6,X5))
| ~ int_leq(int_one,X6)
| ~ int_leq(X6,X0) )
| ~ int_less(int_zero,X5)
| plus(X0,X5) != X1 ) )
| ~ int_leq(int_one,X0)
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,n) ),
inference(ennf_transformation,[],[f15]) ).
fof(f22,plain,
! [X0,X1] :
( ( ! [X2] :
( ! [X3] :
( a(plus(X3,X2),X3) = lu(plus(X3,X2),X3)
| ~ int_leq(int_one,X3)
| ~ int_leq(X3,X1) )
| ~ int_less(int_zero,X2)
| plus(X1,X2) != X0 )
& ! [X4] :
( real_one = a(X4,X4)
| ~ int_leq(int_one,X4)
| ~ int_leq(X4,X1) )
& ! [X5] :
( ! [X6] :
( real_zero = a(X6,plus(X6,X5))
| ~ int_leq(int_one,X6)
| ~ int_leq(X6,X0) )
| ~ int_less(int_zero,X5)
| plus(X0,X5) != X1 ) )
| ~ int_leq(int_one,X0)
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,n) ),
inference(flattening,[],[f21]) ).
fof(f23,plain,
? [X0,X1] :
( real_zero = a(X0,X1)
& X0 = X1
& int_leq(int_one,X0)
& int_leq(X0,X1)
& int_leq(X1,n) ),
inference(ennf_transformation,[],[f14]) ).
fof(f24,plain,
? [X0,X1] :
( real_zero = a(X0,X1)
& X0 = X1
& int_leq(int_one,X0)
& int_leq(X0,X1)
& int_leq(X1,n) ),
inference(flattening,[],[f23]) ).
fof(f40,plain,
real_zero != real_one,
inference(cnf_transformation,[],[f11]) ).
fof(f43,plain,
! [X0,X1,X4] :
( ~ int_leq(X1,n)
| ~ int_leq(int_one,X1)
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X0)
| ~ int_leq(X4,X1)
| ~ int_leq(int_one,X4)
| real_one = a(X4,X4) ),
inference(cnf_transformation,[],[f22]) ).
fof(f44,plain,
int_leq(sK2,n),
inference(cnf_transformation,[],[f24]) ).
fof(f45,plain,
int_leq(sK1,sK2),
inference(cnf_transformation,[],[f24]) ).
fof(f46,plain,
int_leq(int_one,sK1),
inference(cnf_transformation,[],[f24]) ).
fof(f47,plain,
sK1 = sK2,
inference(cnf_transformation,[],[f24]) ).
fof(f48,plain,
real_zero = a(sK1,sK2),
inference(cnf_transformation,[],[f24]) ).
fof(f49,plain,
real_zero = a(sK2,sK2),
inference(definition_unfolding,[],[f48,f47]) ).
fof(f50,plain,
int_leq(int_one,sK2),
inference(definition_unfolding,[],[f46,f47]) ).
fof(f51,plain,
int_leq(sK2,sK2),
inference(definition_unfolding,[],[f45,f47]) ).
fof(f58,definition,
( spl3_1
<=> ! [X0] :
( ~ int_leq(X0,n)
| ~ int_leq(int_one,X0) ) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f59,plain,
( ! [X0] :
( ~ int_leq(X0,n)
| ~ int_leq(int_one,X0) )
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f58]) ).
fof(f61,definition,
( spl3_2
<=> ! [X4,X1] :
( ~ int_leq(X1,n)
| real_one = a(X4,X4)
| ~ int_leq(int_one,X4)
| ~ int_leq(X4,X1)
| ~ int_leq(int_one,X1) ) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f62,plain,
( ! [X1,X4] :
( ~ int_leq(X1,n)
| ~ int_leq(int_one,X4)
| ~ int_leq(X4,X1)
| ~ int_leq(int_one,X1)
| real_one = a(X4,X4) )
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f61]) ).
fof(f63,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f43,f61,f58]) ).
fof(f165,plain,
( ~ int_leq(sK2,n)
| ~ int_leq(int_one,sK2)
| ~ int_leq(int_one,sK2)
| real_one = a(sK2,sK2)
| ~ spl3_2 ),
inference(resolution,[],[f62,f51]) ).
fof(f169,plain,
( ~ int_leq(sK2,n)
| ~ int_leq(int_one,sK2)
| real_one = a(sK2,sK2)
| ~ spl3_2 ),
inference(duplicate_literal_removal,[],[f165]) ).
fof(f173,plain,
( ~ int_leq(int_one,sK2)
| real_one = a(sK2,sK2)
| ~ spl3_2 ),
inference(forward_subsumption_resolution,[],[f169,f44]) ).
fof(f181,plain,
( real_one = a(sK2,sK2)
| ~ spl3_2 ),
inference(forward_subsumption_resolution,[],[f173,f50]) ).
fof(f183,plain,
( real_zero = real_one
| ~ spl3_2 ),
inference(forward_demodulation,[],[f181,f49]) ).
fof(f185,plain,
( $false
| ~ spl3_2 ),
inference(forward_subsumption_resolution,[],[f183,f40]) ).
fof(f186,plain,
~ spl3_2,
inference(avatar_contradiction_clause,[],[f185]) ).
fof(f195,plain,
( ~ int_leq(int_one,sK2)
| ~ spl3_1 ),
inference(resolution,[],[f59,f44]) ).
fof(f199,plain,
( $false
| ~ spl3_1 ),
inference(forward_subsumption_resolution,[],[f195,f50]) ).
fof(f200,plain,
~ spl3_1,
inference(avatar_contradiction_clause,[],[f199]) ).
cnf(s1,plain,
( spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f63]) ).
cnf(s3,plain,
~ spl3_2,
inference(sat_conversion,[],[f186]) ).
cnf(s4,plain,
~ spl3_1,
inference(sat_conversion,[],[f200]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s1,s3,s4]) ).
fof(f201,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV488+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n020.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 11:15:20 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.23 Running first-order model finding
% 0.08/0.23 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
% 0.20/0.27 % (101469)Will run a generic schedule for satisfiability detection.
% 0.20/0.27 % (101478)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=398633599:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.27 % (101478) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-101469-101478"...
% 0.20/0.27 % (101475)% WARNING: option uhcvi not known.
% 0.20/0.27 % (101478)...printing done.
% 0.20/0.27 % (101478)Refutation found. Thanks to Tanya!
% 0.20/0.27 % SZS status Theorem for theBenchmark
% 0.20/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.27 % (101478)------------------------------
% 0.20/0.27 % (101478)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (101478)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (101478)CaDiCaL version: 2.1.3
% 0.20/0.27 % (101478)Termination reason: Refutation
% 0.20/0.27 % (101478)Time elapsed: 0.003 s
% 0.20/0.27 % (101478)Peak memory usage: 12 MB
% 0.20/0.27 % (101478)Instructions burned: 8 (million)
% 0.20/0.27 % (101469)Success in time 0.034 s
% 0.20/0.27 % Vampire exiting
%------------------------------------------------------------------------------