%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : KRS003_1 : TPTP v9.3.1. Released v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n010.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 11:42:04 AM UTC 2026
% Result : Theorem 0.29s 0.62s
% Output : Refutation 0.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 13
% Syntax : Number of formulae : 54 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 125 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 126 ( 55 ~; 57 |; 5 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-1 aty)
% Number of variables : 68 ( 68 !; 0 ?; 68 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
unreal: $tType ).
tff(type_def_6,type,
real: $tType ).
tff(func_def_0,type,
u1r1: unreal > real ).
tff(func_def_1,type,
u1r2: unreal > real ).
tff(func_def_2,type,
u3r1: unreal > real ).
tff(func_def_3,type,
u3r2: unreal > real ).
tff(func_def_4,type,
exist: unreal ).
tff(func_def_5,type,
fmbFreshConstant0: real ).
tff(pred_def_1,type,
f: unreal > $o ).
tff(pred_def_2,type,
d: unreal > $o ).
tff(pred_def_3,type,
e: unreal > $o ).
tff(pred_def_4,type,
s1most: unreal > $o ).
tff(pred_def_5,type,
s: ( unreal * real ) > $o ).
tff(pred_def_6,type,
c: unreal > $o ).
tff(pred_def_7,type,
equalish: ( real * real ) > $o ).
tff(pred_def_8,type,
s2least: unreal > $o ).
tff(f1,axiom,
! [X0: unreal] :
( c(X0)
=> s2least(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_3) ).
tff(f3,axiom,
! [X0: unreal] :
~ ( s2least(X0)
& equalish(u1r2(X0),u1r1(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_5) ).
tff(f4,axiom,
! [X0: unreal] :
( s2least(X0)
=> s(X0,u1r1(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_6) ).
tff(f5,axiom,
! [X0: unreal] :
( s2least(X0)
=> s(X0,u1r2(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_7) ).
tff(f6,axiom,
! [X0: real,X1: real,X2: unreal] :
( ( s(X2,X1)
& s(X2,X0) )
=> ( s2least(X2)
| equalish(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_8) ).
tff(f7,axiom,
! [X0: unreal] :
( d(X0)
=> s1most(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_9) ).
tff(f9,axiom,
! [X0: real,X1: real,X2: unreal] :
( ( s1most(X2)
& s(X2,X1)
& s(X2,X0) )
=> equalish(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_11) ).
tff(f10,axiom,
! [X0: unreal] :
( equalish(u3r2(X0),u3r1(X0))
=> s1most(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_12) ).
tff(f11,axiom,
! [X0: unreal] :
( s1most(X0)
| s(X0,u3r1(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_13) ).
tff(f12,axiom,
! [X0: unreal] :
( s1most(X0)
| s(X0,u3r2(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_14) ).
tff(f13,axiom,
! [X0: unreal] :
( e(X0)
=> c(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_15) ).
tff(f14,axiom,
! [X0: unreal] :
( f(X0)
=> d(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_16) ).
tff(f15,conjecture,
( ~ e(exist)
| ~ f(exist) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1__clause_2) ).
tff(f16,negated_conjecture,
~ ( ~ e(exist)
| ~ f(exist) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
tff(f17,plain,
! [X0: unreal] :
( s2least(X0)
| ~ c(X0) ),
inference(ennf_transformation,[],[f1]) ).
tff(f19,plain,
! [X0: unreal] :
( ~ s2least(X0)
| ~ equalish(u1r2(X0),u1r1(X0)) ),
inference(ennf_transformation,[],[f3]) ).
tff(f20,plain,
! [X0: unreal] :
( s(X0,u1r1(X0))
| ~ s2least(X0) ),
inference(ennf_transformation,[],[f4]) ).
tff(f21,plain,
! [X0: unreal] :
( s(X0,u1r2(X0))
| ~ s2least(X0) ),
inference(ennf_transformation,[],[f5]) ).
tff(f22,plain,
! [X0: real,X1: real,X2: unreal] :
( s2least(X2)
| equalish(X1,X0)
| ~ s(X2,X1)
| ~ s(X2,X0) ),
inference(ennf_transformation,[],[f6]) ).
