%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET022-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 12:39:38 PM UTC 2026
% Result : Unsatisfiable 5.46s 1.95s
% Output : Refutation 5.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 32 ( 11 unt; 3 def)
% Number of atoms : 58 ( 7 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 51 ( 25 ~; 23 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 6 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f11,axiom,
! [X0] :
( little_set(f2(X0))
| ~ ordered_pair_predicate(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pair_predicate1) ).
fof(f12,axiom,
! [X0] :
( little_set(f3(X0))
| ~ ordered_pair_predicate(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pair_predicate2) ).
fof(f13,axiom,
! [X0] :
( ~ ordered_pair_predicate(X0)
| X0 = ordered_pair(f2(X0),f3(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pair_predicate3) ).
fof(f14,plain,
! [X0] :
( ~ ordered_pair_predicate(X0)
| ordered_pair(f2(X0),f3(X0)) = X0 ),
inference(reorient_equations,[],[f13]) ).
fof(f167,axiom,
! [X0,X1] :
( first(ordered_pair(X0,X1)) = X0
| ~ little_set(X1)
| ~ little_set(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_of_first) ).
fof(f169,axiom,
ordered_pair_predicate(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',an_ordered_pair_predicate) ).
fof(f170,negated_conjecture,
~ little_set(first(a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_first_component_is_small) ).
fof(f424,plain,
a = ordered_pair(f2(a),f3(a)),
inference(resolution,[],[f14,f169]) ).
fof(f442,plain,
( first(a) = f2(a)
| ~ little_set(f3(a))
| ~ little_set(f2(a)) ),
inference(superposition,[],[f167,f424]) ).
fof(f451,definition,
( spl0_19
<=> little_set(f3(a)) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f453,plain,
( ~ little_set(f3(a))
| spl0_19 ),
inference(avatar_component_clause,[],[f451]) ).
fof(f455,definition,
( spl0_20
<=> little_set(f2(a)) ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f457,plain,
( ~ little_set(f2(a))
| spl0_20 ),
inference(avatar_component_clause,[],[f455]) ).
fof(f488,definition,
( spl0_28
<=> first(a) = f2(a) ),
introduced(definition,[new_symbols(definition,[spl0_28])],[avatar_definition]) ).
fof(f490,plain,
( first(a) = f2(a)
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f488]) ).
fof(f491,plain,
( ~ spl0_20
| ~ spl0_19
| spl0_28 ),
inference(avatar_split_clause,[],[f442,f488,f451,f455]) ).
fof(f503,plain,
( ~ ordered_pair_predicate(a)
| spl0_20 ),
inference(resolution,[],[f457,f11]) ).
fof(f504,plain,
( $false
| spl0_20 ),
inference(forward_subsumption_resolution,[],[f503,f169]) ).
fof(f505,plain,
spl0_20,
inference(avatar_contradiction_clause,[],[f504]) ).
fof(f508,plain,
( ~ ordered_pair_predicate(a)
| spl0_19 ),
inference(resolution,[],[f453,f12]) ).
fof(f509,plain,
( $false
| spl0_19 ),
inference(forward_subsumption_resolution,[],[f508,f169]) ).
fof(f510,plain,
spl0_19,
inference(avatar_contradiction_clause,[],[f509]) ).
fof(f527,plain,
( little_set(first(a))
| ~ ordered_pair_predicate(a)
| ~ spl0_28 ),
inference(superposition,[],[f11,f490]) ).
fof(f528,plain,
( ~ ordered_pair_predicate(a)
| ~ spl0_28 ),
inference(forward_subsumption_resolution,[],[f527,f170]) ).
fof(f532,plain,
( $false
| ~ spl0_28 ),
inference(forward_subsumption_resolution,[],[f528,f169]) ).
fof(f533,plain,
~ spl0_28,
inference(avatar_contradiction_clause,[],[f532]) ).
cnf(s24,plain,
( ~ spl0_19
| ~ spl0_20
| spl0_28 ),
inference(sat_conversion,[],[f491]) ).
cnf(s29,plain,
spl0_20,
inference(sat_conversion,[],[f505]) ).
cnf(s30,plain,
spl0_19,
inference(sat_conversion,[],[f510]) ).
cnf(s32,plain,
~ spl0_28,
inference(sat_conversion,[],[f533]) ).
cnf(s35,plain,
$false,
inference(rat,[],[s24,s32,s29,s30]) ).
fof(f534,plain,
$false,
inference(avatar_sat_refutation,[],[s35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET022-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.43 % Computer : n013.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Mon Sep 28 00:10:07 UTC 2026
% 0.16/0.44 % CPUTime :
% 0.16/0.44 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/0.49 Running first-order theorem proving
% 0.24/0.49 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
% 5.46/1.95 % (687196)Input is clausal, will run a generic CNF schedule.
