%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM651_8 : TPTP v9.3.1. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n008.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 12:25:11 PM UTC 2026
% Result : Theorem 0.17s 0.47s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 59 ( 13 unt; 0 typ; 5 def)
% Number of atoms : 148 ( 84 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 189 ( 100 ~; 52 |; 12 &)
% ( 5 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 6 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 46 ( 0 sgn 34 !; 12 ?; 46 :)
% 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_5,type,
sK0: nat ).
tff(func_def_6,type,
sK1: nat ).
tff(func_def_7,type,
sK2: nat ).
tff(func_def_8,type,
sK3: nat ).
tff(f1,axiom,
! [X0: nat,X1: nat] : ( X1 != pl(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz7) ).
tff(f2,axiom,
! [X0: nat,X1: nat] : ( pl(X0,X1) = pl(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz6) ).
tff(f4,axiom,
! [X0: nat,X1: nat,X2: nat] : ( pl(pl(X0,X1),X2) = pl(X0,pl(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz5) ).
tff(f5,conjecture,
~ ( ( ( x = y )
=> ~ ~ ! [X0: nat] : ( x != pl(y,X0) ) )
=> ~ ~ ( ( ~ ! [X0: nat] : ( x != pl(y,X0) )
=> ~ ~ ! [X0: nat] : ( y != pl(x,X0) ) )
=> ~ ( ~ ! [X0: nat] : ( y != pl(x,X0) )
=> ( x != y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz9b) ).
tff(f6,negated_conjecture,
~ ~ ( ( ( x = y )
=> ~ ~ ! [X0: nat] : ( x != pl(y,X0) ) )
=> ~ ~ ( ( ~ ! [X0: nat] : ( x != pl(y,X0) )
=> ~ ~ ! [X0: nat] : ( y != pl(x,X0) ) )
=> ~ ( ~ ! [X0: nat] : ( y != pl(x,X0) )
=> ( x != y ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
tff(f10,plain,
~ ~ ( ( ( x = y )
=> ~ ~ ! [X0: nat] : ( x != pl(y,X0) ) )
=> ~ ~ ( ( ~ ! [X1: nat] : ( x != pl(y,X1) )
=> ~ ~ ! [X2: nat] : ( y != pl(x,X2) ) )
=> ~ ( ~ ! [X3: nat] : ( y != pl(x,X3) )
=> ( x != y ) ) ) ),
inference(rectify,[],[f6]) ).
tff(f11,plain,
( ( ( x = y )
=> ! [X0: nat] : ( x != pl(y,X0) ) )
=> ( ( ~ ! [X1: nat] : ( x != pl(y,X1) )
=> ! [X2: nat] : ( y != pl(x,X2) ) )
=> ~ ( ~ ! [X3: nat] : ( y != pl(x,X3) )
=> ( x != y ) ) ) ),
inference(flattening,[],[f10]) ).
tff(f13,plain,
( ( ( x = y )
& ? [X3: nat] : ( y = pl(x,X3) ) )
| ( ? [X2: nat] : ( y = pl(x,X2) )
& ? [X1: nat] : ( x = pl(y,X1) ) )
| ( ? [X0: nat] : ( x = pl(y,X0) )
& ( x = y ) ) ),
inference(ennf_transformation,[],[f11]) ).
tff(f14,plain,
( ( ( x = y )
& ? [X3: nat] : ( y = pl(x,X3) ) )
| ( ? [X2: nat] : ( y = pl(x,X2) )
& ? [X1: nat] : ( x = pl(y,X1) ) )
| ( ? [X0: nat] : ( x = pl(y,X0) )
& ( x = y ) ) ),
inference(flattening,[],[f13]) ).
tff(f15,plain,
( ( ( x = y )
& ? [X0: nat] : ( y = pl(x,X0) ) )
| ( ? [X1: nat] : ( y = pl(x,X1) )
& ? [X2: nat] : ( x = pl(y,X2) ) )
| ( ? [X3: nat] : ( x = pl(y,X3) )
& ( x = y ) ) ),
inference(rectify,[],[f14]) ).