tff(f23,plain,
! [X0: real,X1: real,X2: unreal] :
( s2least(X2)
| equalish(X1,X0)
| ~ s(X2,X1)
| ~ s(X2,X0) ),
inference(flattening,[],[f22]) ).
tff(f24,plain,
! [X0: unreal] :
( s1most(X0)
| ~ d(X0) ),
inference(ennf_transformation,[],[f7]) ).
tff(f26,plain,
! [X0: real,X1: real,X2: unreal] :
( equalish(X1,X0)
| ~ s1most(X2)
| ~ s(X2,X1)
| ~ s(X2,X0) ),
inference(ennf_transformation,[],[f9]) ).
tff(f27,plain,
! [X0: real,X1: real,X2: unreal] :
( equalish(X1,X0)
| ~ s1most(X2)
| ~ s(X2,X1)
| ~ s(X2,X0) ),
inference(flattening,[],[f26]) ).
tff(f28,plain,
! [X0: unreal] :
( s1most(X0)
| ~ equalish(u3r2(X0),u3r1(X0)) ),
inference(ennf_transformation,[],[f10]) ).
tff(f29,plain,
! [X0: unreal] :
( c(X0)
| ~ e(X0) ),
inference(ennf_transformation,[],[f13]) ).
tff(f30,plain,
! [X0: unreal] :
( d(X0)
| ~ f(X0) ),
inference(ennf_transformation,[],[f14]) ).
tff(f31,plain,
( e(exist)
& f(exist) ),
inference(ennf_transformation,[],[f16]) ).
tff(f32,plain,
! [X0: unreal] :
( s2least(X0)
| ~ c(X0) ),
inference(cnf_transformation,[],[f17]) ).
tff(f34,plain,
! [X0: unreal] :
( ~ s2least(X0)
| ~ equalish(u1r2(X0),u1r1(X0)) ),
inference(cnf_transformation,[],[f19]) ).
tff(f35,plain,
! [X0: unreal] :
( s(X0,u1r1(X0))
| ~ s2least(X0) ),
inference(cnf_transformation,[],[f20]) ).
tff(f36,plain,
! [X0: unreal] :
( s(X0,u1r2(X0))
| ~ s2least(X0) ),
inference(cnf_transformation,[],[f21]) ).
tff(f37,plain,
! [X2: unreal,X0: real,X1: real] :
( s2least(X2)
| equalish(X1,X0)
| ~ s(X2,X1)
| ~ s(X2,X0) ),
inference(cnf_transformation,[],[f23]) ).
tff(f38,plain,
! [X0: unreal] :
( s1most(X0)
| ~ d(X0) ),
inference(cnf_transformation,[],[f24]) ).
tff(f40,plain,
! [X2: unreal,X0: real,X1: real] :
( equalish(X1,X0)
| ~ s1most(X2)
| ~ s(X2,X1)
| ~ s(X2,X0) ),
inference(cnf_transformation,[],[f27]) ).
tff(f41,plain,
! [X0: unreal] :
( s1most(X0)
| ~ equalish(u3r2(X0),u3r1(X0)) ),
inference(cnf_transformation,[],[f28]) ).
tff(f42,plain,
! [X0: unreal] :
( s1most(X0)
| s(X0,u3r1(X0)) ),
inference(cnf_transformation,[],[f11]) ).
tff(f43,plain,
! [X0: unreal] :
( s1most(X0)
| s(X0,u3r2(X0)) ),
inference(cnf_transformation,[],[f12]) ).
tff(f44,plain,
! [X0: unreal] :
( c(X0)
| ~ e(X0) ),
inference(cnf_transformation,[],[f29]) ).
tff(f45,plain,
! [X0: unreal] :
( d(X0)
| ~ f(X0) ),
inference(cnf_transformation,[],[f30]) ).
tff(f46,plain,
f(exist),
inference(cnf_transformation,[],[f31]) ).
tff(f47,plain,
e(exist),
inference(cnf_transformation,[],[f31]) ).
tff(f48,plain,
! [X0: unreal] :
( ~ s2least(X0)
| c(X0) ),
inference(consistent_polarity_flipping,[],[f32]) ).
tff(f49,plain,
! [X0: unreal] :
( s2least(X0)
| equalish(u1r2(X0),u1r1(X0)) ),
inference(consistent_polarity_flipping,[],[f34]) ).