% 5.46/1.95 % (687210)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=1407810197:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 5.46/1.95 % (687217)dis-21_1_sil=8000:lcm=predicate:random_seed=1087491644: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)
% 5.46/1.95 % (687213)lrs+10_1_sil=8000:sp=occurrence:random_seed=1221366634:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 5.46/1.95 % (687211)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=349938193:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 5.46/1.95 % (687214)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2053495673:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 5.46/1.95 % (687212)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=668244699:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 5.46/1.95 % (687216)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1109023149:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 5.46/1.95 % (687213)Refutation not found, incomplete strategy
% 5.46/1.95 % (687213)------------------------------
% 5.46/1.95 % (687213)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.46/1.95 % (687213)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.46/1.95 % (687213)CaDiCaL version: 2.1.3
% 5.46/1.95 % (687213)Termination reason: Refutation not found, incomplete strategy
% 5.46/1.95 % (687213)Time elapsed: 0.002 s
% 5.46/1.95 % (687213)Peak memory usage: 88 MB
% 5.46/1.95 % (687214)Refutation not found, incomplete strategy
% 5.46/1.95 % (687214)------------------------------
% 5.46/1.95 % (687214)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.46/1.95 % (687214)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.46/1.95 % (687214)CaDiCaL version: 2.1.3
% 5.46/1.95 % (687214)Termination reason: Refutation not found, incomplete strategy
% 5.46/1.95 % (687214)Time elapsed: 0.003 s
% 5.46/1.95 % (687214)Peak memory usage: 88 MB
% 5.46/1.95 % (687214)Instructions burned: 1 (million)
% 5.46/1.95 % (687217)Instruction limit reached!
% 5.46/1.95 % (687217)------------------------------
% 5.46/1.95 % (687217)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.46/1.95 % (687217)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.46/1.95 % (687217)CaDiCaL version: 2.1.3
% 5.46/1.95 % (687217)Termination reason: Instruction limit
% 5.46/1.95 % (687217)Termination phase: Saturation
% 5.46/1.95 % (687217)Time elapsed: 0.075 s
% 5.46/1.95 % (687217)Peak memory usage: 89 MB
% 5.46/1.95 % (687217)Instructions burned: 118 (million)
% 5.46/1.95 % (687216)First to succeed.
% 5.46/1.95 % (687216)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-687196"
% 5.46/1.95 % (687226)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=2421451826:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 5.46/1.95 % (687226)Refutation not found, incomplete strategy
% 5.46/1.95 % (687226)------------------------------
% 5.46/1.95 % (687226)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.46/1.95 % (687226)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.46/1.95 % (687226)CaDiCaL version: 2.1.3
% 5.46/1.95 % (687226)Termination reason: Refutation not found, incomplete strategy
% 5.46/1.95 % (687226)Time elapsed: 0.002 s
% 5.46/1.95 % (687226)Peak memory usage: 88 MB
% 5.46/1.95 % (687213)------------------------------
% 5.46/1.95 % (687213)------------------------------
% 5.46/1.95 % (687214)------------------------------
% 5.46/1.95 % (687214)------------------------------
% 5.46/1.95 % (687216)Refutation found. Thanks to Tanya!
% 5.46/1.95 % SZS status Unsatisfiable for theBenchmark
% 5.46/1.95 % SZS output start Proof for theBenchmark
% See solution above
% 5.46/1.95 % (687216)------------------------------
% 5.46/1.95 % (687216)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.46/1.95 % (687216)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.46/1.95 % (687216)CaDiCaL version: 2.1.3
% 5.46/1.95 % (687216)Termination reason: Refutation
% 5.46/1.95 % (687216)Time elapsed: 0.025 s
% 5.46/1.95 % (687216)Peak memory usage: 89 MB
% 5.46/1.95 % (687216)Instructions burned: 19 (million)
% 5.46/1.95 % (687216)------------------------------
% 5.46/1.95 % (687216)------------------------------
% 5.46/1.95 % (687196)Success in time 0.669 s
% 5.46/1.95 % Vampire exiting
%------------------------------------------------------------------------------