tff(f16,plain,
( ( ( x = y )
& ( y = pl(x,sK0) ) )
| ( ( y = pl(x,sK1) )
& ( x = pl(y,sK2) ) )
| ( ( x = pl(y,sK3) )
& ( x = y ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f15]) ).
tff(f17,plain,
! [X0: nat,X1: nat] : ( pl(X0,X1) != X1 ),
inference(cnf_transformation,[],[f1]) ).
tff(f18,plain,
! [X0: nat,X1: nat] : ( pl(X0,X1) = pl(X1,X0) ),
inference(cnf_transformation,[],[f2]) ).
tff(f20,plain,
! [X2: nat,X0: nat,X1: nat] : ( pl(pl(X0,X1),X2) = pl(X0,pl(X1,X2)) ),
inference(cnf_transformation,[],[f4]) ).
tff(f24,plain,
( ( y = pl(x,sK0) )
| ( y = pl(x,sK1) )
| ( x = pl(y,sK3) ) ),
inference(cnf_transformation,[],[f16]) ).
tff(f25,plain,
( ( x = y )
| ( x = pl(y,sK2) )
| ( x = y ) ),
inference(cnf_transformation,[],[f16]) ).
tff(f27,plain,
( ( x = y )
| ( y = pl(x,sK1) )
| ( x = y ) ),
inference(cnf_transformation,[],[f16]) ).
tff(f31,plain,
( ( x = y )
| ( x = pl(y,sK2) ) ),
inference(duplicate_literal_removal,[],[f25]) ).
tff(f32,plain,
( ( x = y )
| ( y = pl(x,sK1) ) ),
inference(duplicate_literal_removal,[],[f27]) ).
tff(f34,definition,
( spl4_1
<=> ( x = y ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
tff(f36,plain,
( ( x = y )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f34]) ).
tff(f38,definition,
( spl4_2
<=> ( x = pl(y,sK2) ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
tff(f40,plain,
( ( x = pl(y,sK2) )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f38]) ).
tff(f42,definition,
( spl4_3
<=> ( y = pl(x,sK0) ) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
tff(f44,plain,
( ( y = pl(x,sK0) )
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f42]) ).
tff(f47,definition,
( spl4_4
<=> ( x = pl(y,sK3) ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
tff(f49,plain,
( ( x = pl(y,sK3) )
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f47]) ).
tff(f52,definition,
( spl4_5
<=> ( y = pl(x,sK1) ) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
tff(f54,plain,
( ( y = pl(x,sK1) )
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f52]) ).
tff(f56,plain,
( spl4_4
| spl4_5
| spl4_3 ),
inference(avatar_split_clause,[],[f24,f42,f52,f47]) ).
tff(f57,plain,
( spl4_2
| spl4_1 ),
inference(avatar_split_clause,[],[f31,f34,f38]) ).
tff(f59,plain,
( spl4_5
| spl4_1 ),
inference(avatar_split_clause,[],[f32,f34,f52]) ).
tff(f67,plain,
! [X0: nat,X1: nat] : ( pl(X0,X1) != X0 ),
inference(superposition,[],[f17,f18]) ).
tff(f69,plain,
( ( x != y )
| ~ spl4_5 ),
inference(superposition,[],[f67,f54]) ).
tff(f72,plain,
( ~ spl4_1
| ~ spl4_5 ),
inference(avatar_split_clause,[],[f69,f52,f34]) ).
tff(f106,plain,
( ! [X0: nat] : ( pl(y,X0) = pl(x,pl(sK1,X0)) )
| ~ spl4_5 ),
inference(superposition,[],[f20,f54]) ).
tff(f120,plain,
( ! [X0: nat] : ( x != pl(y,X0) )
| ~ spl4_5 ),
inference(superposition,[],[f67,f106]) ).
tff(f131,plain,
( ( x != x )
| ~ spl4_2
| ~ spl4_5 ),
inference(superposition,[],[f120,f40]) ).
tff(f135,plain,
( $false
| ~ spl4_2
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f131]) ).
tff(f136,plain,
( ~ spl4_2
| ~ spl4_5 ),
inference(avatar_contradiction_clause,[],[f135]) ).
tff(f138,plain,
( ( x = pl(x,sK0) )
| ~ spl4_1
| ~ spl4_3 ),
inference(forward_demodulation,[],[f44,f36]) ).
