%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET038-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 12:39:44 PM UTC 2026
% Result : Unsatisfiable 3.56s 1.48s
% Output : Refutation 3.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 14
% Syntax : Number of formulae : 34 ( 9 unt; 0 def)
% Number of atoms : 90 ( 8 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 114 ( 58 ~; 56 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 57 ( 57 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( ~ member(X0,X1)
| little_set(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2) ).
fof(f15,axiom,
! [X2,X0,X1] :
( ordered_pair_predicate(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| X0 != ordered_pair(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pair_predicate4) ).
fof(f16,plain,
! [X2,X0,X1] :
( ordered_pair_predicate(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| ordered_pair(X1,X2) != X0 ),
inference(reorient_equations,[],[f15]) ).
fof(f79,axiom,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset1) ).
fof(f123,axiom,
! [X2,X0,X1] :
( member(X0,range_of(X1))
| ~ little_set(X0)
| ~ ordered_pair_predicate(X2)
| ~ member(X2,X1)
| X0 != second(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',range_of4) ).
fof(f124,plain,
! [X2,X0,X1] :
( member(X0,range_of(X1))
| ~ little_set(X0)
| ~ ordered_pair_predicate(X2)
| ~ member(X2,X1)
| second(X2) != X0 ),
inference(reorient_equations,[],[f123]) ).
fof(f138,axiom,
! [X2,X0,X1] :
( ~ maps(X0,X1,X2)
| function(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maps1) ).
fof(f139,axiom,
! [X2,X0,X1] :
( ~ maps(X0,X1,X2)
| domain_of(X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maps2) ).
fof(f140,axiom,
! [X2,X0,X1] :
( ~ maps(X0,X1,X2)
| subset(range_of(X0),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maps3) ).
fof(f168,axiom,
! [X0,X1] :
( second(ordered_pair(X0,X1)) = X1
| ~ little_set(X1)
| ~ little_set(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',property_of_second) ).
fof(f170,axiom,
! [X0] :
( little_set(second(X0))
| ~ ordered_pair_predicate(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',second_component_is_small) ).
fof(f177,axiom,
! [X0,X1] :
( little_set(apply(X0,X1))
| ~ function(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',function_values_are_small) ).
fof(f184,axiom,
! [X2,X0,X1] :
( ~ function(X0)
| ~ member(X1,domain_of(X0))
| apply(X0,X1) != X2
| member(ordered_pair(X1,X2),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apply_for_functions2) ).
fof(f185,axiom,
maps(a_function,a_domain,a_range),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_mapping) ).
fof(f186,axiom,
member(a,a_domain),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_of_domain) ).
fof(f187,negated_conjecture,
~ member(apply(a_function,a),a_range),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_mapping_in_range) ).
fof(f191,plain,
! [X0,X1] :
( member(ordered_pair(X1,apply(X0,X1)),X0)
| ~ member(X1,domain_of(X0))
| ~ function(X0) ),
inference(equality_resolution,[],[f184]) ).
fof(f193,plain,
! [X2,X1] :
( member(second(X2),range_of(X1))
| ~ little_set(second(X2))
| ~ ordered_pair_predicate(X2)
| ~ member(X2,X1) ),
inference(equality_resolution,[],[f124]) ).
fof(f196,plain,
! [X2,X1] :
( ordered_pair_predicate(ordered_pair(X1,X2))
| ~ little_set(X1)
| ~ little_set(X2) ),
inference(equality_resolution,[],[f16]) ).
fof(f198,plain,
function(a_function),
inference(resolution,[],[f138,f185]) ).
fof(f199,plain,
a_domain = domain_of(a_function),
inference(resolution,[],[f139,f185]) ).
fof(f201,plain,
member(a,domain_of(a_function)),
inference(superposition,[],[f186,f199]) ).
fof(f202,plain,
subset(range_of(a_function),a_range),
inference(resolution,[],[f140,f185]) ).
fof(f209,plain,
! [X0] :
( ~ member(X0,range_of(a_function))
| member(X0,a_range) ),
inference(resolution,[],[f79,f202]) ).
fof(f250,plain,
! [X2,X1] :
( member(second(X2),range_of(X1))
| ~ ordered_pair_predicate(X2)
| ~ member(X2,X1) ),
inference(forward_subsumption_resolution,[],[f193,f170]) ).
fof(f254,plain,
! [X2,X0,X1] :
( member(X0,range_of(X2))
| ~ ordered_pair_predicate(ordered_pair(X1,X0))
| ~ member(ordered_pair(X1,X0),X2)
| ~ little_set(X0)
| ~ little_set(X1) ),
inference(superposition,[],[f250,f168]) ).
fof(f255,plain,
! [X2,X0,X1] :
( ~ member(ordered_pair(X1,X0),X2)
| member(X0,range_of(X2))
| ~ little_set(X0)
| ~ little_set(X1) ),
inference(forward_subsumption_resolution,[],[f254,f196]) ).
fof(f311,plain,
! [X0,X1] :
( member(apply(X0,X1),range_of(X0))
| ~ little_set(apply(X0,X1))
| ~ little_set(X1)
| ~ member(X1,domain_of(X0))
| ~ function(X0) ),
inference(resolution,[],[f255,f191]) ).
