%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET025-9 : 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 : 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 12:39:40 PM UTC 2026
% Result : Unsatisfiable 3.85s 1.53s
% Output : Refutation 3.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 10 ( 7 unt; 0 def)
% Number of atoms : 13 ( 3 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 5 ~; 3 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 9 ( 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [X0,X1] : little_set(non_ordered_pair(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',non_ordered_pair4) ).
fof(f10,axiom,
! [X0,X1] : ordered_pair(X0,X1) = non_ordered_pair(singleton_set(X0),non_ordered_pair(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pair) ).
fof(f13,axiom,
! [X0] :
( ~ ordered_pair_predicate(X0)
| X0 = ordered_pair(f2(X0),f3(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pair_predicate3) ).
fof(f14,plain,
! [X0] :
( ordered_pair(f2(X0),f3(X0)) = X0
| ~ ordered_pair_predicate(X0) ),
inference(reorient_equations,[],[f13]) ).
fof(f162,axiom,
ordered_pair_predicate(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',an_ordered_pair_predicate) ).
fof(f163,negated_conjecture,
~ little_set(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_predicate_is_small) ).
fof(f279,plain,
! [X0,X1] : little_set(ordered_pair(X0,X1)),
inference(superposition,[],[f8,f10]) ).
fof(f286,plain,
! [X0] :
( little_set(X0)
| ~ ordered_pair_predicate(X0) ),
inference(superposition,[],[f279,f14]) ).
fof(f297,plain,
~ ordered_pair_predicate(a),
inference(resolution,[],[f286,f163]) ).
fof(f298,plain,
$false,
inference(forward_subsumption_resolution,[],[f297,f162]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET025-9 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n020.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 : Mon Sep 28 00:14:20 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 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
% 3.85/1.53 % (3907296)Input is clausal, will run a generic CNF schedule.
% 3.85/1.53 % (3907301)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=3026982446:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.85/1.53 % (3907303)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3192552148:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.85/1.53 % (3907304)lrs+10_1_sil=8000:sp=occurrence:random_seed=270515495:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.85/1.53 % (3907302)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=840156200:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.85/1.53 % (3907304)Refutation not found, incomplete strategy
% 3.85/1.53 % (3907304)------------------------------
% 3.85/1.53 % (3907304)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.85/1.53 % (3907304)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.85/1.53 % (3907304)CaDiCaL version: 2.1.3
% 3.85/1.53 % (3907304)Termination reason: Refutation not found, incomplete strategy
% 3.85/1.53 % (3907304)Time elapsed: 0.001 s
% 3.85/1.53 % (3907304)Peak memory usage: 86 MB
% 3.85/1.53 % (3907305)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3603726998:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.85/1.53 % (3907307)dis-21_1_sil=8000:lcm=predicate:random_seed=3805692563: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)
% 3.85/1.53 % (3907305)Refutation not found, incomplete strategy
% 3.85/1.53 % (3907305)------------------------------
% 3.85/1.53 % (3907305)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.85/1.53 % (3907305)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.85/1.53 % (3907305)CaDiCaL version: 2.1.3
% 3.85/1.53 % (3907305)Termination reason: Refutation not found, incomplete strategy
% 3.85/1.53 % (3907305)Time elapsed: 0.002 s
% 3.85/1.53 % (3907305)Peak memory usage: 87 MB
% 3.85/1.53 % (3907306)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2830250775:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.85/1.53 % (3907306)First to succeed.
% 3.85/1.53 % (3907306)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3907296"
% 3.85/1.53 % (3907307)Instruction limit reached!
% 3.85/1.53 % (3907307)------------------------------
% 3.85/1.53 % (3907307)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.85/1.53 % (3907307)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.85/1.53 % (3907307)CaDiCaL version: 2.1.3
% 3.85/1.53 % (3907307)Termination reason: Instruction limit
% 3.85/1.53 % (3907307)Termination phase: Saturation
% 3.85/1.53 % (3907307)Time elapsed: 0.065 s
% 3.85/1.53 % (3907307)Peak memory usage: 88 MB
% 3.85/1.53 % (3907307)Instructions burned: 118 (million)
% 3.85/1.53 % (3907304)------------------------------
% 3.85/1.53 % (3907304)------------------------------
% 3.85/1.53 % (3907315)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=1234074028:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.85/1.53 % (3907305)------------------------------
% 3.85/1.53 % (3907305)------------------------------
% 3.85/1.53 % (3907315)Refutation not found, incomplete strategy
% 3.85/1.53 % (3907315)------------------------------
% 3.85/1.53 % (3907315)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.85/1.53 % (3907315)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.85/1.53 % (3907315)CaDiCaL version: 2.1.3
% 3.85/1.53 % (3907315)Termination reason: Refutation not found, incomplete strategy
% 3.85/1.53 % (3907315)Time elapsed: 0.001 s
% 3.85/1.53 % (3907315)Peak memory usage: 86 MB
% 3.85/1.53 % (3907306)Refutation found. Thanks to Tanya!
% 3.85/1.53 % SZS status Unsatisfiable for theBenchmark
% 3.85/1.53 % SZS output start Proof for theBenchmark
% See solution above
% 3.85/1.53 % (3907306)------------------------------
% 3.85/1.53 % (3907306)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.85/1.53 % (3907306)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.85/1.53 % (3907306)CaDiCaL version: 2.1.3
% 3.85/1.53 % (3907306)Termination reason: Refutation
% 3.85/1.53 % (3907306)Time elapsed: 0.011 s
% 3.85/1.53 % (3907306)Peak memory usage: 89 MB
% 3.85/1.53 % (3907306)Instructions burned: 13 (million)
% 3.85/1.53 % (3907306)------------------------------
% 3.85/1.53 % (3907306)------------------------------
% 3.85/1.53 % (3907296)Success in time 0.456 s
% 3.85/1.53 % Vampire exiting
%------------------------------------------------------------------------------