tff(f50,plain,
! [X0: unreal] :
( ~ s(X0,u1r1(X0))
| s2least(X0) ),
inference(consistent_polarity_flipping,[],[f35]) ).
tff(f51,plain,
! [X0: unreal] :
( ~ s(X0,u1r2(X0))
| s2least(X0) ),
inference(consistent_polarity_flipping,[],[f36]) ).
tff(f52,plain,
! [X2: real,X0: unreal,X1: real] :
( ~ s2least(X0)
| ~ equalish(X1,X2)
| s(X0,X1)
| s(X0,X2) ),
inference(consistent_polarity_flipping,[],[f37]) ).
tff(f53,plain,
! [X0: unreal] :
( ~ s1most(X0)
| d(X0) ),
inference(consistent_polarity_flipping,[],[f38]) ).
tff(f54,plain,
! [X2: unreal,X0: real,X1: real] :
( ~ equalish(X0,X1)
| s1most(X2)
| s(X2,X0)
| s(X2,X1) ),
inference(consistent_polarity_flipping,[],[f40]) ).
tff(f55,plain,
! [X0: unreal] :
( ~ s1most(X0)
| equalish(u3r2(X0),u3r1(X0)) ),
inference(consistent_polarity_flipping,[],[f41]) ).
tff(f56,plain,
! [X0: unreal] :
( ~ s1most(X0)
| ~ s(X0,u3r1(X0)) ),
inference(consistent_polarity_flipping,[],[f42]) ).
tff(f57,plain,
! [X0: unreal] :
( ~ s1most(X0)
| ~ s(X0,u3r2(X0)) ),
inference(consistent_polarity_flipping,[],[f43]) ).
tff(f58,plain,
! [X0: unreal] :
( ~ c(X0)
| ~ e(X0) ),
inference(consistent_polarity_flipping,[],[f44]) ).
tff(f59,plain,
! [X0: unreal] :
( ~ d(X0)
| ~ f(X0) ),
inference(consistent_polarity_flipping,[],[f45]) ).
tff(f68,plain,
$false,
inference(finite_model_not_found_(exhaustively_excluded_all_possible_domain_size_assignments),[],[f48,f49,f50,f51,f52,f53,f54,f55,f56,f57,f58,f59,f47,f46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KRS003_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.21/0.51 % Computer : n010.cluster.edu
% 0.21/0.51 % Model : x86_64 x86_64
% 0.21/0.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.51 % Memory : 8046.5625MB
% 0.21/0.51 % OS : Linux 6.8.0-71-generic
% 0.21/0.51 % CPULimit : 300
% 0.21/0.51 % WCLimit : 300
% 0.21/0.51 % DateTime : Sun Sep 27 13:15:31 UTC 2026
% 0.21/0.51 % CPUTime :
% 0.21/0.51 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.21/0.57 Running first-order model finding
% 0.21/0.57 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
% 0.29/0.62 % (961480)Will run a generic schedule for satisfiability detection.
% 0.29/0.62 % (961485)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4281414337_2999 on theBenchmark for (2999ds/0Mi)
% 0.29/0.62 % TRYING [1]
% 0.29/0.62 % TRYING [2]
% 0.29/0.62 % TRYING [3]
% 0.29/0.62 % TRYING [4]
% 0.29/0.62 % (961485) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-961480-961485"...
% 0.29/0.62 % (961485)...printing done.
% 0.29/0.62 % (961485)Refutation found. Thanks to Tanya!
% 0.29/0.62 % SZS status Theorem for theBenchmark
% 0.29/0.62 % SZS output start Proof for theBenchmark
% See solution above
% 0.29/0.63 % (961485)------------------------------
% 0.29/0.63 % (961485)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.29/0.63 % (961485)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.29/0.63 % (961485)CaDiCaL version: 2.1.3
% 0.29/0.63 % (961485)Termination reason: Refutation
% 0.29/0.63 % (961485)Time elapsed: 0.003 s
% 0.29/0.63 % (961485)Peak memory usage: 11 MB
% 0.29/0.63 % (961485)Instructions burned: 3 (million)
% 0.29/0.63 % (961480)Success in time 0.043 s
% 0.29/0.63 % Vampire exiting
%------------------------------------------------------------------------------