fof(f315,plain,
! [X0,X1] :
( member(apply(X0,X1),range_of(X0))
| ~ little_set(apply(X0,X1))
| ~ member(X1,domain_of(X0))
| ~ function(X0) ),
inference(forward_subsumption_resolution,[],[f311,f1]) ).
fof(f316,plain,
! [X0,X1] :
( member(apply(X0,X1),range_of(X0))
| ~ member(X1,domain_of(X0))
| ~ function(X0) ),
inference(forward_subsumption_resolution,[],[f315,f177]) ).
fof(f354,plain,
! [X0] :
( ~ member(X0,domain_of(a_function))
| ~ function(a_function)
| member(apply(a_function,X0),a_range) ),
inference(resolution,[],[f316,f209]) ).
fof(f357,plain,
! [X0] :
( member(apply(a_function,X0),a_range)
| ~ member(X0,domain_of(a_function)) ),
inference(forward_subsumption_resolution,[],[f354,f198]) ).
fof(f363,plain,
~ member(a,domain_of(a_function)),
inference(resolution,[],[f357,f187]) ).
fof(f365,plain,
$false,
inference(forward_subsumption_resolution,[],[f363,f201]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET038-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n018.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Mon Sep 28 00:20:55 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.56/1.48 % (2880246)Input is clausal, will run a generic CNF schedule.
% 3.56/1.48 % (2880253)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=181679258:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.56/1.48 % (2880254)lrs+10_1_sil=8000:sp=occurrence:random_seed=4117005835:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.56/1.48 % (2880251)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=1561613309:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.56/1.48 % (2880257)dis-21_1_sil=8000:lcm=predicate:random_seed=2381730959: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)
% 3.56/1.48 % (2880255)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2328527691:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.56/1.48 % (2880252)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2388194597:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.56/1.48 % (2880256)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1600393019:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.56/1.48 % (2880255)First to succeed.
% 3.56/1.48 % (2880255)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2880246"
% 3.56/1.48 % (2880254)Instruction limit reached!
% 3.56/1.48 % (2880254)------------------------------
% 3.56/1.48 % (2880254)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.56/1.48 % (2880254)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.56/1.48 % (2880254)CaDiCaL version: 2.1.3
% 3.56/1.48 % (2880254)Termination reason: Instruction limit
% 3.56/1.48 % (2880254)Termination phase: Saturation
% 3.56/1.48 % (2880254)Time elapsed: 0.069 s
% 3.56/1.48 % (2880254)Peak memory usage: 89 MB
% 3.56/1.48 % (2880254)Instructions burned: 108 (million)
% 3.56/1.48 % (2880257)Instruction limit reached!
% 3.56/1.48 % (2880257)------------------------------
% 3.56/1.48 % (2880257)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.56/1.48 % (2880257)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.56/1.48 % (2880257)CaDiCaL version: 2.1.3
% 3.56/1.48 % (2880257)Termination reason: Instruction limit
% 3.56/1.48 % (2880257)Termination phase: Saturation
% 3.56/1.48 % (2880257)Time elapsed: 0.073 s
% 3.56/1.48 % (2880257)Peak memory usage: 89 MB
% 3.56/1.48 % (2880257)Instructions burned: 117 (million)
% 3.56/1.48 % (2880256)Instruction limit reached!
% 3.56/1.48 % (2880256)------------------------------
% 3.56/1.48 % (2880256)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.56/1.48 % (2880256)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.56/1.48 % (2880256)CaDiCaL version: 2.1.3
% 3.56/1.48 % (2880256)Termination reason: Instruction limit
% 3.56/1.48 % (2880256)Termination phase: Saturation
% 3.56/1.48 % (2880256)Time elapsed: 0.130 s
% 3.56/1.48 % (2880256)Peak memory usage: 90 MB
% 3.56/1.48 % (2880256)Instructions burned: 181 (million)
% 3.56/1.48 % (2880266)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=4257572796:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 3.56/1.48 % (2880265)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=1064144638:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.56/1.48 % (2880265)Also succeeded, but the first one will report.
% 3.56/1.48 % (2880267)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=3324193194:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 3.56/1.48 % (2880255)Refutation found. Thanks to Tanya!
% 3.56/1.48 % SZS status Unsatisfiable for theBenchmark
% 3.56/1.48 % SZS output start Proof for theBenchmark
% See solution above
% 3.56/1.48 % (2880255)------------------------------
% 3.56/1.48 % (2880255)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.56/1.48 % (2880255)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.56/1.48 % (2880255)CaDiCaL version: 2.1.3
% 3.56/1.48 % (2880255)Termination reason: Refutation
% 3.56/1.48 % (2880255)Time elapsed: 0.011 s
% 3.56/1.48 % (2880255)Peak memory usage: 88 MB
% 3.56/1.48 % (2880255)Instructions burned: 12 (million)
% 3.56/1.48 % (2880255)------------------------------
% 3.56/1.48 % (2880255)------------------------------
% 3.56/1.48 % (2880246)Success in time 0.429 s
% 3.56/1.48 % Vampire exiting
%------------------------------------------------------------------------------