tff(f140,plain,
( $false
| ~ spl4_1
| ~ spl4_3 ),
inference(forward_subsumption_resolution,[],[f138,f67]) ).
tff(f141,plain,
( ~ spl4_1
| ~ spl4_3 ),
inference(avatar_contradiction_clause,[],[f140]) ).
tff(f143,plain,
( ( x = pl(x,sK3) )
| ~ spl4_1
| ~ spl4_4 ),
inference(forward_demodulation,[],[f49,f36]) ).
tff(f144,plain,
( $false
| ~ spl4_1
| ~ spl4_4 ),
inference(forward_subsumption_resolution,[],[f143,f67]) ).
tff(f145,plain,
( ~ spl4_1
| ~ spl4_4 ),
inference(avatar_contradiction_clause,[],[f144]) ).
cnf(s4,plain,
( spl4_3
| spl4_4
| spl4_5 ),
inference(sat_conversion,[],[f56]) ).
cnf(s5,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f57]) ).
cnf(s7,plain,
( spl4_1
| spl4_5 ),
inference(sat_conversion,[],[f59]) ).
cnf(s9,plain,
( ~ spl4_1
| ~ spl4_5 ),
inference(sat_conversion,[],[f72]) ).
cnf(s11,plain,
( ~ spl4_2
| ~ spl4_5 ),
inference(sat_conversion,[],[f136]) ).
cnf(s12,plain,
( ~ spl4_1
| ~ spl4_3 ),
inference(sat_conversion,[],[f141]) ).
cnf(s13,plain,
( ~ spl4_1
| ~ spl4_4 ),
inference(sat_conversion,[],[f145]) ).
cnf(s14,plain,
spl4_1,
inference(rat,[],[s11,s5,s7]) ).
cnf(s15,plain,
~ spl4_4,
inference(rat,[],[s13,s14]) ).
cnf(s16,plain,
~ spl4_3,
inference(rat,[],[s12,s14]) ).
cnf(s18,plain,
~ spl4_5,
inference(rat,[],[s9,s14]) ).
cnf(s19,plain,
$false,
inference(rat,[],[s4,s18,s15,s16]) ).
tff(f146,plain,
$false,
inference(avatar_sat_refutation,[],[s19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM651_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.39 % Computer : n008.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 27 20:57:39 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.42 Running first-order model finding
% 0.11/0.42 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
% 0.17/0.47 % (1588604)Will run a generic schedule for satisfiability detection.
% 0.17/0.47 % (1588610)% WARNING: option uhcvi not known.
% 0.17/0.47 % (1588612)dis+10_1_sil=32000:sp=arity:random_seed=2747405729:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.47 % (1588609)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1729577621_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.47 % (1588613)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2627423531:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.47 % (1588611)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1020550632:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.47 % (1588614)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3158115111:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.47 % Detected minimum model sizes of [1,1]
% 0.17/0.47 % Detected maximum model sizes of [max,2]
% 0.17/0.47 % TRYING [1,1]
% 0.17/0.47 % (1588614) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1588604-1588614"...
% 0.17/0.47 % TRYING [1,2]
% 0.17/0.47 % TRYING [2,2]
% 0.17/0.47 % TRYING [3,2]
% 0.17/0.47 % (1588612) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1588604-1588612"...
% 0.17/0.47 % (1588613) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1588604-1588613"...
% 0.17/0.47 % (1588614)...printing done.
% 0.17/0.47 % (1588614)Refutation found. Thanks to Tanya!
% 0.17/0.47 % SZS status Theorem for theBenchmark
% 0.17/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.47 % (1588614)------------------------------
% 0.17/0.47 % (1588614)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.47 % (1588614)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.47 % (1588614)CaDiCaL version: 2.1.3
% 0.17/0.47 % (1588614)Termination reason: Refutation
% 0.17/0.47 % (1588614)Time elapsed: 0.003 s
% 0.17/0.47 % (1588614)Peak memory usage: 13 MB
% 0.17/0.47 % (1588614)Instructions burned: 5 (million)
% 0.17/0.47 % (1588604)Success in time 0.042 s
% 0.17/0.47 % Vampire exiting
%------------------------------------------------------------------------------